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Impact of structural defects on spin-polarized transport ... · Impact of structural defects on spin-polarized transport across magnetic tunnel junctions par FILIP SCHLEICHER Soutenue

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Page 1: Impact of structural defects on spin-polarized transport ... · Impact of structural defects on spin-polarized transport across magnetic tunnel junctions par FILIP SCHLEICHER Soutenue

♥sttt P②sq t ♠ s tér① trs♦r

ès ♦t♦rt ❯♥rsté trs♦r

♠♣t ♦ strtr ts

♦♥ s♣♥♣♦r③ tr♥s♣♦rt

r♦ss ♠♥t t♥♥ ♥t♦♥s

♣r

P

♦t♥ ♣q♠♥t ♠r ♥t r② ♦♠♣♦sé

s r②ss rtr tèsr♥ç♦s ♦♥t♥ ♣♣♦rtrréér Ptr♦ ♣♣♦rtr❲♦♥ ❲r ①♠♥tr ♥tr♥

Page 2: Impact of structural defects on spin-polarized transport ... · Impact of structural defects on spin-polarized transport across magnetic tunnel junctions par FILIP SCHLEICHER Soutenue
Page 3: Impact of structural defects on spin-polarized transport ... · Impact of structural defects on spin-polarized transport across magnetic tunnel junctions par FILIP SCHLEICHER Soutenue

♥♦♠♥ts

② t t♠ ♠ rt♥ ts ♦rs t s r② ♥ ♦r ②s s♥ t♠♠♦r tr♥♦♦♥ ♥ ♦② r ♠② P ♣♦♠ ♥s♦♥ t t ♠♥sr♣t ②♦ r ♦♥ ♥ ♥s ♦r ♠♦r ♣r♦② ts t♦♣② s♠♠r③s ♠♦r t♥ tr ②rs ♦ t ♦r ♣r♦r♠ r♥ ♠②st② t t P ♥sttt ♦r ts ♣ rs s♣ s♥♥ ♦r♠ ♦♥t ①♣t ♦ t tt r ♥ ♥ t r② ♠♦r♥♥ ♦♣t♠r r♦ss t P♦♥t ♥ ♦r t rst t♠ st r ♠② rst♦r♥② ② tr♥ t♦ t ❯♥rst② ♦ ♦s r♥ ♣t ③♥ tr♦t ♥♦ t ♥♠r♦s sts ♦ t ❱♦ss ♦♥t♥s ♥ ♥ ttt s s s♦♠♦ r♥t tt ♠ st ♣ssr② ♥ tt ♦ ♥r ts ♣s ♠♥ t t ❯♥rst② ♦ trs♦r ♥ t s ♥♥ r♥ ♥r r♠♥ r r♦♠ t ♦ ♠② ♦♥t♠ r♥s ♥t ①t♥s ♦r s♥ ♦♦ts ♥ s♦ ♥ r r② s♥♣ s ♦♠ ♦r ♠ t ♥ ♥r♦♥♠♥t t ♥ ♠♥② ②s tr② ♥♥st② r♥t s♣② s ♥♦t s♣ s♥ ♦r ♥ r♥ ♣♦♥rr

t s r t♦ s② t ♣♦♥t strt t♦ s ♦♠ ♥ ♣♦♣r r♥s ♥♥♦t r ♥ t st♦♣ st②♥ ♠♣s s r②♥♦♥ t♠ ② rt ♦♥t r♠♠r ♥ ♥t ♣♦♣ strt t♦ s ♠ ♦tt st tr ♦rs t♦ tr r♦♥ ♥ ♥ strt t♦ ♥sr t♠ ♥ tr♥t ♥ tr ♠♦r t♥ ts ♦r ②rs s♣♥t r ♦♥t t♦ ♦r rs♦♥s ♦r ts ② ♥♥♦t ①s② ttrt♥tr t♦ t t② ♦ s ♥♦r t♦ t ♦ rsr ♥ t P ♦♥②t s s♦ t ♣♦♣ ♦r t

♦ t♦ s② ♦t ♦ ♥ ②♦ t♦ r②♦♥ ♦ ♣ ♠ tr♦♦tt t♠r♠ ♦ ts tss tr② t rst ♦♥ ♦s t♦ rt♥ ♦♥ ♠② t♦ ♦ss ♦ s ♠ tr♦♦t t ♥tr ♥t ♦ t rsr ♣r♦r♠♥ ♦ s ♠② ♣r♠r② s♦r ♦ ♠♦st ♦ t ♥♦ tt ♣♦sss ♥♦ ♦ t♦ t♥ ♣♦♣ r♦♠ t r♦♣ t ♦♠ ♦♣♣♦rt♥t②♥ ♣sr t♦ ♦r s♣② rs r r♣r ♠② ♦rs r②ss rst♦♣ r ♦♥ ♠ ♥♦ t ❯♥rst② ♦ rs ♥♦♥ ♠ ② ♠♠r ♥ ❱r♦♥q ❲r♥r

♦r♦r ♦ ♥♦t ♦rt ♦t ♣♦♣ r ♥♦t ♠♠rs ♦ t

Page 4: Impact of structural defects on spin-polarized transport ... · Impact of structural defects on spin-polarized transport across magnetic tunnel junctions par FILIP SCHLEICHER Soutenue

r♦♣ t t♦t ♦s ssst♥ ♠② rsr ♦ ♥♦t ♣r♦ ♥② rtrs♣② ♦s tt rt ♥ ♦♠♥q ♥ssst♥t ♥♥r

♥ s♣rts ♣r♦ss♦♥ ♦♥tts ♥ t ♣rt ♦ ②♦♥s♥tst s ♥♦t s② t♦ r ♦r t rt♥② r♥s s♦♠r r♦ss ♦s♦ ♦ st♥ts ♦ sr ♦t ♦② ♥ ♠sr② ♦ tr ♦s ♦♠ ♦②♦ ♥♦ ttr s♦♠ ss t♦ t♥ ♦ ②♦ ♦r t t♠ s♣♥t t♦tr rst♥ ♥rs ♥♣tst r♥ ♥ ss s♠ ♦♦ ❱♥♥t s♥ t♠ ♦ ❱♥ r♠r③ ♥♦P♦st♦ ♥ rr r ♦♠♠ r ♥♦ ♣♥t r♥♦ ❯ s♠r ♦♠ ♠ ♥♦♦♥ ♦t♠ r♠ r③♥ trs ♦ ♥♦ ❯♣♣s ❯♥rst② r ❲♦ ③ ♠tr ❳♥♦t ❩♥tt♥ ♥ ❾s③ ❩♦s

♦st ♣rs♦♥② t♥ ♠② tr ♦s s③♦ ♦ s ②s ♦s t♦ ♠♥♦ ♠ttr ♦ r ♠② ♠♠ ♥ r♥♣r♥ts ♦r rst♥ ♦ ♥ t ♥♠

♦r♦r ♦ t♦ t♥ ♣r♦ ♥ s③ r♦♠ t ❲r♦ ❯♥rst②♦ ♥♦♦② ♦r t ♣♦sst② ♦ ♣r♦r♠♥ ♣rt ♦ ♠② sts t t ❯♥rst②♦ trs♦r t♥s t♦ t ♦♦♣rt♦♥ t♥ r♦♥s ♦ s ♥ ♦r ss s t♥ ♦t ❯♥rsts

Page 5: Impact of structural defects on spin-polarized transport ... · Impact of structural defects on spin-polarized transport across magnetic tunnel junctions par FILIP SCHLEICHER Soutenue
Page 6: Impact of structural defects on spin-polarized transport ... · Impact of structural defects on spin-polarized transport across magnetic tunnel junctions par FILIP SCHLEICHER Soutenue
Page 7: Impact of structural defects on spin-polarized transport ... · Impact of structural defects on spin-polarized transport across magnetic tunnel junctions par FILIP SCHLEICHER Soutenue

♦♥t♥ts

és♠é ♥ r♥çs

♥tr♦t♦♥

♦rt ss

ss ♦ ♥♥ ♥t♦rsst♥ r♦♠ s♠♣ t♦ ♣t① rrrs ♦♥③r♦ s♣♥ ♣♦r③t♦♥ ♥ rr♦♠♥ts ♣♥♣♦r③ t♥♥♥ ♥ ♠♥t t♥♥ ♥t♦♥s ②♠♠tr② tr♥ ♥

tr♦♥ ♦ ♥t♦♥s ♥ strtrs ♠♣t

♥s♠ ① r♦♥

r♥s♣♦rt t♦♥s ♥tr♥s sss

❩r♦ s ♥♦♠② ♥tr rs♦♥♥t stts ♠♣t ♦ ♣♦♥♦♥s

tr rrr t②♣s tr♦♥t♠ tt♥t t♥♠ ♦①

r♥t tr♦ ♠trs ♥tr♦t♦♥ ♦ ♦t

♦tr♦♥ ♦②s ♥tr ♦t ②rs

♦ s t①tr s②st♠s 0.7r0.3♥3 ♠t tr♦s

r②st s♣tt♥ ♦ ①♥ ♠♥s♠

Page 8: Impact of structural defects on spin-polarized transport ... · Impact of structural defects on spin-polarized transport across magnetic tunnel junctions par FILIP SCHLEICHER Soutenue

♠♣rtr ♣♥♥ s②st♠

♦ ♦ ts ♠♣rt♦♥s

♠♣t ♦♥ s♣♥♣♦r③ tr♥s♣♦rt ♣t tt② ♥ r②st♥ s②st♠s

♥s♠ ♦① tr♦♥t♠ tt♥t t♥♠ ♦①

♥tr sss ①t♦♥ ♦♥sq♥s ♦ ♥♥♥

♥tr ♦① ②r ♦r♠t♦♥ s♦♥ ♦ ♠trs ♠♦♥ t ②rs

❯♥rt♥ ♥tr tr♠♥t♦♥ tr♦♠rt♦♥ ♥ srt♥ t♥ ♠♥ts♠ ♦♥s♦♥s

①♣r♠♥t r③t♦♥

♠♣ r♦t t♥qs ♥ ♦♣♠♥t ❯tr ♠ ♣♠♣♥ s②st♠s strt ♣r♣rt♦♥ ♣ttr♥

②r ②st♠ s♣ttr♥ ♥② ♣ttr♥

♣♦rt♦♥ Ps sr ♣♦st♦♥

t♦♥ ♥r② tr♦♥ rt♦♥

r♦♠ s♠♣s t♦ s ♥st ♣ttr♥ ♣t t♦r♣②

t♦r♣② ♠s P♦t♦rssts

P♦st ♣♦t♦rsst t ♣♦t♦rsst ❩

Pr♦ss♥ P♦t♦rsst ♣♦st♦♥ ♥ ts t♦r♥ P Pr ♥t♦♥

Page 9: Impact of structural defects on spin-polarized transport ... · Impact of structural defects on spin-polarized transport across magnetic tunnel junctions par FILIP SCHLEICHER Soutenue

P ♦r tr♦ ♥t♦♥ P Psst♦♥ ②r ♣♦st♦♥ P ❱ t③t♦♥

sst♥ ♣r♦♥ ♥ ♦♥tt ♠♦s ♦♣♦♥t ♠sr♠♥t ♦ t ♦♥tts ♦r♣♦♥t ♥t♦♥ st② sst♥r ♣r♦ts

♠♦♥ s t ♥♣ ♠♦♥t ♥ r♦♥♥

st② ♣♣rts ♥ t♥qs st♣ ♣ts ①♣r♠♥t tr♠♥t♦♥ ♦ t rrr ♣♦t♥t ♥s♣

rt ❱ rtrsts ♥②ss g ♠t♦ I ♠t♦ ❱♦tt♠♣rtr ♣♥♥② ♠♣s

♣t sts

st②

r♥st♦♥ ♠t ♦①s tr♦♥t♠ tt♥t

♦♣t tt② ♦2r3♦2

t♥♠ ♦① ♦22♦2 ♦2♦

♦♥s♦♥s ♥ ♠♦ t♦rs

♥s♠ ♦① rrr sts

♣t tt② tr ♠sr♠♥ts

♦♦

♥r ♣r♦♣rts ♥②ss ♦ t ❱ ♣r♠tr s♣

♥ ❱ s♣ ♥♥ s②st♠ ♥♦♥♥♥ s②st♠

Page 10: Impact of structural defects on spin-polarized transport ... · Impact of structural defects on spin-polarized transport across magnetic tunnel junctions par FILIP SCHLEICHER Soutenue

❱ ♦♥s♦♥s ♥ ♣rs♣ts

♠♠r② r♥st♦♥ ♠t ♦①s ♥s♠ ♦①

♦♠♣ r♥st♦♥ ♠t ♦①s ♥s♠ ♦① ♣t ss

♦r♣②

Page 11: Impact of structural defects on spin-polarized transport ... · Impact of structural defects on spin-polarized transport across magnetic tunnel junctions par FILIP SCHLEICHER Soutenue
Page 12: Impact of structural defects on spin-polarized transport ... · Impact of structural defects on spin-polarized transport across magnetic tunnel junctions par FILIP SCHLEICHER Soutenue
Page 13: Impact of structural defects on spin-polarized transport ... · Impact of structural defects on spin-polarized transport across magnetic tunnel junctions par FILIP SCHLEICHER Soutenue

és♠é ♥ r♥çs

étr♦♥ ût ÷r ré♦t♦♥s t♥♦♦qs q ♠♦èr♥t ♣r♦♦♥é♠♥t s♦été ♥s ①è♠ ♠♦té sè ♣réé♥t ♥♦t♠♠♥t è♥♠♥t ♦r♥tr ♣rs♦♥♥ t ♣♣rt♦♥ ♥♦① ♠♦②♥s ♦♠♠♥t♦♥sq ré♠♠♥t ① ♣r♦♣rétés ♥tr♥sèqs étr♦♥ r♥t tsés ♥ss ér♥ts t♥♦♦s r étr♦♥ tsé ♥s t♦t s s♣♦sts étr♦♥qs ssqs ♦♥trôé ♠♦②♥ ♥ ♠♣ étrq t s♦♥s♣♥ tsé à trrs ss ♠♥stt♦♥s ♠r♦s♦♣qs ♣♦r s ♥rstr♠♥ts♠♥étqs ♣r ①♠♣ ♣♥♥t s ① ♣r♦♣rétés ♥♥t ♠s été tsés ♥ ss♦t♦♥ ♣♦r ♦♠♣r ♥ t ♣rés st ♣résé♠♥t à r♦s♠♥tq♥tr♥t s♣♥tr♦♥q s♦♥ ♦t st ♠♦r ♠♦♠♥t s étr♦♥s t ♦♥ ♦♥t♦♥ étrq ♥ ss♥t sr s♣♥ à ♥ ♠♣♠♥étq ①térr

♥ q s♣♥ étr♦♥ s♦t ♦♥♥ t été ♣s ♥♦♠rss ♥♥éssq très ré♠♠♥t s♦♥ tst♦♥ ♥ tr♠ ♣♣t♦♥ à été ♥éé ♥ é♦rt ♠♥ét♦résst♥ é♥t ♣r rt rt t ♥é♣♥♠♠♥t ♣r Ptr r♥r à r♣♠♥t ttré tt♥t♦♥ ♦♠♠♥tés♥tq sr tr♥s♣♦rt étr♦♥q é♣♥♥t s♣♥ ♥s s ♠tér①♦♥sst♥t ♥ ♥ sss♦♥ ♥s ♦s rr♦♠♥étq t ♥♦♥ ♠♥étq é♣ssrs ♥♥♦♠étrqs ♥s ts s②stè♠s st ♣♦ss ♥r résst♥ ♥ ♠♦♥t ♦♥rt♦♥ ♠♥tt♦♥ s étr♦srr♦♠♥étqs ♥ étt ♣rè P à ♥ étt ♥t♣rè P ♥ ♣♣q♥t♥ ♠♣ ①tr♥ ♣r ①♠♣ ♥ ♦♦r ♦sré ♥ ♥♠♥t résst♥ ♥♦r ♣s ♠♣♦rt♥t ♥s s strtrs ♦♠♣♦sés étr♦s rr♦♠♥étqs sé♣rés ♣r ♥ ♥ ♦ ♠tér ♥♦♥ ♦♥tr tsstrtrs s♦♥t ♣♣és s ♦♥t♦♥s t♥♥s ♠♥étqs ♥♠♥t résst♥ ♥s s s②stè♠s à été ♣♣é ♠♥ét♦résst♥ t♥♥ r s étr♦♥s s♦♥t tr♥sérés ♥ étr♦ à ♥ tr ♣r t t♥♥ ♠♥ét♦résst♥ st é♥ ♦♠♠ rt♦♥ rt résst♥ ♥tr étt♣rè t ♥t♣rè TMR = (RAP −RP )/RP

♦r♥ ♠♥ét♦résst♥ ♥s s ♣r♦♥t ér♥ ♥sté étts à é♥r r♠ ♥tr ♣♦♣t♦♥ s♣♥ ♣ t ♦♥ ♥s s ♠tér① rr♦♠♥étqs tt ér♥ st rtérsé ♣r ♣♦rst♦♥ s♣♥ é♥t ♣r P = (N↑ −N↓)/(N↑ +N↓) ♥♦s s♣♣♦s♦♥s

Page 14: Impact of structural defects on spin-polarized transport ... · Impact of structural defects on spin-polarized transport across magnetic tunnel junctions par FILIP SCHLEICHER Soutenue

♦♥srt♦♥ s♣♥ ♦rs tr♥s♣♦rt ♥ étr♦♥ ♣t ♣ssr ♣r t t♥♥ àtrrs rrèr s♠♥t s ♥ étt ♣♦ssé♥t ♠è♠ s♣♥ st ss ♥s ①è♠ étr♦ ♥sté étt ss ♣♦r ♥ étr♦♥ r ♦♥rt♦♥ rt ♠♥tt♦♥ s étr♦s ♣rè ♦ ♥t♣rè t♦♥t à ♥ ér♥ résst♥ ♥tr s ① étts

♠é♦rt♦♥ s t♥qs ①♣ér♠♥ts st ♣♦ss ♦r rqr s t♦t♠♥t é♣t①és ♥s s s②stè♠s s t♦♠s s♦♥t ♠♣és ♠♥èr ♦r♦♥♥é t s étr♦♥s ♣♥t ètr érts ♣r s ♦♥t♦♥s ♦♥ ♦ ♣s té♦r s r♦♣s ♣r♠t ssr s étr♦♥s ♥ ♦♥t♦♥ ss②♠étrs s ♦rts ♦♣és s s②♠étrs s ♦♥t♦♥s ♦♥ ♦ ♦♥t♥ rô ♠♣♦rt♥t ♥s tr♥s♣♦rt t♥♥ ♥s s s②stè♠s é♣t①és t q rrèr s♦t ss rst♥ ♣r♠t ♦♥srr s②♠étr s étr♦♥s♦rs tr♥srt à trrs rrèr ♦♥ ♣r tr♥s♣♦rt étrq ♦ér♥t s ér♥ts s②♠étrs s ♦♥t♦♥s ♦♥ ♦ s♦♥t tté♥és ♠♥èrér♥t ♥s rrèr st ♥s ♣♦ss trr s ér♥ts s②♠étrs ♥s rrèr t ♦♥♥trr tr♥s♣♦rt sr s s②♠étrs t♦t♠♥t ♣♦rsés àé♥r r♠ ♠♣♦rt♥ts rs ♣♥t ♥s ètr ♦t♥s s s rrèrs ♦♠♣♦sés t r3 s♦♥t s ♥ts ♣♦t♥ts♣♦r ♣r♦♥ é♥ért♦♥ s♣♦sts s♣♥tr♦♥qs

♥ s tr① té♦rqs ♦♥t ♣rét s rs ♠♥ét♦résst♥s ♣s ♥s s s②stè♠s t♦t♠♥t é♣t①és ♥ q s ♣rét♦♥s ♥t été és ①♣ér♠♥t♠♥t ①st ♥♦r ♦rts ér♥s♥tr s rs ♣réts t s réstts ①♣ér♠♥t① tt ér♥ st ♣r♥♣♠♥t t q st ①trè♠♠♥t rér ♥ s②stè♠ ♣rt ①♣ér♠♥t♠♥t t ♣srs ♣é♥♦♠è♥s s♦♥t rs♣♦♥ss s rt♠♥t srs ♦t♥s s ♣é♥♦♠è♥s ♦①②t♦♥s t s♦♥s s♦♥t à ♦r♥ ♣♣rt♦♥ ♦s s♣♣é♠♥tr ① ♥trs q ♣♥t ♦r sts ♥ésrs t ss rér ♠♥ét♦résst♥ s éts ♥s rrèrrst♥ ♣♥t é♠♥t ♦r ♥ ♠♣t ♥ésr sr ♠♥ét♦résst♥♥ t s éts rés♥t tr ♠♦②♥♥ rrèr t ré♥t s ♥① ♦♥t♦♥ ♣♦r s étr♦♥s ♥é♣♥♠♠♥t rs s②♠étrs

♦♠♣r♥r ♣②sq s éts ♥s s st ♦♥ très ♠♣♦rt♥t ♥t ♣t ♣r♠ttr rér s ♦♥t♦♥s ♠rs qtés s♣r♦♣rétés ♦♣t♠sés t ♥s s r♣♣r♦r s rs té♦rqs s st é♠♥t ♣♦ss tsr s éts ♣♦r rér s s♣♦sts ♣♦ssé♥t ♥♦s♦♥t♦♥♥tés ♦♠♠ s ♦♥t♦♥s s ♣r♦♣rétés ♠♠rsts ♣r ①♠♣ ①st ér♥ts ♠ét♦s ♣♦r étr s éts ♥s s s ♠srs ♠♥ét♦tr♥s♣♦rt ♥ t♠♣értr ♣r♠tt♥t ér ① trs rrèr① ♥trs ♥s qà trs ♣é♥♦♠è♥s tr♠q♠♥t tés s ♠srs♦♣tqs ♣r♠tt♥t é♠♥t ♦t♥r ♣réss ♥♦r♠t♦♥s sr t②♣ éts tt tès ♣♦r ♦t ♦rr ♦ à ♦♠♣ré♥s♦♥ ♠♣ts éts sr tr♥s♣♦rt t♥♥ ♥s s rst♥s

Page 15: Impact of structural defects on spin-polarized transport ... · Impact of structural defects on spin-polarized transport across magnetic tunnel junctions par FILIP SCHLEICHER Soutenue

s ♦♥t♦♥s t♥♥s s rrèrs t r3 ♥s q s é♥t♦♥s ♦♥t♥♥t s♠♥t s rrèrs r♥t rqés ♣r ♣érst♦♥ t♦q t ♣r P ♣s sr ♣♦st♦♥ rt♥s s é♥t♦♥s ♦♥t été rqés ♥ ♦♦rt♦♥ ♥tr♥ trs é♣rt♠♥ts à P ♥♦t♠♠♥t ♣♦r s é♣♦st♦♥s P ♦ ♥ ♦♦rt♦♥ ①tr♥ ♥♦t♠♠♥t ♥ é♣rt♠♥t P ♥sttt ♥ ♠♦r ♥② ♣♦r sé♥t♦♥s ♦♦

s ①♣ér♥s tés sr s rqés ♣r ♣érst♦♥ t♦q s rrèrs ♠♦♥tr♥t q rt♥ t②♣s éts ♥s strtr rst♥ rrèr ♣♥t ètr é♠♥és ♥ rq♥t s é♥t♦♥s♥s rt♥s ♦♥t♦♥s é♣ôt s rrèrs ♥♠ ♦♥t étérqés ér♥t t① ♦①②è♥s é♣ôt t s ①♣ér♥s ♦♣tqs ♦♥tété tés s réstts ♠♦♥tr♥t q♥ ♠♥tt♦♥ rt♦ ♦①②è♥r♦♥à ♣♦r t rér s ♣s s♦r♣t♦♥ à s é♥rs q ♦rrs♣♦♥♥t ①s♦r♣t♦♥s ♦♣tqs éts ♣ès

s ♣s s♦r♣t♦♥ à ❱ ♦rrs♣♦♥♥t à ♦♠♥s♦♥ ① ♥s♦①②è♥ ♥trs F2 s ♣s à ❱ ♦rrs♣♦♥♥t à ♥ ♥ ♦①②è♥ ♥tr♦ ♦♥sé F F+ t♥s q s ♣s à ❱ ♦rrs♣♦♥♥t à ♥ ♥ ♦①②è♥ ♦♠♥t ♦♥sé F+

2 s ♣s rést♥t s ♥trs FF+ s♣rss♥t s♣tr s♦r♣t♦♥ ♣♦r ♥ rst é♣♦sé ♥s ♥ t♠♦s♣èr ♦♠♣♦sé ♦①②è♥ t r♦♥ s réstts sèr♥t s♣rt♦♥ séts ♥s strtr rst♥

♥ ♦♥r♠r tt ②♣♦tès s é♥t♦♥s ♥♠♥♠ r♥trqés s rt♦s ♦①②è♥r♦♥ t s ①♣ér♥s ♠♦♥tr♥t q ♦ tr♥ ♣♦ssè ♠♦♥s ♦ts♣♦ts ♣♦♥ts ♣s♦♥trs ♦rsq t♠♦s♣èr st ♥r ♥ ♦①②è♥ été éré q sréstts ♥ s♦♥t ♣s és à s ér♥s t♦♣♦r♣

s♣rt♦♥ s ♣s FF+ s♣tr s♦r♣t♦♥ t ♠é♦rt♦♥ s ♣r♦♣rétés s é♥t♦♥s ♦rrs♣♦♥♥ts ♦♥♦rt é s♦♥ q s ♥trs Fs♦♥t rs♣♦♥ss ♠♦rté tr♥s♣♦rt étr♦♥q ♥s rrèr û ① éts P♦r ♦♥r♠r s ♦r ♦r♥t♦t ♦♥t été ♠sréssr s ① t②♣s é♥t♦♥s ♦♠♣rs♦♥ s ♦♥♥és ♣♦r ♥ t♥s♦♥♣♣qé ♣♦st ♦rrs♣♦♥♥t à ♥tr s♣érr ♦♥♥ s ♥♦r♠t♦♥s♣rt♥♥ts sr ♣rés♥ s éts t r ♠♣t sr tr♥s♣♦rt t♥♥ tr rrèr ♣ss ❱ à ❱❱ ♥s rrèr♣♥ t ❱ à❱ sr s ♦ts♣♦ts ♦♥ ss♠ q é♥r r♠ s tr♦ ♠ ♣ ♦rs tr t rrèr sr ❱ à s ♥trsF t F+ stés à ❱ ♥s rrèr ♣s s♣rt♦♥ ♣ ♦♥t♥ à ❱ ♥s s ♦rs ❱ sr é♥t♦♥ rqé ♦①②è♥♦♥r♠ ♥ q ♦♥t♥ ①ss ♣r♦♥t s sts F t F+ qs♦♥t é♠♥és ♥s s ♦♥t♦♥s é♣ôt

Psrs é♥t♦♥s ♦♥t été rqés ♥ ♦♦rt♦♥ ♥sttt ♥

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♠♦r ♥② s ♣r♠rs é♥t♦♥s s♦♥t s étér♦strtrs t②♣ ♦♦ sr sqs s ♠srs ♠♥ét♦tr♥s♣♦rt ♦♥t été tés s♦♥ t②♣ é♥t♦♥ ♦♥r♥ s étér♦strtrs ♥ ♣♦ssé♥t ♣s ♦♥tr étr♦ rrèr st ♦rs r♥èr ♦ strtrs ♠srs ♣♦t♦♠♥s♥ ♦♥t été tés ♥s t étr♠♥r ♠♣t rt sr tr♥s♣♦rt étr♦♥q à trrs ts ♦♥t♦♥s P♦r qt②♣ étér♦strtrs s é♥t♦♥s rts à ♥s q s é♥t♦♥s♥♦♥ rts ♦♥t été étés t ♦♠♣rés

s ♣s ♦srés ♦rs ♠srs ♣♦t♦♠♥s♥ tés à ér♥ts♦♥rs ♦♥ ♣r♠tt♥t étr♠♥r é♥r s éts ♥tr♦ts ♣s s♥s ♦①②è♥ ♥s rrèr s ♦srt♦♥s s♦♥t ♥ ♦r trstr①éts ♣rés♥ts ♥s ttértr rt♦♥ ♦♥t♦♥s t♥♥ ♠♥étq été té ♣r ♥ ♣r♦t♦♦ t♦r♣ st♥r s ♦♥t♦♥s♥s ♦t♥s ♣rés♥t♥t ♥ ♣r♦t ♥♦r♠ réstt sèr q é♥t♦♥ st ♦♠♥t ♦♠♦è♥ s ♠srs ♠♥étqs tés à t♠♣értr♠♥t s♦♥t ♦ér♥ts s ♠srs ♠♥étst♦♥ té à ♥❯ ♥s s s é♥t♦♥s ♥♦♥ rts étt ♥t♣rè ♥st ♣s ♥é♥ rést♥t ♥ ♥ s♥ ♥ r♥ sr s é♥t♦♥s rtétt ♥t♣rè st ♥ é♥t t ♦sré st ♣s ♥s s t é♠♥t ♣r♥r ♥ ♦♠♣t rstst♦♥ rrèr ♦rs rt ♣s ♥♦s ♦sr♦♥s sr s é♥t♦♥s ♥♦♥ rts q tr rrèr st ♥tq ♥s étt ♣rè t ♥t♣rè ♦rs q st ♥é♥s s s é♥t♦♥s rts ❱ ♣♦r P t ❱ ♣♦r P

é♣♥♥ ♥ t♠♣értr résst♥ ♥s q ♠♥ét♦résst♥ ♠♦♥tr♥t ♥ ♥♠♥t ré♠ à ♥s s ① s rt t ♥♦♥rt ♣♦♥t sr str ♣s tr ♥ ♣t é♠♥t ♦srr ♥ ♣tà ♣rtr sq① ♣s s t♠♣értrs ♥s s s s é♥t♦♥srts ♣rés♥ ♣t ♣t êtr ttré à s♥ éts srt♦♥s ♠♥ét♦résst♥ ♥ ♦♥t♦♥ t♥s♦♥ t t♠♣értr❱ ♠♦♥tr♥t q ♠♥ ♣s r♣♠♥t ♥ t♥s♦♥ t ♥ t♠♣értr ♥s s s é♥t♦♥s rts

♥②s s ♥① ♦♥t♦♥ tr♠q♠♥t té sr s ♦♥t♦♥s rts ♠♦♥tr ♥ ♠♥t♦♥ r♣ ♥ ♦♥t♦♥ t♠♣értr t♦r ❱ tt t ♣t êtr ttré ① sts F t F+ ♥ ♦♠♣r♥r s♣é♥♦♠è♥s és à tt♦♥ tr♠q ♦♥t♥ ♥s q s ér♥s tr rrèr ♥ ét rt♦♥ ♦♥tté ♥ ♦♥t♦♥ t♠♣értr été té ss ♣♣é ♣ ♦ ❰ ♦♥tté é♥t♦♥ ♥♦♥ rt st ♦♠♥é ♣r tr♥s♠ss♦♥ ♣♦rtr rs s ♥trs F F+ t F+∗ à ♣rtr s ♦♥tté st ♦♠♥é ♣r s stsF+∗ sq t♠♣értr à ♣rtr q tr♥s♣♦rt st ♦♠♥é ♣r s♥trs F2 P♦r tt rs♦♥ ♥ ♠♥t♦♥ s♥t résst♥ st ♦sré à tt t♠♣értr ♥s s s ♦♥t♦♥s rts ♠♥tt♦♥

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♦♥tté ♥ ss♦s st ♦♠♥é ♣r s ts strtr ♥ ♥s s P ♦rs q♥ t s♠r ♥♣♣rt ♥s s ♣rè st ♥ ①♣t♦♥ à ♣rés♥ ♣t ♦sré ♥s s ♥s q s ♣♥♥t sss s ♥trs F t F+ ♦♠♠♥♥t à ♦♠♥r tr♥s♣♦rt t ré♠ ♣rsst sq sss tt t♠♣értr s♥trs F+∗ ♦♠♠♥♥t à tr tr♥s♣♦rt rést♥t ♥ ♥ ♠♥t♦♥ r♣ résst♥ t ♣s ♠♣t s ♥trs F+∗ ♥st ♣s ♠ê♠♥s étt P t P ♦ù ♥ ér♥ ♥s tr rrèr ♥s s ①♦♥rt♦♥s

♦s ♦♥s é♠♥t ♦t♥ s réstts ♥térss♥ts ♥s s s♣♦sts ♣♦ssé♥t s rrèrs r3 s ♦♥t♦♥s ♦2r3♦2 ♦♥t étérqés ♣r P ♥ étr ♠♣t t♠♣értr é♣ôt sr ♥tr ♦2 strtr à été rqé ♥ étr♦ ♥érr é♣♦séà t♥s q rrèr à été é♣♦sé à ♦ ♥♦♠♠é é♥t♦♥ ss t t rs♣t♠♥t ♦ s♣érr à été é♣♦séà s ① é♥t♦♥s ♦♥t été rtérsés t ♣♦ssè♥t ♥ ♦♥♥ strtr rst♥ s ♠srs à t♠♣értr ♠♥t ♦♥t été tés t♠♦♥tr♥t ♥ rt♦r♥♠♥t ♥t ♠♥tt♦♥ s étr♦s ♦♥ r♠rq é♠♥t q ♠♣ ♦rt st s♣érr ♣♦r é♥t♦♥ t qsèr q é♣ôt à t♠♣értr éé ♠♥t t① ♦①②t♦♥ ♥tr ♦2

tt ♦①②t♦♥ rt ♦r ♥ ♠♣t ♥ét sr tr♥s♣♦rt ♦ér♥t à trrs rrèr t t rt ♠♥r ♦rt♠♥t rt♦ ♠♥ét♦résst♥ à été ♦♥r♠é ♥ ♠sr♥t s ♦rs sr s ① é♥t♦♥s ♦sré st ♣♦r é♥t♦♥ ♦ t ♥ ♥ ♣ ètr ♦sré♣♦r é♥t♦♥ t tt ér♥ ♣t s①♣qr ♥s tr♥s♣♦rtt♥♥ st ♦♠♥é ♣s s s②♠étrs étr♦♥q ∆2 t ∆5 à trrs ♥s s étr♦s ♦♠♣♦sés r strtr ♥ ♣♦r s s②♠étrs ♦♣é♥r r♠ ♣♦r s s♣♥s ♠♦rtrs t ♠♥♦rtrs ♦♥ tr rst tr ♣rt ♥s ♦t s ♥s ∆2 ♥ ∆5 ①st♥t s♠♥t ♣♦rs s♣♥s ♠♥♦rtrs t s♦♥t ♦♥ t♦t♠♥t ♣♦rsé à é♥r r♠ q♣r♠t ♦t♥r s rt♦s ♠♣♦rt♥ts P♦r ♦t♥r tt ♣♦rst♦♥ tq ♦ ç♦ s♦t ss③ r ♥ ♦t q ♣t ♥ ♣s ètr s ♥s ♥♦sé♥t♦♥s ♦ù rt♦ ❯♥ tr tr ♣t ètr strtr rrèr à ♥tr rrèr ♦♥sst ♥ ♥ sss♦♥ tr♥é ♦ r t 2 ♥ q s ①♣ér♥s ♦♥t ♦♥r♠é ♥ strtr rrèr♦rrt s ♠rs t♦♠qs à ♥tr s♦♥t ①trè♠♠♥t à étrt s♥ ♣t é♣♥r ♦ tr♠♥s♦♥ rrèr ♥s s②stè♠ été ♦ à ♥tr ♣t ♦♥sstr ♥ ♥ ♠é♥ r t 2 ♦♥t ♣♦rst♦♥ ♦♠♥é ♣♦st t ♥ét rést ♥♥ rt♦ ss③

rs♦♥ ♣♦r q ♥ ♥st ♦sré ♣♦r é♥t♦♥

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♣♦rrt été t♠♣értr é♣♦st♦♥ ♠è♠ t ♣rss♦♥ ♥s ♠r é♣ôt ♠♥t ♥ ♦rr r♥r q ♣t ♦♥t♠♥r sr ç♦ tt ②♣♦tès st ♦rr♦♦ré ♣r r ♠♣ ♦rt♣s éé ♣♦r s é♥t♦♥s P♦r ♦♥r♠r tt ②♣♦tès ♦♥ ♣rés♥t s♦rs ❱ ♣♦r q é♥t♦♥ à ♣rtr sqs s trs rrèr àq ♥tr à été ①trt ❯♥ tr rrèr s♣érr ❱ ♣♦rs ① é♥t♦♥s ♥s ♦♥t ♦t♥ q ♦rrs♣♦♥ ♥ t q s♥trs ♦♥t été é♣♦sés ♥s s ♠è♠ ♦♥t♦♥s ①♣ér♠♥ts tr ♣rt♥ tr rrèr ❱ ❱ à été ♦t♥ ♥tr ♥érr♣♦r t ss ♠♦♥tr ♠♣t ♦①②t♦♥ étr♦♥érr q st ♣s ♠♣♦rt♥t ♣♦r é♥t♦♥ t t q ér♦ît ♣s r♣♠♥t ♦rsq s étr♦♥s s♦♥t ♥tés à ♣rtr étr♦s♣érr ♠♦♥tr q ♥tr s♣érr s♦t♥t ss ②♣♦tès ♥ étt♦①②t♦♥ ♣s ♥é étr♦ ♥érr

♥②s s réstts sèr q ♠é♦rt♦♥ s ♣r♦♣rétés s ♦♥t♦♥s♣t ètr ♦t♥ ① ç♦♥s ér♥ts ♥ ♦♥trô♥t tr♠♥s♦♥ rrèr ♦♥ ♣t ssrr r♥èr ♦ à ♥tr t ♥s é♠♥r sér♥ts trs s②♠étr ♦♥t ♦♥trt♦♥ ♦♠♥é rést ♥ ♥ r ♠♣r rrèr 2 ♣t é♠♥t ♦trà s réstts ♥térss♥ts ♥srt♦♥ ♦t à ♥tr ♣t ♥♦♥ s♠♥t♣r♠ttr étr ♦r♠t♦♥ ♦①② à ♥tr ♠s ss ♠♥tr tr s②♠étr r s étts ∆2 ♥ ∆5 ♥ s♦♥t ♣rés♥ts q ♣♦r ♥ ♣♦♣t♦♥ s♣♥ à é♥r r♠ ♥s ♦t

♥ ♦♥s♦♥ s tr① ♦♥t ♠♦♥tré ♦♠♠♥t ♣rés♥ éts ♥s rrèr ♣t ♥♥r s ♣r♦♣rétés ♠♥étqs t ♠♥ét♦ tr♥s♣♦rt s s♣♦sts ♦s ♠♦♥tr♦♥s ♥♦t♠♠♥t ♦♠♠♥t ♦♥trôr ♥tr t ♥sté s éts s♥ ♦s t ♦♥s sté ♠♣t s éts sr s trs rrèr étrq ♦s éts sr s ♥tér♥t s rrèrs â s ♦①②s ♠ét① tr♥st♦♥ ♠♦♥tr♥t té ♠îtrsr ré ♦①②t♦♥ s étr♦s rr♦♠♥étqs â s ♠ét① tr♥st♦♥ q ♦♠♣♦s♥t s

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♥tr♦t♦♥

♦tt♦♥

♥ s♦r② ♦ t tr♦♥ ♥ ssq♥t② ts ♣rt ♣♣t♦♥ ♥ t s♥t ♥ ♥♥r♥ ♦ t ♥♦②s tr♦♥s t s♣♥ ♦ ttr♦♥ s ♦r ♦♥ t♠ ♥t ♥ ♦♥t①t ♦ ♣rt s tr♦♥ssrs ♠♥t② r② ♦♥ t♦ ♦♣ t ♥ st♦♥s♥ s♣ ♦♠♣rt♦ ♣r♦r ♦♣♠♥t ♦s② ♦♠♣tr③t♦♥ ♦rts t t② ♦ ♣r♦r♠♥♠♦st ♦ t♦♥s ♦♥ ♣♦♣ t♦ ♣r♦r♠ tss ♠♦r ♥t② ♥ ♥trst♥② t♦ rt t t♥♦♦ ♥♠♥t ♥ ♠♦r ♦ ♥t♦r♦s ♠♥t② t♦ ss ♥ sr ♥♦r♠t♦♥ ♠♦st t♦t ♥② ♣②s ♦rrs ♥ ts ♣r♦ss s st ①♣♥♥ s③ ♦ s♥ tr♥sst♦r ts ts ♣♦r♦♥s♠♣t♦♥ ♥ t♠ ♥tr rqr t♥ ♦♥st ♥♠r ♦♣rt♦♥s ssr♥♥ ②r ② ②r ♥ t ②♣♦tss rs ♥ ② ♦r♦♥ ♦♦r❬❪ ♣rt tt t ♥♠r ♦ tr♥sst♦rs tt ♥ ♣ ♦♥ ♥ ♥trt rt ♦ ♦ ♣♣r♦①♠t② r② t♥ ♠♦♥ts s ♣♣s t♦t rt♦ t♥ ♦♠♣t♥ s♣ ♥ t ♣r s s ②♣♦tss s st t♦ t s s♦② ♣♣r♦♥ s ♦ ss s ♦ ♣②ss♠② ♥♦t ♥②♠♦r ♥ q♥t♠ ts strt t♦ ♦r ♥ ♦tr ♦rs ts ♥♦t ♣♦ss t♦ ♠♥tr③ ♠♥ts ♥ss② t rt♥ ♠♦♠♥t ♦♥ s t♦strt ♦♦♥ ♦r tr♥t ♠♥s ♦ ♥ ttr ♣r♦r♠♥s ♣♥tr♦♥ss ♦♥ ♦ s rsr s

♣♥tr♦♥s s♣♥tr♦♥s s ♦ ♣②ss ♥ tr♦♥s tt♥♦♠♣sss ♠t♣ st sts ♦r t♥ ♥t ♦ t t ttt tr♦♥ s ♥ ♥tr♥ ♥r ♠♦♠♥t♠ s♣♥ t tt ♥ ♣rs♥♦ ♠♥t tr♦♥s t r♥t s♣♥s ♠② r♥t② ♥ r ♠♣t ♦♥ t ♦r ♦ ♣r♦t♦t②♣ ♦r ♥ ♦♠♠r s ts♦r♥ sr trs s♦rtr rs♣♦♥s t♠ str s♣s ♠♦r rr♦rrt ♣r♦ss♥ ♦r r ♣t②

♥ ♥ t s ♦sr s♣rt② ② r♥r ♥ rt ❬ ❪ ②s♦r tt ♥ rr♥t ♦s tr♦ t♥ strtr ♦♥sst♥ ♦ ♥♦♥♠♥t ♦♣♣r s♥ t♥ t♦ rr♦♠♥t r♦♥ ②rs trsst♥ ♦ t s②st♠ ♥s ② ♣r♥ts ♥ ♥ ①tr♥ ♠♥t

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sts t rt ♦r♥tt♦♥ ♦ ♠♥t③t♦♥ ♦ t tr♦s r♦♠ ♣r Pt♦ ♥t♣r P s r♥ ♥ t rsst♥ t♥ t P ♥ P♦♥rt♦♥s s ♥♦②s ♥t ♥t♦rsst♥

♦ t ♦s rsst stt ♦ tr ② ♣♣②♥ ♥①tr♥ ♠♥t s♠ t♦ r② ♣r♦♠s♥ ♥ t t s r②♥ ♣♣ ♥ r s r s ♥rs♥ tr st♦r ② ♦r ♦♥ ♦rr ♦♠♥t ❬❪ s♠ t s s♦ ♣♣ t♦ ♠♥② ♠♥t s♥s♦rs

tr♦♥s s♣♥ ♠② s♦ ♥♥ ♣r♦♣rts ♦ ♥ t ♠t②r s r♣ ② ♥ trt♥ ♥st♦r s t ♠♥tt♥♥ ♥t♦♥ ②♦♥ ♥t ♣r♦♦♦♦♥♣t ①♣r♠♥ts ♥ t s ❬❪ ♦♦r t r♣♦rt t ♦srt♦♥ ♦ s♣♥♣♦r③ t♥♥♥ r♦ss ♥♠♦r♣♦s 23 rrr t r♦♦♠ t♠♣rtr ❬❪ ♥trst♥② t t♥♥♥♠♥t♦rsst♥ ♠♣t ♦ ts ♥ s t s ♠r t♥ tt t②♣ ♦ s②st♠s ss t♥ t ♥ ts rstr♦♥ ♣♣t ♥trst

♦s rsts t♦ ♣r♦♠s♥ r st ♠t rt♦ ♦t♥r♦♠ t strtrs t ♠♦r♣♦s s♣rs ♥r ① t t r♦♦♠ t♠♣rtr ❬❪ t♦♥s ♣r♦r♠ ♥ ② r♥ t ♦♥ strtrs t❩♥ s♠♦♥t♥ rrr s♦ tt ♣t① s②st♠s ♦ ② r s t♦ tr s♣ tr♥ ♠♥s♠s ❬❪ ♥ t t♦rt t♦♥s② t♦♥ ♥ ❯♠rs ♣rt ♣ t♦ ♦r r②st♥ sstrtrs ❬❪ s♦rt② ♦♦ ② rst rsts ♦ ♦♥ t ❬❪ P♦♣♦ t ❬❪♥ ❨s t ❬❪ s s ♣♦ss t♦ ♦r♥t s②♠♠tr②♣rsr♥t♥♥♥ ♦ tr♦♥s tr♦ t r②st♥ rrr

♦r ♥ s s ♦t♥ ♦r t s②st♠s t t s♣rs s♥ t♥ t ♦r ♦ tr♦s t stst♦r② ♦♥♦t ♦ t♦s strtrs t♦ s ♦r ♣rt ♣♣t♦♥s s s t♦t ♣rt ♣♣t♦♥s rqr♠♥ts ♦r t ♠♥t③t♦♥ ♦ ♦♥ ♦ ttr♦s ♥s t♦ ♣♥♥ ts r♠♥ ① ♥ s♣ t ♠♥t③t♦♥♦ t r ②r s st t♥ ♣r ♥ ♥t♣r ❬❪ ♥str② s♣♥t♠♦r t♥ t♦ rt strtr ♦ ts t②♣ t♦t ♥② str♥ s s♦t♦♥ ♥♦r♣♦rts ♦ tr♦s ②s t s♥ ♣ t♦ t t r♦♦♠ t♠♣rtr ❬❪ s sss r ♣rs♥t t♥ ♦t t♦rt♥ t ①♣r♠♥t ♣rt ♦ ts tss

♦ rtr t ♥s t ♦ s♣♥tr♦♥s ② rqrs s♦r ♦ tr♦♥stt s ② s♣♥♣♦r③ ♦♠♣ss ts tr♦ t tr♥ ♦♣♣r♦♣rt tr♦♥ s②♠♠trs ♥ t ♦rs ♦ t s♦stt t♥♥♥ ♣r♦ss♥♦tr ♣t s t♦ s rr♦♠♥ts tt ♣r♦ tr♦♥ ♦♥t♦♥ ♦♥② ♦ ♦♥s♣♥ t②♣ s ss ♦ ♠trs s ♠ts ②♦♥ ♥t ♦srt♦♥s❬❪ ♥trt♦♥ t♥ t♥♥ ♥t♦♥s t♦ t ♦srt♦♥ ♦ ♦r rt♦ ❬❪ ♣r♦♠ rs♥ r♦♠ s♥ ♠ts s tt tr ♦tst♥♥♣r♦♣rts ♥ ♥trt ♥t♦ ♠♥t t♥♥ ♥t♦♥s ♥s ♦ t r

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t♠♣rtr ♦ t ♥t♦♥ ♥tr s ♦ t r♦♦♠ t♠♣rtr t♦ t ♥tr ♠♦t♦♥ ♦ t tr♦♥ strtr s s t s♦r t ♠♦st ♦♠♠♦♥② st ♠t t 0.7r0.3♥3 ❬❪

♦r ♦ t ♦r♠♥t♦♥ ♠♥t t♥♥ ♥t♦♥ s②st♠s ♣r♦♠ sr ② r②st♥ strtrs ♥♠② ts ❱r♦s s♦t♦♥s ♥♥s ♥ t t♦♠ ♥t♦r ♥ str♦♥② t t rrr ♣r♦♣rts ♥♥st♦rs tr ♥tr♥s ♥ ♣ ♠② t t stts t ♥rs②♥ t♥ t t♦♣ ♦ t ♥ ♥ ♥ t ♦tt♦♠ ♦ t ♦♥t♦♥ ♥r ♣rs♥ t② rs t rrr t ♥ ts t ♦r♥t tr♥s♣♦rt ♦ tr♦♥s ② ♣r♦♠♦t♥ ♦♣♣♥ r♠ ♦ tr♥s♣♦rt s ♣rs♥t♥tr ♦①t♦♥ ssttt♦♥ ♦ sts t♥ stts t♦♠ s♦♥ ♥♥rt♥ tr♠♥t♦♥ ♦ ♦t rrr ♦r tr♦ ②rs ♥ s♦ str♦♥② t ts♣♥♣♦r③ tr♥s♣♦rt

♥ t② t♦ ♦♥tr♦ t ts r♥ t rt♦♥ ♥ ♠♦♥t♦r trtt② r♥ t t♥♥♥ ♣r♦ss ♦ s♥ ♥ t♦♥ t t tr r♦♥ t s♣♥♣♦r③ tr♥s♣♦rt ♦♥rr♥t② t ♣♦sst② t♦ rt s♣ t②♣s♦ ts ts ♦ ♦ t♦ ss② tr ♣r♦♣rts ♥ ♣♦t♥t② ♠ ♥ s♦ t♠ ♥ ♦rr t♦ rtr ♥♥ ♣r♦♣rts ♦ ♠♥t t♥♥ ♥t♦♥s ♥t♦ s♣ ♣♣t♦♥s ♠♠rst♦rs ♥ ts s ♥s r r♥ ②t rr♥t ♦ rsts ♥ trt♦♥ ♦ t tr♦♥ tr♥s♣♦rt ♣r♦♣rts t t sts ♥ ♦♥sq♥t② ♥ t rsst♥ ♦ t s②st♠ ❬❪

trt rsr s ② ♥♦ t♦ r ♦r ♥rst♥♥t ♣r♦r♠♥ ♦ s s ♦♥ s♠♦♥t♥ ♠trs s♦♥ r♠♥♠ ♦r ♠ rs♥ ♦r t s♠ ♦ ts ♦♥tr♦ ♦s ♥♦t ①st♦r ♦① trs ♥ t♦ t② r ♦♥sr t s ♦r tr s♣♥tr♦♥♥ ♠♠rst ♠trs ♠ ♦ ts tss s t♦ sts ♣r♦sss tt t♦ t t ♦♥tr♦ ♥ ♠♥t t♥♥ ♥t♦♥s s ♦♥ r3 ♥ 2

rrrs ❲ sr t r♦t rtr③t♦♥ ♥t♦♥ ♣ttr♥♥ ♥♠♥t♦tr♥s♣♦rt rsts ♦♥ sts ♥ ♦s ♦♥ t ♥tr ♦ t stts♥ tr r♦ ♦♥ s♣♥♣♦r③ tr♥s♣♦rt

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♥sr♣t r♥③t♦♥

rst ♣rt ♦ t tss ♦rt ss s ♥ t♦ ♣trs♥ t rst ♦♥ ss ♦ t s♣♥♣♦r③ tr♥s♣♦rt r ①♣♥ ❲t♥ trst tr st♦♥s strt♥ r♦♠ t s♠♣ s ♦ t s♣♥♥♣♥♥t tr♦♥tr♥s♣♦rt tr♦ t ♣♦t♥t rrr t s♣♥♣♥♥t ♣tr s ♦♥st②♥tr♦ r ♠♦ t ♠♦rt② ♥ ♠♥♦rt② tr♦♥ s♣♥ ♣♦♣t♦♥s♥ t ♦ ♥st② ♦ stts ♦♥♣t ♥ tr♦s r ①♣♥ ♥ st♦♥ t ♠♣t ♦ ♦ s②♠♠trs ♦♥ t t♥♥ ♠♥t♦rsst♥ s s♦♥ s♥t ①♠♣ ♦ t ♠♦ s②st♠ s t s ♥rst♦♦ ♥ s ♣♦ ①♠♣ t♦♥ srs r♥s ♥ s♣♥♣♦r③ tr♥s♣♦rtr♦ss ♥ r32 r②st♥ rrrs s①t st♦♥ ♥tr♦s♥t♦♥s t r♦♥ tr♦s r♣ ② ♦ ♦ ♦ ♥ 0.7r0.3♥3t s♣ tt♥t♦♥ ♥ t♦ t st t♦ s s t♦ t♦ ts s♥♥t ♣rt ♦ ts tss ♦♥r♥s s ♥♦r♣♦rt♥ ♦ tr♦s ♥ ♠t s ♥ ♥trst♥ ♥t ♦r t tr♦ ♠tr ♥ ♠♥tt♥♥ ♥t♦♥s s♦ rt♦♥ ♦ s s ♦♥ ts ♦♠♣♦♥ s s♦ tt♠♣tr♥ ts tss t♦♥ ♥tr♦s t s②st♠ ♦♥ t st s♥ s ♦sr ♣ t♦ t

s♦♥ ♣tr ♦ t t♦rt ♣rt srs t ♠♣t ♦ ts ♥ r②st♥ s②st♠s ♦♥ s♣♥♣♦r③ tr♥s♣♦rt rst st♦♥ ♦♥♥trts ♦♥ tsts ♣rs♥t t♥ tr r②sts ♥ ♦ t② ♠② ♦♣t② ♥ tr②♣r♦ rs t s♦♥ st♦♥ srs t ♦r♥s ♥ ♦♥sq♥s ♦ ♠♣rt♦♥s ♣rs♥t t ♠t♥st♦r ♥trs tr st♦♥ ssss sss♦ tr♦♠rt♦♥ ♥ ♣rs♥ts t ♣♥♦♠♥♦♥ s t♦♦ t ♠♥tt♥♥ ♥t♦♥s ♠② ♥♥r ♥ ♦rr t♦ tr tr tr♥s♣♦rt ♣r♦♣rts ♦rt st♦♥ ♥tr♦s t♥ ♠♥ts♠ ♥ tr ♥st♦rs ♥ ts♣r♦♠s♥ ♣♦ssts ♦ tr t♥♦♦ ♣♣t♦♥s

s♦♥ ♣rt ①♣r♠♥t r③t♦♥ srs q♣♠♥t ♠trs ♥♣r♦rs s ♦r rt♦♥ ♣r♦ss♥ ♥ ♠sr♠♥ts ♦ strtrs stt♥ t t♠r♠ ♦ ts tss rst ♣tr ♦ ts s♦♥ ♣rt r②♥tr♦s sr ❯❱ ♣♠♣♥ s②st♠s t s♦♥ ♦♥ ssss t ♣r♦r ♦ sstrt ♣r♣rt♦♥ ♦r t s♣ttr♥ ♣♦st♦♥ s ♣r♦r♠ ②♦r r♦♣ ♥ ♠s r♦t t♥qs ♥ ♣r♦rs ♦ s♣ttr♥ ♣♦rt♦♥♥ ♣s sr ♣♦st♦♥ r ♣rs♥t ♥ st♦♥s t♦ rs♣t② ❱r♦sqt② ♦♥tr♦ s②st♠s ♦r ♦t rt♦♥ ♥ ♣r♦ss♥ r s♦ ♣rs♥t st ♥tr ♦ ts tss s ♠♦st② ①♣r♠♥t ♥ ♦t t rt♦♥ ♦ s♠♣s ♥ tr ♣r♦ss♥ t♥q ♦♣♠♥t r ts ss♥t tss ♠♥② ♦①♣r♠♥t rsts s s tt♠♣ts r ♣rs♥t ♥ ts st♦♥

s♦♥ ♣tr ♦ t s♦♥ ♣rt ♣tr srs ♣r♦rs t♦ ♦♥rt♥tr ♠t②rs ♥t♦ ♠sr s ts rst st♦♥ srs ♥ ♥ sts♦♠s ♣ttr♥♥ t♥q ♥tr♦ t♥ ♦r s♣ttr♥ s②st♠ r♥

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t t♠r♠ ♦ ts tss t s ♦♦ ② ♦♥ st♦♥ tt srs ♣r♥♣s♦ ♠tst♣ ♦♣t t♦r♣② ♦rt st♦♥s t♦ sss ♥t ♣r♦♥ ♦ t♣r♦ss s ♣rs tt♥ sss ♥ t ♥ ♦♥♣ ♠♦♥t ♥ t r♦♥♥ rs♣t②

tr ♣tr ♦ t s♦♥ ♣rt ♣tr ♥tr♦s ♦r t♥qs t♦♠sr s ♣ts ♦ t st♦♠♠ st♣ ♦♥ ♠♦st♦ rt ①♣r♠♥ts r ♣r♦r♠ r ♣rs♥t ♥ st♦♥ s♦♥ st♦♥ ♣rs♥ts ①♣r♠♥t t♥qs ♦ t rrr t tr♠♥t♦♥ tr st♦♥ ♣rs♥ts ♣r♦♣rts ♦ ♦♣t st♣s t s♦r♣t♦♥ ♥♣♦t♦♠♥s♥ s♣tr ♣rs♥t ♥ t ♠♥sr♣t r ♦t♥

tr ♣rt st② ♣rs♥ts rsts ♦t♥ ♦♥ tr r②sts♥ ♠♥t t♥♥ ♥t♦♥s st t♥ t t♠r♠ ♦ ts tss rstt♦ st♦♥s ♦ t rst ♣tr ♣tr sr rsts rt t♦ r3 ♥2 tr r②sts ♥ s s ♦♥ ts ♠trs tr st♦♥♣rs♥ts tt♠♣ts t♦ ♠♣r♦ ♣r♦♣rts ♦ ts ♠♥t t♥♥ ♥t♦♥s ② r♣♥ tr tr♥st♦♥ ♠t tr♦s t 0.7r0.3♥3 s♦♥ ♣tr♣tr ssss rsts ♦ ①♣r♠♥ts ♣r♦r♠ ♦♥ rrrs st♦♥ ♥ ♠♥t t♥♥ ♥t♦♥s ♥ t rrr s s♥ t♥t♦ t②♣s ♦ tr♦s t s②st♠s rt t t s♦♠st♥q st♦♥ ♥ t ♦♦ s ♦♥ ①♣r♠♥tsr ♣r♦r♠ ♥ t ♥ ♠♦♥ts ♦ ts tss st♦♥ ttr st♦♥s ♣rtr② ♦♥ t♦ t t ♥②ss ♦ t ♦t ♥ t♠♣rtr♣♥♥ ♦ t s♣♥♣♦r③ ♦♥t♥

♦rt ♥ t ♥ ♣rt ♦♥s♦♥s ♥ ♣rs♣ts s ♥ t♦♣trs t s♠♠r② ♥ t r♦♠♣ rst ♦♥ r② rs ①♣r♠♥ts♥ rsts ♦t♥ ♦♥ ♦t t②♣s ♦ s tr♥st♦♥ ♠t ♦①s ♥ r♥ ts tss ♥ s♣rt st♦♥s s♦♥ ♦♥ ♣rs♥ts ♣♦t♥t s♦t♦♥s ♦rt♦♥ ♣r♦ss♥ ♥ tr♥s♣♦rt sss ♥♦♥tr r♥ t t♠r♠ ♦ tstss ♦r♦r ♣r♦♣♦st♦♥s ♦ rtr ①♣r♠♥ts tt ♦ s♥ t♦♥t ♦♥ ♠♣t ♦ strtr ts ♦♥ s♣♥♣♦r③ tr♥s♣♦rt r ♣rs♥t

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Prt

♦rt ss

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♣tr

ss ♦ ♥♥ ♥t♦rsst♥

rst st♦♥ ♦ ts ♣tr srs t ② tr♦♥s t♥♥ r♦ss t ♣♦t♥t rrr s♦♥ ♦♥ ①♣♥s ♦r♥s ♦ t ♥♦♥③r♦ s♣♥ ♣♦r③t♦♥ ♥rr♦♠♥ts tr ♦♥ ss t ♥♦r♠t♦♥ r♦♠ t ♦r♠r t♦ ♣rs♥t♥ s②st♠ ♦♠♣♦s ♦ ♥ ♥st♦r s♥ t♥ t♦ rr♦♠♥ts ♥ t rr♥t ♦ s s♣♥♣♦r③ ♣r♥♣ ♦ ♦♣rt♦♥ ♦ ts s②st♠ ♥t ♥♥ ♥t♦♥ s ♣rs♥t ♥ t ♦rt st♦♥ s ♦♥ t ①♠♣♦ t s②st♠ ♥♥ ♦ tr♦♥ ♦ ♥t♦♥s rs♥r♦♠ t ♥ strtr ♦ t ♠trs s sss ♥ t♦rt t♦♥s♦ tr♥s♣♦rt ♥ ♥tr♥s trs ♦r♥ t r ♣rs♥t t st♦♥♣rs♥ts ♣r♦♣rts ♦ t♦ r②st♥ rrrs r♥t t♥ ♥♠② r3

♥ 2 s①t ♦♥ ♥tr♦s sr r♥t tr♦ ♠trs ♥ srs ② ♦ tr♦s r ♦ ♥trst ♥ tr♠s ♦ ♣rt ♣♣t♦♥s s s sss rt t♦ ♦s s ♥ r♥s r♦♠ t ♥ tr♠s ♦ s♣♥♣♦r③ tr♥s♣♦rt 0.7r0.3♥3 tr♦s r s♦ ♣rs♥t♥ ts st♦♥ t ♠♥s♠ ♦ ♦ ①♥ ♥ rs t♦ t ♠t ♦r ♥ tr♥s♣♦rt ♣r♥♣s ♦ t tr♦ s ♣rs♥t st st♦♥ ♦ ts ♣tr ♣rs♥ts t ♠♥t t♥♥ ♥t♦♥ ♦♥ t st ♣ t♦ t s ♦sr t s②st♠

r♦♠ s♠♣ t♦ ♣t① rrrs

t ♠② s♠ ♠♣♦ss r♦♠ t ss ♣♦♥t ♦ tt ♦♥ ♠② s♠♣② tr♦ ♦r t♦ t ♣rt t② ♦ ♠ttr ts t♥sr ♣♦ss ♥ ♥♥♦s s②st♠s ♦r q♥t♠ s ♦ ♣②ss ♣♣② sstrt ♦♥ ♦♥ ♠♥s ♥ tr♦♥ t ♥r② ♥ t♦r ♣♣r♦♥ s♠♣ rrr t ♣♦t♥t ❱ tr s ♥t ♣r♦t② tt t ♣♥trt tr♦ t rrr t ts ♠♣t tt♥t ①♣♦♥♥t② tt rrr t♥ss ♥ ts ② ♣r♠tr κ = (2m/h)(V − E) r V > E❬❪

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P ❯

r ♠t ♣tr ♦ ♥ tr♦♥ t♥♥♥ tr♦ s♠♣ rrr rst♥ ♦♥t♥ s rt t♦ t ♥s♥t stt ♦ t tr♦♥ ♥ ts② ♣r♠tr t♥ t ♥st♦r t rrr s t♥ ♥♦ s♦ ts ♠♣t♦s ♥♦t t♦ ③r♦ t tr♦♥ ♠② r t ♦tr s t t ♣r♦t② ♦ ts♥t♦♥ ♠♥s ❬❪

s♣t rt♥ ①♣r♠♥ts tt ♥♦ ♠ rrrs ♥♦♥♦♥tt ♠♦♦ s♥♥♥ tr♦♥ ♠r♦♦♣② ts tss s t t♥♠ s②st♠s ♥ t rrr s ♦♠♣♦s ♦ t♦♠s rrrs ♥ ts t♦♠s r ♦rr r ♦s♣ ♥trst ♦ ts st② ♥ s r②st♥ s t ♦ ♦♥t♦♥ ♦r stts♣r♦♣t♥ r♦♠ st r t♦ ♥♦r♥ st r + ♠② rtt♥ s Ψk(r + ) =cΨk(r) r c = exp(i · )

♦ qt♦♥ srs ♠♦t♦♥ ♥ ♣r♦ ♣♦t♥t t t♦r s r q♥tt② ♦r tr♦♥ ♠♦t♦♥ ♥ ♠t t s ♠♥r②♥ t tr♦♥ trrss s♠♦♥t♦r tr♦ t t♥♥♥ ♣r♦ss ♥ tts t ♥t♦♥ ②s ①♣♦♥♥t② s t tr♦♥ ♣r♦♣ts tr♦ t♦♥ ②r tr♦♥ stt s t♥ ♥s♥t

❲♥ ♥ tr s s ♣♣ t♦ t strtr t ♥r② s r r♥ ♦t♦ t qr♠ s s s♠t② s♦♥ ♦♥ ♠♠♦♥s ♣r♦r♠ t♦rt t♦♥s ♦♥ rr♥t ♦♥ r♦ss ♣♦t♥t rrrs ♥r r♥t s♦ts ♥ sts ♥♦♥ qt♦♥s ♦ tr♦♥ t♥♥♥ tr♦ ♥r③ rrrs ❬❪ s ♠♦ s rtr ①t♥ ② r♥♠♥ ♦ ♣rt t♣♥♦♠♥ ♦r s②♠♠tr rrrs ② ♥ ∆φ = φright − φleft ♣r♠tr ❬❪s ①♣t t ♠♦♥t ♦ rr♥t t♥♥♥ tr♦ ♣♦t♥t rrr ♥rsst t ♣♣ s t r ♥ V = φ0/e ♥ ♦rr t♦ tr♠♥♣r♠trs ♦ ♥ ♥♥♦♥ rrr ♦♥ ♠② t ts rr♥t♦t rtrsts t

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P P❳

r ♠t ♥r② r♠ ♦r rrr ♥r t s ❱ ♣♣ ♦rt ♥ r rt t♥ t rrr t φ0 ♦t tt ♥ t ttr s ♥♦t♦♥② t rrr t s r t ts t t♥ss ∆s s

♦r ♥ r s ♦r♥ t♦ t ♠♦ ♦ r♥♠♥ ♦r ts ♠♦st srs r♦♠ s♥ts rst♥ r♦♠ t ♦♠ss♦♥ ♦ rt♥ ts t③r♦ s ♥♦♠② st♦♥ ❲♥r ♣♦ss ♥ ①♣r♠♥t ♣r♦r I s s ♥ ♦rr t♦ tr♠♥ t rrr ts s st♦♥

r ♦r ♠♦st t♥♥♥ s②st♠s t tr♦♥ tr♥s♠ss♦♥ ♣r♦t② s♥♣♥♥t ♦ ts s♣♥ ♦r♥tt♦♥ r t s♣♥ ♣♦r③t♦♥ qs ③r♦ ♦♥ ♦tss ♦ t rrr ❬❪

♥ ♠♦st ♦ r s②st♠s t rr♥t ♦ ♠♥s ♥♦t ♦♥② ♦♥ t r ♥♠r♦ tr♦♥s tr♦♥ s r♠♦♥ s ts s♣♥ ♦ h s ♥ ♣♦st ♦r ♥t s♣♥♣ ↑ ♦r s♣♥♦♥ ↓ rs♣t②♦r ♥♦♥♠♥t ♠trs t ♠♦♥t ♦ s♣♥ ♣ ♥ s♣♥ ♦♥ tr♦♥s s ts♠ ♥ ♦♥ ♠② s② t s♣♥ ♣♦r③t♦♥ qs ③r♦ ♥ s s ♥♦ tr♥s♣♦rt♣r♦♣rts ♣♥ ♦♥ t s♣♥ s s♣♥ ♣♦r③t♦♥ ♥ ♠tr

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P ❯

♠② sr t t qt♦♥ ♦ ♥ ♥♠r ♦ t tr♦♥s t tr♠ t rs♣t ↑ ♦r ↓ s♣♥s

P =N↑ −N↓

N↑ +N↓

♦♥③r♦ s♣♥ ♣♦r③t♦♥ ♥ rr♦♠♥ts

r ①♥ s♣tt♥ ♦ s♣♥ ♥st② ♦ stts ♦r t♦ t①♥ s♣tt♥ ♦ s♣♥ s♥s t t t r♠ s r♥t ♦r s♣♥↑ ♥ s♣♥ ↓ ♣♦♣t♦♥s t♦♣ ♥ ♦tt♦♠ ♣rts rs♣t② ❬❪

tr♦♥ ♣r♦♣rts ♦ ♠trs ♥ r♣rs♥t ② tr ♥ strtr❲♥ r ♦r s♣ t ♥r② ♣♥♥ ♦ t ♥ strtr ②s t♠trs ♥r②♣♥♥t ♥st② ♦ stts ♦♥t♥ ♥ ♠tss ♦♦s② rr ♦t ② t tr♦♥s ②♥ t t r♠ F ♦r r② ♦st♦ t s ♥♦t ♦r ♦r ♥♦♥♠♥t ♠trs t strt♦♥ s q♦r ♦t s♣♥ ♣♦♣t♦♥s s♦ t s♣♥ ♣♦r③t♦♥ ♥ ♥t ♦r ♥♠trs tt ①t rr♦♠♥t ♣r♦♣rts tr t♦ s♣♥ s♥s r t② t ①♥ s♣tt♥ s s♦♥ ♦r t ①♠♣ ♦ r♦♥ ♦♥ s r②ts t tr♦♥ ♣♦♣t♦♥ t t r♠ ♥♠r ♦ stts t F ♦r tr♦♥s t rs♣t s♣♥s s ♥♦♥q ♥ ♦♥ ♠② t ♦t ♥♦♥③r♦ s♣♥ ♣♦r③t♦♥

t t ♠r♦s♦♣ rr♦♠♥t s rtr③ ② t s♣t ♦r♥tt♦♥♦ ts ♠♥t③t♦♥ s ♠♥t③t♦♥ rts t t tt t♦ ①♥s♣tt♥ ♦♥ s♣♥ s♥ s ♠♦r t♥ t ♦tr r ♦ ♥♣♥s ♦♥ t rr♦♠♥t ♦♥sr s ♠♣s tt ♦♥ s♣♥ ♣♦♣t♦♥

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PP❩ ❯ ❯ ❯

t ♠♦rt② s♣♥ ♦r s♣♥♣ ♣♦♣t♦♥ s ♠♦r ♥♠r♦s t♥ t ♦tr ♠r♦s♦♣ ♠♥t③t♦♥ ♦ t ♠tr ♥ t q♥t③t♦♥ ①s ♦ ♠♦rt② s♣♥tr♦♥s r ♥ t♦ ♥t s♣♥ q♥t③t♦♥ ①s ♦r t ♠♥♦rt②♦r s♣♥♦♥ tr♦♥s s tr♦r ♥t♣r t♦ t ♠♥t③t♦♥ ①s

♣♥♣♦r③ t♥♥♥ ♥ ♠♥t t♥♥ ♥

t♦♥s

strtr ♥ ♥♥♦♠trst ♥st♦r s s♥ t♥t♦ rr♦♠♥t tr♦s s ♥t t♥♥ ♥t♦♥ ♥qs s t♦ rt s s②st♠s r ①t♥s② ♣rs♥t ♥ t s♦♥ ♣rt♦ t ♠♥sr♣t r t ♥r ♥♦r♠t♦♥ ♦t rr♦♠♥t♥st♦rrr♦♠♥t s②st♠ s ♥

r ♦r r♥t ♠♥t③t♦♥ ♦♥rt♦♥s ♦ t rr♦♠♥t tr♦s ♥ ♠♥t t♥♥ ♥t♦♥

t ♦r s ♦ t t♦ ②rs r r♥t t♥ s ♥ ①tr♥♠♥t s r♠♣ r♦♠ ♣♦st tr♦ ③r♦ t♦ ♥t t♠♥t③t♦♥ ♦ ②r ♣ s♣rt② ♥ tt s t strtr ♠②t ♦♥ ♦ ♦r r♥t ♦♥rt♦♥s ♦ rr♦♠♥ts s s♦♥ ♦♥

♥ s♥ ♦ ♥② s②♠♠tr② r♥ ♥ ② t ①♥ s ♦ ♥ ♥trr♦♠♥t t ♣♦st ♥ ♥t rt♦♥s ♦ ♠♥t③t♦♥ ♦r ②r r q♥t ♥ ♥r② ♥ tt s t ♦r ♣rs♥t ss ♦ trt ♠♥t③t♦♥ ♦ t rr♦♠♥ts ♥ s♠♣ t♦ t♦ Pr P♥ ♥t♣r P

t t r② ♥♥♥ ♦ t s♣♥tr♦♥s t♠♥ r ♣r♦♣♦s tttr♦♥ ♦♥t♦♥ r♦ss ♠t s②st♠ s♦ ♦♥sr s ♦rr♥ ♣r♠r② t♥ t♦ s♣♥ s♥♥s ❬❪ s ♠♥s tt t t♦t ♦♥t♥ ♦t s②st♠ ♥ t P ♦r P ♦♥rt♦♥ s t s♠ ♦ t ♦rrs♣♦♥♥ ♠♥♦rt②♥ ♠♦rt② ♦♥t♦♥ ♥♥s GP = G↑↑ + G↓↓ ♥ GAP = G↑↓ + G↓↑♦r♦r ♣r♦♣♦s tt rr♥t t♥♥♥ tr♦ ♥♥ ♣r♦♣♦rt♦♥t♦ ts t t r♠ ♦r ♦t tr♦s ♥ ts tr♠s tr s♣♥ ♣♦r③t♦♥ ♥ rtt♥ s P = (D↑ −D↓)/(D↑ +D↓) ♦r t t♦rr♥t ♠♦

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P ❯

r ♠♣ s♣♥♦♥sr♥ t♥♥♥ r♣rs♥tt♦♥ ♦r ♦t ♣r ♥ ♥t♣r ♦♥rt♦♥ ♥♦t ♥sts ♦ stts ♦ t rs♣ttr♦s ♦t tt ♥ t P ♦♥rt♦♥ t s♣♥♣ stts ♥ t ♠♥t③t♦♥rr♥t ♦ ♦♥ tr♦ ♦♠ s♣♥♦♥ stts ♥ t ♠♥t③t♦♥ rr♥t♦ t ♦tr ♥ rs ❬❪

♥t t s♣♥♦rt ♥trt♦♥ s rtr ①t♥ ② ♦♥③s ♦rt s ♦ t♥♥♥ r♦ss ♠♥t t♥♥ ♥t♦♥s t ♥ ♠♦r♣♦s rrr❬❪ ♣♥♦♠♥ s tr sr ♥ ♠♦r t ♦r r②st♥ rrrs ②tr ♥ t♦♥ ❬ ❪ s♣♥♦♥sr♥ t♥♥♥ s s♠t② s♦♥♦♥ t s ♠♣♦rt♥t t♦ ♥♦t tt ts ♠♦s ♣♣② t♦ t ♣rt s②st♠s♥ ♦ ♥♦t t ♥t♦ ♦♥t t♦♥ ts ♣♦♣t♦♥ ♠①♥ t♦ ts♣♥♣♣♥ ♦r ♦t ①tt♦♥s ♦ s♣♥s ♥♦♥ s ♠♥♦♥s

②♠♠tr② tr♥ ♥

sst♥t ♣rt ♦ ts tss s t t♦ t s②st♠ ♣♦st t♦♣ t ♣rt ♠♦♥♦r②st r♦s r②st♥ ♦r r♦tt ②

s t tt ♦♥st♥t s r♦②√2 rr t♥ tt ♦

tt ♠s♠t s r♦♥ ♣r♥t s ♥♦t ♥♦ t♦ st♦rt t r②st ❬❪ t s s♦ t♦rt② ♥rst♦♦ strtr tt ♥ sr s ♣♦ ♠♦ t♦ sr t s♣♥♣♦r③ t♥♥♥ tr♦ t ♠♥tt♥♥ ♥t♦♥s s ts st♦♥ ♣rs♥ts t ♠♣t ♦ ♦ ♥t♦♥s♥ ♥ strtrs ♦♥ t t♥♥♥♥ tr♥ ♦ tr♦♥s t ♣rtrs②♠♠tr② r♦ss t ♠♥t t♥♥ ♥t♦♥s

tr♦♥ ♦ ♥t♦♥s

♥ r②st♥ s②st♠s r ①s② st t♥ ts tss t t♦♠♥rt ♣r♦ ♣♦t♥t t ② t tr♦♥ s t trrss t tt ♣♥s♦♥ t rt♦♥ ♦ ♣r♦♣t♦♥ t♥ t tt s ♦t ♥ t rrr ♥ ♥

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❨❨

r ♦♣ ♥ r♦ssst♦♥ ♦ t r♦♥ t♦♣ t ♠♦♥♦r②st ❱t♦rs ♦ ♥♦t r②st♥ ♦r♥tt♦♥s ♦ ♦t ♠trs ❬❪

r t♦♠ ♦rts r♦♣ ② s②♠♠tr② ♣r♦♣rts ♥ t rt♦♥ ♦♣r♦♣t♦♥ r tr♥srs ♥♦s r s♠t② r♥ ♦♥ t rt ♦ s②♠♠tr② ❬❪

t tr♦s t tr♦♥s ♥ sr t tr ♦♠♣♦♥♥ts ♦ t ♦t♦rs ♣r t♦ t ♥trs ♣r♣♥r t♦ t rt♦♥ ♦ ♣r♦♣

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P ❯

t♦♥ s♣ ♣ ♥ s② ∆1 ∆5 ♥∆2∆2′ rs♣t② ♣♥♥♦♥ t ♥ strtr ♦ t ♠tr tr ♠t ♦r ♥st♦r tr♦♥s t s♣ tr♥srs ♠♦s s②♠♠trs ♥r♦ tr rs♣t sttr♥ rts ♦rts rs♦♥ ♦♥ ♠② s♣ ♦t s♣ ♦♥t♦♥ ♥♥s

♥ strtrs ♠♣t

r r♦♥ ③♦♥ t s②♠♠tr② ♣♦♥ts ♥♦t Γ− s t rt♦♥ ♦ t ♣r♦♣t♦♥ ♦ tr♦♥s sr ③♦♥ s s♦r♥ ♦♥ t rt t t Γ−X rt♦♥ s♣ ❬❪

♥ ♦rr t♦ ♥rst♥ t ♠♣t ♦ tr♦ ♥ rrr ♥ strtrs ♦♥ ts♣♥tr♦♥ rs♣♦♥s ♦ t s②st♠ r♦♥ ③♦♥ ♦r s♥tr s②st♠ s ♣rs♥t ♦♥ ♥ s②st♠s tr♦♥s r♠ t♦ ♣r♦♣t ♦♥ t Γ− rt♦♥ t♥s t♦ ♥ ①tr♥ ♣♣ tr

♥s♠ ①

♥r rs♦♥ ♦r s♥ r②st♥ rrrs s tr t② t♦ ♣rsr t s②♠♠trs ♦ tr♦♥s r♥ t tr♥s♣♦rt s ♦r♥t tr♥s♣♦rt s t ♠♥♥t ♦r ♠♦r♣♦s ♥st♦rs 23 ♥ ♥tr♠①♥ ♦ s②♠♠trs t♥ t rrr rsts ♥ tr ♣♦♦r tr♥ ② t ♦t♦r ♥ t s ♦ r②st♥ rrr s♦s t s tr♦♥s ♦ s②♠♠tr② ♥r♦ tr rs♣t s②♠♠tr②♣♥♥t tt♥t♦♥ t♥t rrr

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❨❨

r ♠t ♦♠♣rs♦♥ ♦ ♥ ♥♦r♥t t♥♥♥ tr♦ t 23

♠♦r♣♦s rrr ♥ ♦r♥t tr♥s♣♦rt tr♦ t r②st♥ ❬❪

r ♥tr ♥ ♦♠♣① ss ♥ strtr ♦ ❬❪ ♠rs♥♦t rs♣t ∆ tr♦♥ s②♠♠trs ❬❪

s ♠♥t♦♥ ♥ st♦♥ ♥t♦♥s ♦♠ ♦♠♣① ♥ t♥♥♥♦rs ♥ ♦rr t♦ ♥rst♥ t ♠♥s♠ ♦ ② t♥ t ♥st♦r ♦♥ s

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P ❯

t♦ ♦♦ t ts ♦♠♣① ♥ strtr s strtr t ♦r t r②st♦♥ t ♦♥trt♦♥s ♦ ts rs♣t tr♦♥ s②♠♠trs s s♦♥ ♦♥ ❬ ❪ ss♥t ♦♥♣t ♦ t ♦♠♣① ♥ strtr s t ♥tr♠t♥ ♦ ♥t♦♥s t t ♦♥r② ♦ t t♦ r②sts ♥ s ♦t ♠t♥st♦r ♥tr r ♠t♥ ♣ stts s sttsr t♥r♥t ♥ t ♠t t ② ①♣♦♥♥t② ♥ t ♥st♦r t♦ ♣rs♥♦ t ♥ ♣ ♦r♠♥ t ♦♠♣① ♥ strtr ♦ t ♥st♦r ❬❪ t♦r♠♥t♦♥ ♥s♥t stts r ② ♣r♠tr s t ② ♣r♠tr κ❬❪ ♦s s♣rs♦♥ s ♣♦tt s s ♥t♦♥ ♦ ♥r② r♦ss t ♥ ♣ ♦ ts♠♦♥t♦r ♦♠♣① ♥ ♦♥♥ts t ∆1 ♥ ♥ ♦♥t♦♥r ♥s s s♠r t♥ ♥② ♦tr ♥ t ♦s ♥♦t ①t♥ t♦rs t rs ♦ t ② ♣r♠tr κ tt rs t tr♥s♠ss♦♥ ♣r♦t② e−2κds ♠♣s tt t s t ∆1 stt tt s t ♦st ② rt s ♦r rr♥t ♥♦♠♣ss♥ s②♠♠trs tt ♠♣♥ ♦♥ t t♥♥ rrr ♠♦st♦ t rr♥t t♥♥♥ r♦ss t rrr s t② ♦ t ∆1 s②♠♠tr② ♦rt r♠ ②♥ ♥ t ♥tr ♦ t ♣ tr s ♦♥② ♦♥ ∆1 κ ♥s♥tstt tt ♦♥♥ts ♦♥t♦♥ ♥ ♥ ♥s s②♠♠tr② κ ♦ t ∆5 ♥s s♦♥ t♦ tt ♦ ∆1 ts t ②s t♥ t rrr str ∆2′ ♦♠♣①♥ ①t♥s rtr t♦rs κ s s♦ tr♦♥s ♦ t ∆2′ s②♠♠tr② ♦♥trt t♦ t t♥♥♥ rr♥t ♠ ss t♥ ts ♦ ∆1 ♥ ∆5 s②♠♠trs

♦t tt t s ♣rs♥t ♦♥r♥s t r②st ♥②ss ♦ t♦♠♣① ♥ strtr ♥s t♦ ♣r♦r♠ ♦r t②♣ ♦ t ♦① rrr ♥♦rr t♦ tr♠♥ ts tt♥t♦♥ rts ♦r s♣ s②♠♠trs s s♦♥ ♥st♦♥ ♦r rrrs r♥t t♥

r♦♥

ts t ♦♦ t t ♥ strtr ♦ t rr♦♠♥t ♦r ♦t s♣♥♣♦♣t♦♥s ♦♥ t Γ− tr♦♥ ♣r♦♣t♦♥ rt♦♥♦♥ ♥ s tt stts t rt♥ ♥t♦♥ s②♠♠trs ①st t t r♠ ♦♥② ♦r ♦♥ ♦ t s♣♥ ♣♦♣t♦♥s s s ♣rtr② tr ♦r ∆1 ♥ ∆2♦s ♥s r♦ss r♠ ①s② ♦r ♠♦rt② ♦r ♠♥♦rt② s♣♥ ♥♥rs♣t② ∆2′ ♥ ∆5 s②♠♠trs r♦ss t F ♦r ♦t s♣♥ ♣♦♣t♦♥s s♦t② ♦ ♥♦t rs t♦ s♣♥ ♣♦r③t♦♥ ♦ t rr♥t s t② ♣r♦ rr♥t ♦♥ ♥② rt ♦r♥tt♦♥ ♦ t rr♦♠♥ts

tr♦♥s t♥♥♥ r♦ss ♣rt② r②st♥ s②st♠ ♦♥sr ♦t tr s♣♥♥ s②♠♠tr② ♥ ♦ t P ♥ P ♦♥rt♦♥s t t♦t s②st♠ ♦♥t♥s t s♠ ♦ ♦♥t♥s rst♥ r♦♠ tr♦♥s t♥♥♥ ♦t ♠♦rt② ♥♠♥♦rt② ♥♥s r ♥ tr♥ t s♠s ♦ ♦♥t♥s ♦ s②♠♠trs ♥ ts ♥♥s s ♦♦♥ t t♦t ♦♥t♥ ♥ t Pstt s t s♠ ♦ ∆1 ∆2′ ♥ ∆5 ♥ t ♠♦rt② ♥♥ ♥ ∆2 ∆2′ ♥ ∆5 ♥t ♠♥♦rt② ♥♥ rs♣t② ♥ t P stt ♦r ♠♦rt② ♠♥♦rt②

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❨❨

r ①♥ s♣t ♥ strtr ♥ ♦r ♦t ♠♦rt② ♥ ♠♥♦rt② s♣♥ Γ− s t Σ ♥ Λ ♥♦t ♥ ♣r♦♣t♦♥rt♦♥s ♥ t r s♣ rs♣t② ❬❪

tr♦♥s r♦♠ t ♥t♥ tr♦ t♥♥ ♥t♦ stts ♥ t ♠♥♦rt②♠♦rt② ♥♥ t♥ t ♦t♥ tr♦ t t♦t ♦♥t♥ s t s♠♦ ∆2′ ♥ ∆5 ♥ ♦t ♠♦rt②t♦♠♥♦rt② ♥ ♠♥♦rt②t♦♠♦rt② ♥♥s s♥ ♦ t t♥♥♥ ♦ ∆1 ♥ ∆2 s②♠♠tr② tr♦♥s ♥ t ♥t♣r s②s s♥♥t r♥ t♥ P ♥ P ♦♥rt♦♥s ♦ t s②st♠ st ♥ strtr ♦ t rr♦♠♥t tr♦s s ②t ♥♦tr ♣r♦♣rt② ♦ t♠♥t t♥♥ ♥t♦♥s tt s rs♣♦♥s ♦r t s②♠♠tr② tr♥

r♥s♣♦rt t♦♥s

tr t ♣r♦r♠ t♦♥s ♦r t s②st♠ ♥ sr t♥♥♥ ♦r ♦ t s♣rt ♦♥t♦♥ ♥♥s ② r ♣rs♥t ♥r ♥ ♥ s tt t ♠♦rt② ②♥ ∆5 s②♠♠tr② s ♣rs♥t ♥ t ss tts ♣ ♦ ♥t♥ t tr♦ ♦r ♦t♥ rt tr♦tr♦♥s t ∆5 s②♠♠tr② ①st t r♠ ♦r ♦t ♠♦rt② ♥ ♠♥♦rt②♣♦♣t♦♥s ♦ r♦♥ s♠ ♣♣s t♦ t ∆2′ ♥♥ ②t t♦ ts ②rt t s ♥♦t t♦ t② t♥♥ r♦ss t rrr

r r♥ s ♥ ♣rs♥ ♦r s♥ ♦ t ∆1 s②♠♠tr② ♥ t♦ ssr ①t♥t t ∆2 ∆1 s t s♦st ②♥ ♥♥ ♠♣sts rs♣♦♥st② ♦r ♠♦st ♦ t t♦t ♦♥t♥ ♦r ts s②♠♠tr② ♦s♥♦t stts t t r♠ ♠♦♥ t ♠♥♦rt② ♣♦♣t♦♥ s♦ t ♥♥♦t ♥t ♥t♦ t rrr r♦♠ t ♠♥♦rt② ♣♦♣t♦♥ ♦ t ♥t♦r ♥ t ♦tr♥ ♥ t ♥t♣r ♦♥rt♦♥ ∆1 s♣♥♣ tr♦♥s t♥♥ t♦rs ∆1 s♣♥♦♥ stts ♥ t ♦t♥ tr♦ ♥ tr r ♥♦ ∆1 s♣♥♦♥stts t② ♦♥t♥ t♦ t♥♥ ♥ s♥ ♦ s♣♥ ♦r s②♠♠tr②sttr♥ ♠r②

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r ♥♥♥ ♦r s②st♠ t t rrr ♥ ♠♦♥♦②rs t t♦♣ t♦ r♣s s♦ t♥♥♥ ♥ t♣r stt t t ♦♥ ♦r ♠♦rt② ♥ t rt ♦♥ ♦r ♠♥♦rt② s♣♥ ♣♦♣t♦♥s ♦tt♦♠ r♣s ♣t t ♥t♣r ♦♥rt♦♥ ♦♥sst♥ ♦ t♥♥♥r♦♠ ♠♦rt② t♦ ♠♥♦rt② stts t ♣♥ ♥ r♦♠ ♠♥♦rt② t♦ ♠♦rt② sttsrt ♣♥ t♦♥ ♦tr ②rs r r♥ ♥ t ♥t♣r ♦♥rt♦♥t♦ s♦ ♦ ♥ s♥ ♦ s♣♥ ♥ s②♠♠tr② ♦r♥ t♥♥♥ ②♦♥ t rrr ♥ ♦r ♥ t ♦t♥ ♠t ②r s s②♠♠tr② s s♥t s ② t s②♠♠tr② ♦ t ♥♥t ♦ stt t t r♠ ♦ t ♥t♦r ♦t tt t ♥st② ♦ stts ss r ♦rt♠ ❬❪

♠♥♦rt② ∆2 stts ♥t ♥t♦ t rrr r ♣t t t ♦t♦r ♥ t P♦♥rt♦♥ t rt t② ♦♥t♥ t♦ ② ♥ t P stt

② s♠♣② s♠♠♥ ♣ t s②♠♠tr② ♥♥s ♠sr t t ♥ ♦ t♦t♦r ♦r ♦t ♣r ♥ ♥t♣r ♦♥rt♦♥s ♦♥ ♠② r② s tr♥ t♥ ♦♥t♥s ♥ ♦t P ♥ P ♦♥rt♦♥s s r♥♠♦st ♦t♥ s♦♥ s t r♥ ♥ rsst♥s s t ♥♥ ♥t♦r

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sst♥ ♥ sr t t ♦♦♥ ♦r♠

TMR =GP −GAP

GAP

=RAP −RP

RP

[%]

G ♥ R r t ♦♥t♥ ♥ rsst♥ ♦ t s②st♠ ♥ t ♣r P♥ ♥t♣r P ♦♥rt♦♥s rs♣t②

r ♥♥ ♠♥t♦rsst♥ rt♦ rss ♣♣ ♠♥t r♣♦rt♦♥ ① µm2 ♥t♦♥s t ♥♠ t rrr t r♦♦♠ t♠♣rtr rs ♥ ♠♣t② tr♥s ♦t♥ ② r❱♥♥t t ❬❪

s♦s t②♣ rsst♥ rss ♣♣ r ♠♥t s ♣♣ ♦♥ t s② ♠♥t③t♦♥ ①s ♦ t ②rs s♦ s t♦ P stt s② ①s s ♥ ♣♥ tr♦r t s ♣♣ ♥ ♣♥ s♣r♣♥r t♦ t rt♦♥ ♦ rr♥t ♦ ♥ ♠② s tt strt♥ t t ♥t t rt ♠♥t③t♦♥ ♦ t rr♦♠♥ts s ♣r ♦t♥ ♦♥ t ♥t ♥s ♥ t rsst♥ ♦ t s②st♠ s ♦ rt♦♥ ♦ t str♥t t♦ ♦s ♥♦t t t ♠♥t③t♦♥ ♦ t s②st♠♥t t rs ♣♦st ♥ ♦♥ ♦ t rr♦♠♥ts sts ts♠♥t③t♦♥ ♥ ♥s ♦♥ t ♣♦st rt ♦r♥tt♦♥ ♦ tr♦ ♠♥t③t♦♥ ♦♠s ♥t♣r ♥ t ♦r s②st♠ rsst♥ ♥rss ♠♥t③t♦♥ ♦ t s♦♥ tr♦ r♠♥s ♥♥ t ts ♣♦♥t t♦ts r ♦rt② ♥rs ♦ t ♠♥t str♥t t♦rs r ♣♦st s ss t ♠♥t③t♦♥ ♦ t s♦♥ tr♦ t♦ ♣ s ♥ t♦♥rt♦♥ ♦♠s ♣r ♥ ♦r ts t♠ ♥ ♦♥ t ♣♦st rt♦♥ rst♥ ♥ t ♥t ♦ rsst♥ ♥ ♠rr♦r ♦r♦rs ♦♥ t rtr♥ s♣ ♦ t r♦♠ ♣♦st t♦rs ♥t s

s t ∆1 s②♠♠tr② tr♦♥s r r② ② tt♥t t♥ t rrr t s♥ ♦ stts t ts s②♠♠tr② t♥ t ♠♥♦rt② s♣♥ ♥♥

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rst② rs ts t♦t ♦♥t♥ ♥ ♥ ♣rs♥ ♦ t♦♥ str♦♥②tt♥t ∆2 s②♠♠tr② stts ♦s ♥♦t ♦♠♣♥st t ♦r♠r ♦ss s ♦♥ ♠②♦♥ r♦♠ t t r♥ t♥ ♠♦rt② ♥ ♠♥♦rt② ♥♥♦♥t♥s ♥ s♦ t rt♦ ♥rss t t rrr t♥ss s t∆2,2′ ♥ ∆5 s②♠♠trs ② ♠ str t♥ t ∆1 s♠♣ t♥ss♦r ♥♥♦t ♥rs ♥♠t② ♥ r♥ ♥♥♦♠trs t② r♦ss ②rs ♦♠s s♦ tt tr♥s♣♦rt ♠② r③ ♦♥② r♦ss tsts ♥ tr♥ strs ts ♦r♥② ♥♥ ♦ ts ts ♦♥ tr♥s♣♦rt r♦ss ♠♥t t♥♥ ♥t♦♥s sss ♥ t st♦♥ ♦r♥ ♣rt② r②st♥ s②st♠ ♦♥t♥ rt♥ ♥tr♥s trs ♥t②t ts s♣♥♣♦r③ t♥♥♥

♥tr♥s sss

❩r♦ s ♥♦♠②

r sst♥ ♣♥♥ ♦♥ ♣♣ s ♦ ♦23♦ ♠♥tt♥♥ ♥t♦♥ ♥ ♥ ♦r P t♦♣ ♥ P ♦tt♦♠ ♥♠♥tsst♥ r♦♣ ♦ ♠❱ s rrr t♦ t ③r♦ s ♥♦♠② ❬❪

❩♥ t ♦r t rst t♠ r♣♦rt ♥ ♥s② ♥♦♠♦s rs r♦ss 23s s t♥ s♠ s r♥ ♣ t♦ ♠❱ t s ♦sr ♦t t r♦♦♠ t♠♣rtr ♥ t t ♠ ♠♦r♣r♦♥♦♥ ♥ t ttr s s♣② ♥ t P ♦♥t♥ ♥♥ s t♥r② s ♦ ts ③r♦ s ♥♦♠② s ♦ t s♠ ♦rr s tt ♦ t ♠♥t①tt♦♥s t s ss♠ tt t tr♦♥s st ♦ t r♠ ♣r♦♦t ①tt♦♥s ♦ ♦ ♥tr s♣♥s rst ♥ ♥ t♦♥ t♦r ♥♦r♥ t s♥ t♥ ts s r♥ t rst t♦r ♥ t st♥rrrr t ♦r♥ ❬❪ t s ♦r t rst t♠ ♦sr ♥ sr♦r ♠♦r♣♦s rrrs t t s ♦♠♠♦♥② ♦sr ♥ r②st♥ s②st♠s s

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♥tr rs♦♥♥t stts

r ♦rt t♦♥ ♦ ♠♦rt② t ♥ ♠♥♦rt② rt ♦♥t♥ ♥♥s ♥ s②st♠ t ♠♦♥♦②rs t rrr r♣s t k‖ 6= 0 rst r♦♠ ♥tr rs♦♥♥t stts ❬❪

r ♠t sr ♥r② ♥s s♣rs♦♥ ♦r ♠♥♦rt② s♣♥ ♥♥ ♥ r② ③♦♥ ♣ts t ♥s rs t s ♥ s t s♣rs♦♥♦ sr stts ❲♥ t t♦ ♦r♣ t② ♦r♠ ♥tr rs♦♥♥t stts ♥ ♦♥trt t♦ t tr♥s♣♦rt t♦rs t ①♠♣ rs ❬❪

t♦♥s ♣r♦r♠ ② tr t ❬❪ s♦ tt ♥ t♦ ♠♥♦rt②♥♥ ♦♥t♥ r♦ss s s s ♠ ♦r t♥ t ♦♥ ♦ t♠♦rt② t s ♦♠♥t ② r ♣s ② r♦♠ t k ♥♦r♠ t♦ t rrr s trs r rt② rt t♦ t ♠♥♦rt② s♣♥ sr stts ss♠t sr stts r♦ss F t rt♥ k‖ ♦♥trt♦♥s r♦♠ts stt ♦♠ s♥♥t ♦♥ t ②r③s t ♥ s ts srstts ①st ♦♥ ♦t ss ♦ t rrr t② ♠② ♦♣ t♦ ♦tr rst♥ ♥

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♥tr rs♦♥♥t stts tt r rs♣♦♥s ♦r r ♦♥t♥ ♣s ♥ t♠♥♦rt② ♦♥t♥ ♥♥ s ♥tr♥s trs ♦r t Gmaj/Gmin rt♦ s♥♥t② ts t t

♠♣t ♦ ♣♦♥♦♥s

♦ ♠♥t t♥♥ ♥t♦♥s s♦ rs ♦ t rt♦ t ♥rs♥t♠♣rtr ♣rt r♦♠ strtr ts sr ♥ ♣tr ts ss s♦t♥ ttrt t♦ tr♠② ♦r ♦t♥ ①tt♦♥s ♦ t rrr t♦♠s ♣♦♥♦♥s t♦ rt② ♦rs r♣♦rt tr rt ♠♣t ♦♥ t s♣♥♣♦r③ tr♥s♣♦rt rrr ♣♦♥♦♥s t ♥r② ♦ ♠❱ ♥ ♠❱ r r♣♦rt ♦♥ sr s②st♠s t ♦rrs♣♦♥♥ s ♥ t s♦♥ rt ♦rr♥t ♦t rtrsts d2I/dV 2(V ) s♦ ♥st tr♦♥t♥♥♥s♣tr♦s♦♣② ❬ ❪

tr rrr t②♣s

rrr s ♣rs♥t ♥ t ♦r♠r st♦♥s s ♥ s② ①♠♣ ♦ s♦stt s♣♥♣♦r③ t♥♥♥ ♥ t s②st♠ ♦r t♦ ♥trst♥ s②♠♠tr② tr♥ ts ♥ t♦ t rt sst② ♦ tr ♦♣t stss s ♦♥ r3 ♥ 2 ♥st♦rs r s♦ st r♥ ts tsss st♦♥ ♣rs♥ts ♣r♦♣rts ♦ ts ♠trs r♦♠ s♣♥tr♦♥ st♥♣♦♥tt♦ sr ♠♦r ♦♠♣① ♦♠♣♦♥s r ♣r♦♣♦s s rrrs ❬ ❪t② ②♦♥ t s♦♣ ♦ ts tss

tr♦♥t♠ tt♥t

r3 rt t♦ r②st③s ♥ ♥tr ♣r♦st 3

strtr s s♦♥ ♥ t ts tt ♦♥st♥t ♥ t s st♦ tr♥t♥ r ♥ 2 ♣♥s ❬❪

♦♠♣① ♥ strtr ♦r t ♣r♦st str♦♥t♠ tt♥t s ♣rs♥t ♦♥ ♦♠♣r t t rs♣t t♦♥ ♦r ♦♥ ♥ s② s tt t tr♦♥ tr♥s♣♦rt s ♥♦t ♦r♥ ② t s♠ tr♦♥ s②♠♠trs r3 rrr ①ts r② r♥t ♥ strtr ♣r♦r♦♠ tt ♦ s ts ♥ ♥ s ∆1 ♥ ∆5 s②♠♠trs rst♥ r♦♠♦①②♥ 2p ♦rts t ♦♥t♦♥ ♥ s ∆2′ ♥ ∆5 s②♠♠trs r♦♠ sts s t ♦♥sq♥ ♠♦r t♥ ♦♥ κ ♦♦♣ ①sts ♥ t ♣ ♥ t r♥trt② ♥ s t ♥trst♦♥ t♥ ts ♦♦♣s s ♦srt♦ t t ♦♥t♦♥ ♥ ♥ s♦ s t r♠ ♥ s ♦ ♦♥tt t ♠t s s s ♠♣r② t ♠ ♣♦t♥t ♦ s ♦♥ t♦ ♦st♦ t ♦♥t♦♥ ♥ ♠♥s tt F ♥ t st ♦r t♦ t ♥♦t ♦r ♦r tr♦♥ ♣r♦♣t♦♥ ♦♥ t rt♦♥ t tr♦♥ rrr

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r Pr♦st 3 strtr ♥ s ♦ r3 A st②s ♦r r ♥ B♦r st rs♣t② ♦♠♠♦♥ ♦tr 6 r♣rs♥tt♦♥ t t B st♥ t ♥tr s s♦♥ ♥ t ♦tt♦♠t ❬❪

r ♦♠♣① ♥ strtrs ♦ r3 st②s ♦r t r ♥trt② ♠rs ♥♦t t ∆ tr♦♥ s②♠♠trs ❬❪

t ∆2′ ♥ ∆5 s t♥ ♦r t♥ tt ♦ t ♦s ∆1 ♥ ∆5 ❬❪ ♦r♦rt ①t♥s♦♥ ♦ t ∆5 s②♠♠tr② ♥ s t ♦♥ ①t♥♥ t st t♦rs κ s rst♥ ♥ t ♦♠♥♥t ♦♥tt② ♦ ts ♥♥ t♥ t rrrs ♥ ♦♥trr② t♦ t ♥ strtr ♣r♦ ♦r t r ♥trt② s ♥ t ♥tr ♦ t ♣ s ♦♥② ♦♥ ∆1 κ ♦♦♣ ♦♥♥ts ♦♥t♦♥ ♥♥ ♥s s②♠♠tr②

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t♥♠ ♦①

tr♥t♥ ♦rr♥ ♦ r ♥ 2 ♣♥s t♥ t r3 r②st ♥ t♦ ♥ ♥rt♥ ♥tr tr♠♥t♦♥ ♥ t♦ 2 tr♠♥t♦♥ s♦sr t♦ ♠♦r ♥rt② ♦r t♥ r t ♥tr ♠①♥ ♠② r ♠♣t ♦♥ t t♥♥ ♠♥t♦rsst♥ rt♦ ♠♥s♥ ts ♦r♥ st♥ t s♥ ❬❪ ♥rt♥ ♥tr tr♠♥t♦♥ sr♥ ♣tr ♥ ♦rr t♦ ♦ t ss t t♦♥ 2 ②r ♠② ♣♦str♦♠ s♣rt ♣r tt♥♠ ♦① s♦r ♥tr ②r ♦ ♥sr t♥tr tr♠♥t♦♥ ♦ t rrr ♦r s♦♠ r♦♣s s♦ ♣rttt ♦② 2 rrrs ♦ ♦♦ ♥ts ♦r t s♣♥tr♦♥ ♣♣t♦♥s❬❪ tt♥♠ ♦① rrrs ♠t t♥ sr s ♥ tr♥t t♦ t str♦♥t♠tt♥t

r r②st♦r♣ tr ♠♥s♦♥ ♥ ♣♥r strtr ♦ ♥ts2 ❬❪

♥ts ♣s 2 s ♥ ♣ ♦ ❱ ❬❪ s t s♦ tt ♥♠♣t①② r♦♥ ②r s♦s ♦t rsstt② ♥ tr ♦♠♦♥t② t♥♦ ♦♥t ♦ts♣♦ts ❬❪ ts tt ♣r♠trs ♦r ♥ s♣② ♦r t rt♦♥ ♣r♦♠s s♠ tt ♠s♠t t ♣r♦st♠trs

t♥♥♥ ♦r ♦ t ♥ts 2 rrr s s♠r t♦ tt ♦ tr3 t♦ tr ♦rrs♣♦♥♥ ♥ strtrs s②♠♠trs ♦ t ♥ ♥r ♦ ∆1 ♥ ∆5 t②♣s t♦ ♣ ♦rts rs t ♦tt♦♠ ♦ t ♦♥t♦♥♥ ♦♥ssts ♦ s②♠♠trs rst♥ r♦♠ t♦♠s ∆2′ ♥ ∆5 ❬❪

s t t ♥ts ♣s ♦ 2r♦s ♣♦♥ ♦tr ♣r♦stss ♥ t♦♥ sst♦♥ tt t ♥ s s t ♦r tr♠♥t♦♥②r ♦ t r3 rrrs ♦r ♠② ♥ ♦♠ ts r♣♠♥t ♦r ts rs♦♥s♥ t♦ rt② sr ①♣r♠♥t rsts ♦♥ 2s strtrs trst② s s♦ ♣♣r♦ t♥ t t♠r♠ ♦ ts tss

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r♥t tr♦ ♠trs

r♦♥ s sr s t ♠♦ tr♦ ♠tr s ♦ ts ♥rst♦♦♥ strtr ♥ s②♠♠tr② tr♥ ♣r♦♣rts ♥ t s②st♠ ♦r tr r sr s♥ts ♦ t ♠♥t♦♥ s②st♠ t♦ ♣r♦♣rts ♦r♦♥ ts s② ♦①t♦♥ ♥ s♠t♥♦s ①st♥ ♦ rt♥ s②♠♠tr② ♥s♦r ♦t s♣♥ ♣♦♣t♦♥s s st♦♥ ♣rs♥ts ♣r♦♣rts ♦ r♥t ♠trstt ♠② s s rr♦♠♥t tr♦s ♥ ♠♥t t♥♥ ♥t♦♥s

♥tr♦t♦♥ ♦ ♦t

♥ ts sst♦♥ ♦tr♦♥ ♦②s ♥ ♣r ♦t tr♦s r ♣rs♥t s t②♣r♦ t♦ rt ♥ts ♦r ②♥ ♠♥t t♥♥ ♥t♦♥s t♦ tr ♦♦ s②♠♠tr② tr♥ ♣r♦♣rts ❬❪ ♥ ♦r ♥t♣② ♦ ♦①t♦♥ st

♦tr♦♥ ♦②s

r ♠t ♥ s♣rs♦♥ ♦ ♥ ♦ ♦♥ t ❬❪ Γ−rt♦♥ s♦ ♥ ♦tt ♥s r♣rs♥t ♠♦rt② ♥ ♠♥♦rt② s♣♥ s♥srs♣t② ♦tt♦♠ s ♦ t ♠♦rt② ∆1 s♥ r ♥ ♥ ♦rr t♦♦♠♣r t F ♣♦st♦♥ ♥ ♦t ♠trs ❬❪

s ♣rs♥t ♦r ♠♥t t♥♥ ♥t♦♥s ♦♠♣♦s ♦ r♦♥ tr♦s srr♦♠ t♥♥♥ rt♥ s②♠♠tr② ♥♥s ♥♠② ∆5 ♥ t♦ ssr ①t♥t t

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r ♦t t♥♥♥ ♦r ♦♦ s②st♠ tt rrr ♥ ♠♦♥♦②rs t ♥ P t ♥ P rt rt ♦r♥tt♦♥ ♦ t tr♦s ❬❪

∆2′ tt r ♣rs♥t ♦t ♥ P ♥ P ♦♥rt♦♥s rsts ♥ ♦ ♦♥t♥ r♥ Pr♥ t ♣rs♥ts tt ② r♣♥ t ♦ tr♦s♦♥ ♠② ♥♥ t rt♦ s ♥ s② ①♣♥ ♦♥ ♦♠♣rs ♥s♣rs♦♥s ♦ ♥ ♦ ♦♥trr② t♦ t r♦♥ s ♦t ∆5 ♥∆2′ s♥s ♥ ♦t ② ♦ t r♠ ♥ t ♠♦rt②s♣♥ ♥ s♠♣s tt tr♦♥s ♦ ts s②♠♠trs ♥ ♦♥trt t♦ t t♦t ♦♥t♥♦♥② ♥ t ♣r ♦♥rt♦♥ rsts ♥ t r♣♦rt ♦♥ ♦s♥t♦♥s ♥ r t♥ ♦r tr r♦♥ ♦♥tr♣rts ❬❪ t♦♥s ♦ tt♥♥♥ ♣r♦r♠ ② ❩♥ t r s♦♥ ♦♥

s ♣r♦s② ♠♥t♦♥ r②st③s ♥ t strtr t tt ♦♥st♥t tt ♥ ♦r♠ r②st♥ ♥tr t ♦t ♦♥ ♦♥trr② ts t①♦♥♦s♣ ♣ ♦r♠ s♦♥ t ♦rrt tt ♠t♥ t t rrr ♦r t s ♥♦♥ tt t ♦ ♦♠♣♦♥ rt♥ t r♦♥ strtr ♣ t♦ ♦ rt♦ t ts tt ♦♥st♥t ♥ r② s♠r t♦tt ♦ r♦♥ ❬❪ ♥ t♦ ♥tr♠①♥ ♦ ♦ ♥ ♥ strtrs♥ ♦ s ♥t r♣♦rts s♦ tt t s t ♦ ♥tr tr♠♥t♦♥ tts ♥rt② ♠♦r ♦r rsts ♥ t sr ♠♦r ♦t ♥strtr t t ♥tr ❬❪ ♥ t ♦♥trr② r② r♥t rsts ② ♦♥ t s♦ tt ① t♥ t ♦x1−x♦r♠ ♠② s♦ t♦ ♥ ♥♥ rt♦ t♦ s♣ ♥ strtr ♠♦t♦♥ t ts rt♦ ❬❪

♥tr ♦t ②rs

s t s t ♦ ♥ strtr tt ♦rs ∆5 ♥ ∆2′ tr♦♥s r♦♠ t♥♥♥ ♥t P stt ♥ ♠♦r ♣r♦♥♦♥ ts r ①♣t ♦r t ♦ ♥tr

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r rt♦ ♦r ♦x1−x strtrs rt ♥rs♠ ♦♥t♦♥s ♥ ♠sr t r♦♦♠ t♠♣rtr s s t t ♠❱ s❬❪

r ♦t t♥♥♥ ♦r ♦♦ s②st♠ t t rrr ♥ ♠♦♥♦②rs t ♥ P t ♥ P rt rt ♦r♥tt♦♥♦ t tr♦s ❬❪

♣r♦♠ rst♥ r♦♠ t ♦r♠♥t♦♥ ♣ r②st♥ strtr ♦ ♦ts ♥♦t ♣rs♥t ♥ s ♦ ♣ t♦ ♠♦♥♦②rs t ♥♠ ♥tr ♦ ②rs ♦♦ t strtr ♦ t ♦r ♦ tr♦ t② r r♦♥ ♦♥t t tt ♦♥st♥t ♥ ❬❪ ❨s t ♦♠♣r t t♥♥ ♠♥t♦rsst♥ rt♦ ♦r sr strtrs rt t ♦♠♣r ♦♥t♦♥s ♦x1−x s②st♠s t t ① ♥ 1/2 ♦r r

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sts r ♣rs♥t ♦♥ s ♦t♥ ♦r t ♣r ♦ ♦rtr♦ r r② ttr t♥ ♦r t ♦trs rt② ♦ ♦rt ♦s s②st♠ s ①♣♥ ② t ♥ ♦ t♦ ♣r♦r♠ tr♦ ♥♥♥t ♥ ♦rr t♦ ♦t♥ t tt ♣♥s t tr♥t♥ ♦ ♥ ♦♣t♦♥❬❪ t♦♥s ♣r♦r♠ ② ❩♥ t ♦♥ ②♣♦tt s②st♠s t ♦tr♦s s♦ s♠r rsts s ts ♣r♦r♠ ♦♥ t ♦s s②st♠

♦ s t①tr s②st♠s

s t s s②st♠s s♦ rs♦♥② s♥s t r♦♦♠ t♠♣rtrt② r ♣r♦♠s♥ ♥ts ♦r ♥tr♥ t ♥str st ♦r t ststrtr rqr ♦r ♣♦t♥t ♣♣t♦♥s rqrs ♦♥② ♦♥ ♦ t rr♦♠♥t②rs t♦ t♦ st t t ♠♥t ♣♣ t ♦tr s t♦r♠♥ ① s ♥♥♦t ♦♥ t trt♦♥ r♦♥ ♦r ♦ts s②st♠s sr ♣♦sst② t♦ ♣♥ ♦♥ ♦ t ②rs ♦r rsrrs t♦ ♦♦ ♦r ♥♦trs♦t♦♥s

r t strtr ♦ ♠♥t t♥♥ ♥t♦♥ rqr ② t ♥str② s②♥tt rr♠♥t ② ts s ♣♥♥ ②r ♦ t strtr ♥srs str♦♥ ①♥s ♥ s♠ str② ♠♥t s t♥ ♦♥ t t♦♣ ②r♥② t t♦♣ r ②r ♥ st ts ♠♥t③t♦♥ t s ♣♣ ❬❪

♣♥♥ ♦r tr♦ ♥ rt s s②♥tt rr♠♥t ② ♦♠♣♦s ♦ ♥trr♦♠♥t② ♦♣ rr♦♠♥t♦♥rr♦♠♥trr♦♠♥t strtr ①♥s ② t ♥trr♦♠♥t ②r ♥ ①♠♣♦ s strtr s s♦♥ ♦♥

♦r ♠♦r t♥ ②rs ♠tr ♥♥rs r ♦♦♥ ♦r ♥ ② strtr t str♦♥ ①♥s ♥ ♠♥♠♠ str② ♠♥t s t♥ ♦♥ tr ②r ♦ r t ♠♦st ♣r♦♠s♥ ♥ts r r♥ ♦r Pt♥ s t ♥trr♦♠♥ts ♥ ♦♦ s t s②♥tt rr♠♥t ❬❪ ♦r t

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♠♥ ♦st ♥ ♣♣t♦♥ ♦ ts ♠trs ♥t♦ t ♠♥t t♥♥ ♥t♦♥ss tt tr r②st♥ ♦r♥tt♦♥ ♦s ♥♦t ♦♦ t strtr ♦ t rrr ♥st t s ♦r♠ ②♥ r tt ♠s♠t tt♦s ♥♦t ♦ t rrr t♦ r♦ t♦♣ ts ② ♠t②r s t sr♠♦♥♦r②st s♦t♦♥ t♦ ts ♣r♦♠ s ♦♥ ♥ ♦r♠ ♦ t ♦ tr♦s

r ♠t ♣tr ♦ t ♦♦ strtr rr②st③t♦♥ r♥ t ♥♥♥ ❬❪

♦ s ♥ ♠♦r♣♦s ♠tr s♦ t rst ♠♦♥♦②rs ♦ r♦ ♠♦r♣♦s② ♦♥ t♦♣ ♦ t ♦r ♦♥ rt♥ ♥♠r ♦ ②rs s r♦♥ ♠♦r♣♦s② t r②st♥ strtr strts t♦ ♣♣r ❬❪ s s ♥♦t ♣t①t rtr t①tr r②st ♦♠♣♦s ♦ r②st♥ ♦♠♥s s♣rt ②r♥ ♦♥rs ♥ ♠♦r♣♦s r♦♥s ♣♣r ♦ tr♦ ♥ r♦s♦♥ s t①tr ♠♦r♣♦s② s ♣rs♥t ♦r t r②st♥t② ♦ t♠♥t t♥♥ ♥t♦♥ s ss♥t ♦r rs♦♥ rt♦ r②st③t♦♥ s tr♦r ② ♥♥♥ t ♥tr st t t♠♣rtr ♥♦t ♦rt♥ rsts ♥ s♣r ♦ t r②st♥ strtr ♦r♥t♥ r♦♠t t①tr rs ♦ t rrr ❬ ❪ ♥ t r②st③t♦♥ rs t♥st♦rrr♦♠♥t ♥tr t ttr strts t♦ ♦r♠ t strtr s ♣t♥ t♦ t strtr ♥st ♦ ♦r♠♥ ts st ♣s ③ t s♦ tt s♣t t ♣♦②r②st♥ ♥tr♦ t rrr tr s r② tt ♦r ♥♦ ♥♥ ♦♥ t tr♦♥ tr♥s♣♦rt ② tr♥ ♦♥rs ❬❪ s ♦ ①♣t t t♥♥ ♠♥t♦rsst♥ sr② s♠ ♦♥ t ♥♦♥♥♥ ♠♦r♣♦s s②st♠s s ♦♠♣r t♦ t ♥♥♦♥s s ♦ t s②♠♠tr② ♠①♥ rst♥ r♦♠ t ♥♦r♥t tr♥s♣♦rt tts t②♣ ♦r ♠♦r♣♦s rrrs ❬❪

♦s ♠♥t t♥♥ ♥t♦♥s ♣r♦ t♦ ♥♦t ♦♥② ♣r♦♠s♥ ♥ts ♦r ♥str ♣♣t♦♥s t t t♥♥ ♠♥t♦rsst♥ ♦sr ♥ts strtrs s ♠ r t♥ tt ♥ st♥r ♥ ♦s s②st♠s❬❪ s s t♦ t♦ t ♠♣t ♦ t t①tr③t♦♥ ♣r♦ss ♦♥ qt②♦ t ♥trs sss ♥ st♦♥ ♥ t ♦tr ♥ r② r♥t ♦r ②

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r t sr♣rs♥② s♦s tt ♣ t♦ rt♦ ♠② s♦ r♦♠ t t①tr s②st♠ ❬❪ ♦r♦r rr t r♣♦rttt r♣♥ t ♦r ♦ tr♦ t t ♦♦ ②r ♠♣r♦s♦t r②st③t♦♥ ♥ ♥ tr♠ stt② ♦ t ♥t♦♥ ♦♥sq♥t②s t♦ ts ttr ♣r♦r♠♥ ♥ ♦♠♣rs♦♥ t♦ t st♥r ♦s s②st♠❬❪

0.7r0.3♥3 ♠t tr♦s

♥ tr ♥t ♥♥ ♥t♦♥s r② ♦♥ tr t♦rs s♣♥♣♦r③t♦♥ ♥ t ♥t♦r ♣♦ss② ♦r s♣ tr♦♥ s②♠♠tr② r♥ ♥s②♠♠tr②♣♥♥t ② rts t♥ t rrr ♥ ♣t♥ ♦r rt♦♥♦ s②♠♠tr②♣♥♥t stts ♥s t ♦t♦r ♥♦② t♦ t ♣♦♥t ♥ st s②st♠ ♠♦t♦♥ ♥ t♦ rr s♣♥ ♣♦r③t♦♥ ♠②♥♥ t t♥♥ ♠♥t♦rsst♥ ❯♥♦rt♥t② t s♣♥ ♣♦r③t♦♥t♥ t rr♦♠♥ts s rt♥ ♥t ♦s ♥♦t ♦ t♦ ♥♥t rt♦ rtr

♥ r♦♦t t ♥tr♦ ♠trs t ♥ strtr ①♥ s♣tt ② tt ♦♥ ♦ tr s♣♥ ♣♦♣t♦♥s ♦ ♦♥t♥ rs t ♦tr♦♥ ♦ s♠♦♥t♥ ♦r ♥st♥ ❬❪ ② r ssq♥t② ♥♠♠ts

❲t♥ t t♠r♠ ♦ ts tss ♣r♦ss ♦ ♦t♥♥ ♥t♦♥s t ♠t ♥t♥♠ str♦♥t♠ ♠♥♥t 0.7r0.3♥3 tr♦s rt s ♣♣r♦ s st♦♥s srs ♥♠♥t ♣r♦♣rts ♦ tsstrtr

r②st s♣tt♥

♥ ♦rr t♦ ♥rst♥ t ♠t ♦r ♦ rt♥ ♠trs tr ♣②s ♣r♦♣rts ♥ t♦ sr 0.7r0.3♥3 ♦♠♣♦♥ s ss♥t②t r♦♣ ♥t♥♠ ♠♥♥t ♥3 ♦r r②st③s ♥ t♣r♦st 3 strtr r② ♣rs♥t ♦r t r3 rrrs ♦♥ ♥ t s t A ♥ B s♣rs ♦rrs♣♦♥ t♦ ♥t♥♠ ♥ ♠♥♥srs♣t② ❯♣♦♥ ♦♣♥ t t str♦♥t♠ s♣ ♣r♦♣♦rt♦♥ ♦ t sts s r♣ ② r

♥♥s ♥ tr♥st♦♥ ♠t s ts ♠♦ ♥ ♣r♦strtr ♥ s ♦ t ♦tr 3 s②♠♠tr② ♦ ♠♥♥ts t♦ ♦ ts♦ ♥rt s ♥♠ g r rt t♦rs t ♥t② r♦①②♥ sts tr ♦ t♠ t2g r ♥ ♦♥s t♥ t♦s sts

t♦ t ♦♦♠ r♣s♦♥ t♥ t ♥ ♦rts ♥ ♥t② r♥s sts t ♥r② ♦ t g ♦rts rt t♦rs t sts rss s

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r s♣ ♦ t ♥ st ♥t♦♥s r♦♠ t t♦ rt ♦♣ g ♦rts dx2−y2 dz2 ♦tt♦♠ t2g ♦rts dxy dxz dyz ①tr♥ rs♣t ♦①②♥ sts ❬❪

r ♥r② s♣tt♥ ♦ ♦ ♥rt ♥ ♦tr r②st❬❪

♦♠♣r t♦ t ♥r② ♦ t t2g s s ∆CF ♥ s♣tt♥ ♦♥r② s t♦ t r②st

♦r♥ t♦ ♥s r tr♦♥s ♦rts s♦ s t♦ ♠♥♠③ t ♦r♥r② ♦ t s②st♠ ♦r ♥ ♦♥ t ♦r tr♦♥s s t s ♦r t♥3+ ts ♥ ♦♥ t♦② rst tr tr♦♥s ②s ♦♣② t ♦st♥rt t2g s t ♦ tr s♣♥s rt ♦♥ ② t t ♦r ♦t ♦rt tr♦♥ s r♥ ② t rt♦ t♥ t ∆CF ♥ t ♥s rst③t♦♥ ♥r② H ∆CF > H t s ♠♦r ♦r ♦r t tr♦♥ t♦

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r P♦ss ♦s♣♥ ♥ s♣♥ stts ♦ ♥3+ ♥ ♦trr②st t ttr ♥ ♦r ♥ tr♥st♦♥♠t ♦①s ❬❪

st ts s♣♥ ♥ ♦♣② t ♦st t2g ♦r ♥ t ♦♣♣♦st H > ∆CF

stt♦♥ t tr♦♥ ♦♦ss t g s t♦ stt♦♥s r rs♣t② ♦s♣♥ ♥ s♣♥ stts ♥ s ♦ ♠♦st ♦ tr♥st♦♥♠t♦①s ♥3+ ♥ ♥♦ ①♣t♦♥ t s♣♥ stt ♦♥rt♦♥ s ♥rt②♠♦r ♦r t2g tr♦♥s ♦r♠ t tr② ♥rt ♦r s♣♥ t gtr♦♥ s ♦♣ t♦ t ② ♥s r ♦♣♥

♦ ①♥ ♠♥s♠

♥ ♦rr t♦ ①♣♥ t ♠t ♥tr ♦ t t s ♠♣♦rt♥t t♦ ♥rst♥ t ♠♣t ♦ t ♦♣♥ t r t♦♠s s ♥ ♥trr♦♠♥t♠tr ♥ ts ♥ ♦♥ stt s s s♦♥ ♦♥ ❲t♦t ♦♣♥ts t x ♥t 1−xrx♥3 ♦r♠ s ③r♦ ♥ ts ♦♥ ♦♠♣♦st♦♥ s 3+♥3+2−

3 ♦r r♣♥ ♦♥ tr♥t t♦♥ ♦ ♥t♥♠ t ♥t str♦♥t♠ r♠♦s♦♥ tr♦♥ r♦♠ t s②st♠ s rst t ♥3+ ♦♥ ♦♠s qr♣② r♥4+ ♥ ♦ ♥ t g s♥ s ♦ t r②st♥ s②♠♠tr② ♦t s②st♠ t ♥ ♦♥s r t♦♦ r ♣rt t♦ ♦r♣ ♥ ♥ tr♦♥ ♥♥♦t tr♥srr rt② t♥ t♦ r♥t② ♦♥③ ♥ sts ♥ 2− st s t♦ ♣② r♦ ❩♥r s♦ tt t tr♦♥ tr♥sr t♥ t♦ ♥ sts s r③ ②♦♣♣♥ ♦ ♦♥ tr♦♥ r♦♠ t ♥ st t♦ t 2− st ♥ t s♠t♥♦s ♠♣♦ ♥♦tr tr♦♥ r♦♠ ts 2− st t♦ t ♦tr ♥ st ❬❪ s ♣♥♦♠♥♦♥s ♦ ①♥ ♦r♦r ♦♥ tt t s♣♥ ♦ t tr♥srrtr♦♥ ♦ ♦♣ t ♦t ♥♥s ♦♥ ♦rs ♦♣♣♥ ♠♣t tsstr♦♥② ♣♥s ♦♥ t rt s♣♥ ♦r♥tt♦♥ ♥ ③r♦ ♦r t ♥t♣rs ❬❪ s ♥ ♥ t ♣r ♥♠♥t ♦ s♣♥s tr s ♦♥② ♦♥ s♣♥t②♣ ♦tr♦♥s ♠♦♥ t t g s ts rsts ♥ t ♠tr ♥ ♦♥t ♦rt ♠♦rt② s♣♥ ♣♦♣t♦♥ ♦♥② ♥ rs t♦ t ♠t ♦r ❩♥r ♠♦ s rtr ①t♥ ② ♥rs♦♥ ♥ s ❬❪

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s t ♣♦♥ts ♦t tt t ♦ ①♥ ♠♥s♠ s ♥♦t t ♦♥②rs♦♥ ♦r t rrr ♦♣♣♥ ❬❪ ② ♦♥ s♦t♦♥ t♦ t sr♣♥② t♥rt♥ s♣ts ♦ t t ② ♣r♦♣♦s♥ str♦♥ tr♦♥♣♦♥♦♥ ♥trt♦♥ rs♥r♦♠ t ♥r ♥r② t♥ ♦ t ♦tr ♥ s ❬❪ ss♥t②s♣♥ t ♥r s♣tt♥ rss r♦♠ t ♦♠tr st♦rt♦♥ tt r②st♥ s②st♠ ♥r♦s ♥ ♦rr t♦ ♦r ts ♦r ♥r② t s ts st♦rt♦♥tt ts t ♥r②

r t ♠t ♣tr ♦ t ♦ ①♥ ♠♥s♠ ♥0.7r0.3♥3 t♥ ♥3+ ♥ ♥4+ sts ssst ② ♦①②♥ ♣ ♦rts gs s♣t ♥ ♥3+ s s ② t ♥r r②st♥ tt st♦rt♦♥ t ♣♥rs♦ ♥ strtr ♦ t 0.7r0.3♥3 ❬❪

s♠t ♣tr ♦ ♦ ①♥ t♥ ♥3+ ♥ ♥4+ sts t①②♥ ♣ ♦rts ♣t♥ t ♥r ♥r② st♦rt♦♥ ♦ ♦t g ♥t2g s ♦ ♥3+ s s♦♥ ♦♥ ♦♥ t t rst♥ ♠t ♥strtr ♦ t ♠tr

s ♥3 s ♥ ♥trr♦♠♥t ♠tr t t ♥rst ♥♦rs ♥♦♣♣♦st s♣♥s ♥ tr♦♥ ♥♥♦t s♠♣② ♦♣ t♦ t ♦tr st s t str♦♥♥ r ♦♣♥ ♦rs t t♦ ♣ ts s♣♥ ♣r t♦ t ♦♥ ♦ t st t ♦♣♣♥ ♦ t tr♦♥ s t♥ rst② r ♦r t sts t t s♣♥s♥t♣r rt② t♦ tt ♦ t tr♦♥ s s♦♥ ② ♥♥s ♥rs♥t ♠♦♥t ♦ r rrrs t♥ t ♠tr ss t ♦r♥ ♥trr♦♠♥t strtr t♦ ♦♠ ♥t ♥ rr♦♠♥t② ♦rr ♦♠♣♦♥♥ts strtt♦ ♣♣r ❬❪ t rt♥ ♦♥♥trt♦♥ ♦ ♦♣♥ts t strtr ♦♠s ②rr♦♠♥t s x ♦♣♥ rt♦ s ♦♥ t♦ t♥ ♥ s♦ t s tsrt♦ rt♦ tt s ♦♠♠♦♥② s ♥ ♦♠♣♦♥s rt♦♥ s s② s t♦ sr s r ♦♣♥ ♦ t strtr ♥ s ♥♦tt♦♥

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s t♥ ts ♠♥sr♣t t ♠② ♥trst♥ t♦ ♥♦t tt ♦r♦♣♥t ♥3 s②st♠ t str♦♥t♠ ②s ♥st♥ stt s ♥♥t ♦rt ①♣r♠♥t ❬❪

♠♣rtr ♣♥♥

♠♥ ♦st ♥ ♠♣♠♥tt♦♥ ♦ ♠t ♠trs t♥ ♦♠♠r♠♥t ♥t♦♥s s t t♠♣rtr ♣♥♥ ♦ tr ♣r♦♣rts ♦ ♠♥♥ts ♥t♦♥s rss r♣② t t♠♣rtr ♥s♣♣rs ♦ t r♦♦♠ t♠♣rtr ② ♦ r t♠♣rtr ♦ t s ❬❪ t s ①♣♥ ♥ ♦r♠ ♦ ♣r♠tr ♦ss♦ ♣♦r③t♦♥ t ♥trs s t s t ♥tr s♣♥ ♣♦r③t♦♥ tttr♠♥s t t♥♥♥ ♣r♦♣rts Pr t s♦ ❬❪ tt t s♣♥ ♣♦r③t♦♥♦ r sr rss ♠ str t ♥rs♥ t♠♣rtr t♥t ♠♥t③t♦♥ ♦ t ♠tr r t♠♣rtr ♦r♥ s♠r♠♥t③t♦♥ ♥ rt♦♥ ♦ t ♠t rtr ♥ ♥♠ t ♠♥♥t②rs r r♣♦rt t♦ rst ♥ tr ♥ rr♦♠♥t ♣r♦♣rts ❬ ❪

r ♠♣rtr ♣♥♥ ♦ t ♥tr s♣♥ ♣♦r③t♦♥ ♦r r♥trrrs ♦♠♥ t ♦♠♣r t♦ tt ♦ t r sr ♥ t♦ ts ♠♥t③t♦♥ ♦t♥ ② Pr t ❬❪

r t ♣r♦r♠ ♠sr♠♥ts ♦♥ t t♠♣rtr ♣♥♥ ♦ ♣♦r③t♦♥ ♦r r♥t ♥st♦r ♥trs ❬❪ ♥ ♦♠♣r t♠ t ts♦t♥ ② Pr ♦r t ♥ r sr ♦ t rsts♦s tt t ♥tr ♣♦r③t♦♥ rs rs♠ t ♦♥ ♦ t ♠♥

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t③t♦♥ rtr t♥ sr ♣♦r③t♦♥ ♥t♥ tt t ♠♥ts♠ s♣rsr ♥♦t st t t sr t ♥ t ♥t② ♦ t ♥tr t♦ trt t♠♣rtr s r♦♥ ♦r

r♥ ♥ t s♣♥ ♣♦r③t♦♥ ② t♥ t sr ♥ t ♥tr s ♥ t ♣rsrt♦♥ ♦ t 6 ♦tr t t sr B sts ♥♠♥♥s s r t ♦tr♠♦st ②rs ♠② ♦①②♥ ♥t rsts ♥ r s♣tt♥ ♦ t g s s rst t ♦ ①♥ ♠♥s♠ s ♥ ♥ t ♠♥t♦♥ t♠♣rtr ♣♥♥ s♦s r② r♥trtr r♦♠ tt ♦ t ♥tr ❬❪ ♥ t ♦tr ♥ t ♦♥t♥t② ♦ ts♦tr s ♣rsr t t ♥trs t t ♠♥t♦♥ ♦r 2 ♥♥ ♥ t ♣rs♥ ♦ st♦rt♦♥s ts ♠♣t ♦♥ t tr♦♥ strtr s ♦rt♥ ♥ t s ♦ t r sr rsts ♥ ♠♦r rtr t t t s t rs ♦ t r rrr ♥st② ♥ t trt♦♥ ♦ t6 strtr ♦♠tr② t t ♥trs tt r rs♣♦♥s ♦r t C rt♦♥❬❪

s②st♠

r ♥st② ♦ stts ♦ t s②st♠ t qr♠ Φe

♥ Φh ♥♦t tr♦♥ ♥ ♦ rrr ts rs♣t② t2g ♦rrs♣♦♥s t♦ t∆2′ ♥ ∆5 s②♠♠trs t g r♣rs♥ts ∆1 ♥ ∆2 s ♣r♦s② s♦♥ ♦♥t ❬❪

s♠t qr♠ ♥♠♥t ♦ t ♦r♠♥t♦♥ ♥s ♦r t ♦♠♣t ♦r♥t s②st♠ s s♦♥ ♦♥ s ①♣♥

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r rsst♥ ♣♥♥ ♦♥ ♠♥t ♣♣ ♦r µm2 t ❬❪

♥ st♦♥ t s♥t② ♦ t♠♣rtr tr r ♦♥② ♠♦rt② s♣♥ stts t t r♠ ♦ tr♦s rs t ♠tr s ♥st♥ ♦r t ♠♥♦rt② s♣♥ s♣♥ ♣♦r③t♦♥ ♦ t tr♦♥s t♥♥♥ tr♦t strtr s tr♠♥ t♦ t ♥ ♥ r ❬❪ rst♥ ♥r② t♦t s♣♥ ♣♦r③t♦♥ t ♦ t♠♣rtrs s rs t♦ r s ♦♦ss t♥♥ ♠♥t♦rsst♥ ♦r s♦rt② ♦♦ss ♠♥t♦rsst♥ ♠sr♠♥t ②♥ s s♦♥ ♦♥ ②s r♣② t t t♠♣rtr ♥ t s♣♣rs t t♦ t ♦ss ♦ t s♣♥♣♦r③t♦♥ t t ♥trs ❬❪

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♣tr

♦ ♦ ts

r②st♥ s②st♠s ♣rs♥t ♥ t ♣r♦s ♣tr ♠② sr r♦♠ ♠♣rt♦♥s rst♥ r♦♠ t r♦t ♦ s♥ ②rs ♦♥ t♦♣ ♦♥ ♥♦tr s♠♣s tt t ♥② ♦ t s♣♥tr♦♥ rs♣♦♥s ♣rt t♦rt② s ♦t♥s♣♣rss ② t♦♥ ts rs♥ r♦♠ t ♣rs♥ ♦ ts s t t♦♥tr♦ ♥ rtr③t♦♥ r r t♦ ♦t♥ s s♦♥ sr ♦r t s tr♦r ss♥t t♦ ♥rst♥ tr ♦r♥ ♥ ♣r♦♣rts s ♣tr♦ss ♦♥ sr t②♣s ♦ t♥ stt♦♥s tt t♦ t ♣rss ♠♥t♦rsst rs♣♦♥s rst st♦♥ ♥♦♠♣sss t ♦ t st② t♥r②st♥ trs tt s s t♥♥ rrrs ♥ t ♥♥ ♦ ts ts ♦♥ t s♣♥♣♦r③ tr♥s♣♦rt t ♥ ♠♣ss ♦♥ ♦♣t ♠♥s t♦ ♥t②ts ts s♦♥ st♦♥ ♦♥♥trts ♦♥ t♦♥s r♦♠ ♥♦♠♥ r②ststrtr t ♥trs t s♦ srs sts ♠t♦s ♦ s♣♣rss♥ ♦r♠♥s♥ t r♦ ♦ ts strtr ♠♣rt♦♥s tr st♦♥ srs♣♥♦♠♥ ♦ tr♦♠rt♦♥ ♥ ♦ ♦♥ ♥ s t s t♦♦ t♦ ♥♥ ts♣♥tr♦♥ ♣r♦♣rts ♦ tr ♥t♦♥s st st♦♥ ♥tr♦s rs ♦rsr ♦♥ ♠♥ts♠ t♥ r②st♥ trs t♦ ♣rs♥ ♦ ts ♥♥♦♣ ♥st♦rs

♠♣rt♦♥s

s st♦♥ srs ♣r♦♣rts ♦ strtr ts ts rst sst♦♥♦♥♥trts ♦♥ tr ♠♣t ♦♥ s♣♥♣♦r③ tr♥s♣♦rt ♥ rst♥ sr♣♥st♥ t♦rt ♣rt♦♥s ♥ ①♣r♠♥t ♦srt♦♥ rs t s♦♥♦♥ ♣rs♥ts ♦♣t ♣r♦♣rts ♦ t t sts

♠♣t ♦♥ s♣♥♣♦r③ tr♥s♣♦rt

rs♦♥ ♦r ①♣r♠♥t rsts ♦♥ ♠♥t t♥♥ ♥t♦♥s rr② ♠tt t♦rt ①♣tt♦♥s s ♣rt② ♥ ♣rs♥ ♦ ts t♥ tr r②s

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r ♠t ♣tr ♦ ♦ ♦r♥ ♦ t t rrr t t♦♣rs♥ ♦ t stt

t♥ ♥t♦rs ♥ t ♣rs♥t t♥ rrr rts ♥ t♦♥ ♥r② ♥ t ♥ ♣ ♦② r♥ t t rrr t ♦ t ♠tr tr♦♥s r♦ss♥ t rrr ♦ t♥♥ ts stts ♦ ♦r ♥r②t r sttr♥ ts ♠♥s♥ t ♦r ♥t♦♥ rsst♥ ❨t ♣rtr♦♠ t r s②st♠ ♦♥t♥ ts t ②t ♥♦tr ♠♣♦rt♥t ♣r♦♣rt②♦ ♠♥t t♥♥ ♥t♦♥s s♣♥ ♣♦r③t♦♥ ♥ s②♠♠tr② tr♥ ❬❪

rs ♥ ♣rs♥t ♥ t rst ♣tr ♦ ts ♠♥sr♣t s♦ ♦♠♣① ♥ strtrs ♦ r②st♥ ♥st♦rs r ♦ t ♥trst ♦ ts tsst s ♣rs♥t ♦r♥ ♦ t s②♠♠tr② ♦ ♥s tr♠♥s t s②♠♠tr②♦♥sr♥ ♦r♥t tr♦♥ tr♥s♣♦rt r♦ss t rrr ♥ ♥r stt ②♥♥ t ♥ ♦r ♦♥t♦♥ ♥ ♦ t ♥st♦r s ♦♣t t s②♠♠tr② ♦ tt♥ s ♦♥ ♥rt② trrss t ♥ ♣ ♥ t s ♦ t sttt s②♠♠tr② rtr ♦ tt t stt s ♦ r♦♠ tt ♦ t ♥t♦ tt ♦ t ♦♥t♦♥ ♥ ♠ s ♦ ♠t♥ ♣ stt rs♥r♦♠ r tr♥sr t ♠ttr ♥tr ❬❪ s t ♥ ♥r② t stt ♦♣t t rtr ♦ t ♥ ♥ ♦♥t♦♥ ♥stts ♣r♦♣♦rt♦♥ ♦ ♦ ts rtrs s ♥ tr♥ ♥rs② rt t♦t κ ♦ t ♦♠♣① ♥ ♦♦♣ ♦ t rtr ♦♥sr ♥ t ts t st ♣rt② ♦ t ♥♦♠♥ tr♦♥ s②♠♠tr② t ♠② ♣t ts tr♦♥♥ t t stt s ♦♣ t t♠ ♦t♦♥ ♦ t t stt s ♣r♦ s ♥r ♦♠♥t♦♥ ♦ t t♦ ♥ ♥ ♦♥t♦♥ ♥ s②♠♠trsr♥s♣♦rt ② r♦♠ t t stt s t♥ ♣r♦ s ♥r ♦♠♥t♦♥ ♦t t♦ s②♠♠trs tt sr t t stt ts t② ♥ t♦ ♠①♥ t♥ s②♠♠tr②♣♦r③ ♦♥t♦♥ ♥♥s ♣♥♥ ♦♥ t ♥st②

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♦ t t stts t♥ t rrr s ♣r♦sss ♠② ♣♣♥ ♠t♣ t♠srst♥ ♥ s♥♥t rt♦♥ ♦ t s♣♥♣♦r③ tr♥s♣♦rt ♦r♥② ♥ ♦♥sq♥t② ♦ t s♥ ♦ t s②st♠ ♦r♦r ♥ ♦rr t♦ ♦r♦♠ t♥r② r♥ s ♦♣♣♥ t stts ♠② ♦♠♣♥ ② ♣♦♥♦♥♠ss♦♥ ♦r s♦r♣t♦♥ r♥ t tr♥st♦♥ ❬❪ s ♥tr♦s ♥ t♦♥♥st t♠♣rtr♣♥♥t ♦♥t♥ ♥♥ ♠② rs♣♦♥s ♦rs♣♥♣♣♥ ♥ts ❬ ❪

r t♦♣ ♥ rsst♥ ♦tt♦♠ s t ♥t♦♥ ♦ t rrrt♥ss ♦r ♦t♦ s r♦♥ ♦♥ r♥t r ②rs❬❪

♥ t♦ t t♦rt t♦♥s ♣rt tt tr s ♥♦ ♠t ♦ rt♦ ♥ ♣rt② ♣t① ♥t♦♥ t r② t rrr ❬❪ ♥ ♥♦r ♥♠ t rrrs t t♦r② ♣rts r② s♥s ♦r r♦s s②st♠s♣r♦♣rts ♦ tr r ♦♥tr♣rts r s♥♥t② ss stst♦r② r s♦s tt ♥ t♦ rsst♥ ♦ t ♥t♦♥ ♠♦st ♥r② ♥rss t tst♥ss t rt♦ ♦sr rs rt♥ ♠①♠♠ tr t strts t♦rs ♥ ♥t② rs ③r♦ t s ♥t ts ♠①♠♠ tt t ♦r♥t t♥♥♥ sr ♥ st♦♥ ♦♠♥ts t ♦♥t♥ trrs r♠♥♥

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tr♦♥s t♥♥ ♦♠♥♥t② t sts r② ♠①s tr s②♠♠trs♥ ♥t② rsts ♥ t s♣♣r♥ ♦ t s♥

r♦♣ ♣r♦t rrr t tMgO anneal r❬❪ ❬Ωµm2❪ ❬❱❪ ❬♥♠❪ ❬❪

♦② ❬❪♥② ❬❪rts 20K 20K F+∗ ❬❪♦♦r ❬❪♦♥t♥ ❬❪Ptr♦ 3K ❬❪Ptr♦ 3K ❬❪ 5K 5K ❬❪ 5K ❬❪ 5K 5K) ❬❪❨s 20K 20K) ❬❪ ❬❪ ❬❪❳♦ ❬❪

♦♠s 13K ❬❪

♦♠♣rs♦♥ ♦ r♥t st rt♦s r♣♦rt ② sr r♦♣s ♦♥♦s s②st♠s ♦♥ t tr rs♣t ♥♥♥ t♠♣rtrs

r♦♣ ♣r♦t tMgO rrr t r❬❪ ❬Ωµm2❪ ❬♥♠❪ ❬❱❪

♥ ❬❪s♥ ❬❪❨s 20K ❬❪

♦♦r 1K def bar MF ❬❪♦♥t♥ ❬❪❨s 20K 20K RT M ❬❪s♥ ❬❪❲♥ ❬❪

sts ♦r s②st♠s s t♦rt ♣rt♦♥s ② ❲♥ t

♥② r♦♣s t ♦tst♥♥ ①♣r♥ ♥ t♥ ♠s r♦t ♥ rt♦♥♦ t ♠♥t t♥♥ ♥t♦♥s r♣♦rt s ♥t② ♦r t♥ ts♣rt ② t t♦r② s s♠♠r③ r♥t r♣♦rts ♦♥ sr t②♣s♦ s ♠♥t t♥♥ ♥t♦♥s r♦♠ r♥t r♦♣s

♥ t s ♦ ♥♦♥♦s s ♦r t♦rt t♦♥s r♣r♦r♠ ♦♥ ♠② s r sr♣♥② t♥ t ①♣r♠♥t ♥ t t♦r②

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r♦♣ ♣r♦t tMgO rrr t r❬❪ ❬Ωµm2❪ ❬❱❪ ❬♥♠❪

Pr♥ 5K F F ∗ ❬❪♥r 20K ❬❪❩♥ ❬❪

sts ♦r ♦♦ s②st♠s s t♦rt ♣rt♦♥s ② ❩♥t rst♥ r♦♠ t t♦♥s ♠② ♦rst♠t s tt♦rs ♦ ♥♦t ♥ ♥tr rs♦♥♥t stts ♥ t ♠♥♦rt② ♥♥ s st♦♥

r♦♣ ♣r♦t tMgO rrr t r❬❪ ❬Ωµm2❪ ❬❱❪ ❬♥♠❪

❨s 20K 20K ❬❪❩♥ ❬❪

sts ♦r ♦♦ s②st♠s s t♦rt ♣rt♦♥s ② ❩♥ t rst♥ r♦♠ t t♦♥s ♠② ♦rst♠t s tt♦rs ♦ ♥♦t ♥ ♥tr rs♦♥♥t stts ♥ t ♠♥♦rt② ♥♥ s st♦♥

r ♦♠♥ ♣♥♥ ♦♥ t ♣r♦t ♦r r♦s s♠♥t t♥♥ ♥t♦♥s ①trt r♦♠ ts

♦r♦r rrr ts r♣♦rt s♦ s ♠ ♦r t♥ ①♣t r♦♠ ♥ t♦ t s ♥♦♥ tt t ♥♣ ♦ t t♥ ♠ ♥st♦r ♥

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♦r t♥ ♦ ts ♦♥tr♣rt t♦ ♥t s③ ts ❬❪ t r♣♦rt sr st sr♣rs♥② ♦ r s♠♠r③s t ♥r ♣♥♥ ♦♥t rsst♥r ♣r♦t ♥t t♥♥ ♥t♦♥s t ♣r♦t ♦s t♦103µΩ♠2 s♠ t♦ s♦ s♦♠t r s ♦st ♦ t♠ ♥♦r♣♦rt♦ tr♦s ❲ rr t♦ t r♣ ♣r♦r♠♥ ♥②ss ♦ ♦r rsts♥ st♦♥

r r t ♦r ①♣r♠♥t②♦sr t ♥r② s ♦ t 2 ♥ r3 s②st♠s st t♥ ts tss r t ♥②sss ♣r♦r♠ ♥ t t①t ♥r② ♣s r ♥ ♦♥ t rt s ♦ ♣tr♥ t s②♠♠trs ♦ ♥ ♥ ♦♥t♦♥ ♥s ♦ ♥ ♦ rs♣t②❬ ❪

♥r② ♣♦st♦♥s ♦ rt♥ ♥♦♥ t s ♥ t ♥ ♣ ♦ st trs r s♠t② s♦♥ ♦r r②sts ♥ s ♥ ♠♣♦rt♥t♥♦t t t②♣ ♥ ♥st② ♦ ts ♥ t t ♣♥♥♥ str♥t ♦ t r♥trt② ♥ ts tr t t rrr ts tr rt t♦ tst s ♦r t♦ t ♦♥t♦♥♥ ♥ s rtr♠♦r s t ♣rs♥♦ ts t♥ t ♥r② ♣ ♥tr♦s t♦♥ ♥♥s ♦ tr♦♥ tr♥sr t② ♠② tr② ♣r♦ ♦r♦r t r②st♥ s♠♦♥t♥s②st♠ ♦♠s ①♣♦s t♦ t t ♦ ♥ ♣♣r♦♣rt ♥t ♥ s♦r♣t♦♥ ♦rs ♦♥ ts sts rst♥ ♥ ♥ ①t stt ♦♥st r①t♦♥ ♦ ts②st♠ s t♦ ♥ ♠ss♦♥ ♦ ♣♦t♦♥s t ♦rrs♣♦♥♥ ♥rs s sststt ♦t s♦r♣t♦♥ ♥ ♠ss♦♥ s♣tr ♠② ss♥t ♥♦r♠t♦♥ ♦t t♥tt② ♥ ♥st② ♦ t strtr ts s♠t rs s♦ tt♦♣♥ ♦ ts ♥st♦rs ♠② s♦ t♦ t ♣♣r♥ ♦ rt♥ ♥r② s

t ♦ ♥t t♥ ts st② t♦ t ♥t♦ ♦♥t rt♦♥s ♥ rrr t♥ss t ts t♥ss s t st ♥♦♠♥ ♥ t s ♥②t② t t♦ ♦♥sr t rrr t♥ rrr t♥ss ♣r♠trs ♥tr ♥t♦ t ♣r♦t s♣rt②

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ts ♦♥ ♦♣♥ ♦ ts ♠trs ♥ ♦rr t♦ ♦t♥ t♦♥ ♥t♦♥ts r①t♥s② ♣r♦r♠ ♦r ♦r ♦♣♥ ♥♦t rss t st①♣t② t♥ ts tss rtr ♠s t♦ ♥ ♣r ♥sts ♥t♦ ts♦ t tr ♠tr① rtr t♥ ts rst♥ r♦♠ ①♣t ♦♣♥ts

❲t♥ ts tss tr② t♦ rt t ♦ t rrr ts t♦ ♦rrs♣♦♥♥ strtr ts ♥ t r②st♥ rrrs ①t t♦ r♣♦rt rrrts ♥ t ♦ ts ♣r♦♣♦s ♣♦ss ♦rrs♣♦♥♥ t t②♣s rs♣♦♥s ♦r t s ♦sr t s ♥ ♣♦ss tt rrr ts ♦ ❱r♣♦rt ② r♦♣s ♦ ♦♦r ❬❪ ♥ ❨s ❬❪ s s ❱ ♦sr ② tr♦♣ ♦ Pr♥ ❬❪ ♦rrs♣♦♥ t♦ t♥♥♥ t ♥trs ♦ F2 ♥ FF+ t②♣rs♣t② ♣r♦♣rts ♦ ts t sts ①♣♥ ♥ t ♦♦♥sst♦♥

♣t tt② ♥ r②st♥ s②st♠s

♥s♠ ♦①

r ♠t r♣rs♥tt♦♥ ♦ r②st♥ tt ♥s ♦♥ ttr ♥♦♠♥tr ❲t t♦♠s r t♦♠s ♦♥s ♣t ❬❪

♠♦♥♦r②st s ♦♠♣♦s ♦ tr♥t♥ ♥ t♦♠s s ♣r♦s②s♦♥ ♦♥ ❱♥s t♥ t r②st♥ tt ♥ r♦♣ s s♥

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♦①②♥ ♦r ♠♥s♠ ♥s F ♥ V ♥trs rs♣t② ♦①②♥ ♥s ♥♠ F2 ♦r M ♥ ♥♦r♥ ♦①②♥♠♥s♠ ♥s ♠rs P ❬❪ r ♦♠tr ♣♦st♦♥ t♥ t r②st s s♠t② s♦♥ ♦♥

t ♦r♠t♦♥ ♥r② ❬❱❪F F+ F 2+ F2M V V − V 2− P

t ♦r♠t♦♥ ♥rs ♥ r②sts s♣rsr♣ts♥♦t t ♥r② rqr t♦ r♠♦ ♥ t♦♠ t♦ t♦♠s ♠♥s t ♦s♥r② t t ♥r② ♣r ♦r♠ ♥t ❬❪

F ♥ V ♥trs ♠② ①st ♥ tr ♥tr stts s s ♥ t r ♦r♦② r rtt♥ F+ F 2+ V − V 2− ♥ s ♦ t F ♥ V ♥trst ♦r♠t♦♥ ♥rs ♦ t ts r ♣rs♥t ♥ t s trt♦♥ ♦ F t s ♥rt② ♠♦r ♦r t♥ tt ♦ M t ♣rs♥ ♦ ts t♦♥ stts ♥ t r②st rts t♦♥ ♥r② st♥ t ♠♥♠♠ ♦ t ♦♥t♦♥ ♥ ♥ ♠①♠♠ ♦ t ♥♥ ❱

t♦♥s ♦ t ♦r♠t♦♥ ♥rs ♦ t ts ts s s tr♣♦st♦♥ t♥ t ♥r② ♣ ♥ ①t♥s② st s s♦♥ ② ♦s♥tt t F ♥ F+ ♥trs ♦s t♦ t ♠ ♦ t rrr ♥♣❬❪ s ♦ r ♠♣♦rt♥ s t ts ♥ ♦♣t② st t t♦ ♥r② ♣♣r♦①♠t② tt ♦ t ❱ ♥♣ ♥♠ ♦ t sr♠♥ts t ♥ t s ♦ ♥t ♦r t ♠sr♠♥t t♦ ♣r♦r♠♥ ♠ ♥ ♦rr t♦ ♦ ♥t♥s ♦♣t tt② ♦ t t♠♦s♣r

♥t② ❯♥ ♥ ❯♥♦ ♣s t ♥②ss ♦ t t♠rs♦♣♦t♦♠♥s♥ r♦♠ t s②st♠ s♣② rr♥ t F ♥ F+ ♥trs❬❪ ♦♣t s♦r♣t♦♥ ♦♥ ♦t t t②♣s ♦rs t ♥♠ ❱ ♦r F♥ ♥♠ ❱ ♦r F+ ♥tr s② ♦sr s t ♦♥♦t ♣ r♦♥♥♠ ♥ s s♠ r♥ tr ①tt♦♥ s② ♦rs s♠t♥♦s②❬❪

s♠t r♣rs♥tt♦♥ ♦ t F+ s♦r♣t♦♥ st② s s♠t② r♥♦♥ ♥ s r② sr ♦ ♦r t ♦♠♣t ♥②ss ♦♥ s♦ rrt♦ t rt

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r t♠rs♦ ♠♦ ♦ ♥ts rt t♦ s♦r♣t♦♥ ♦ ♣♦t♦♥ t F+

♥tr r♦♥ stt ♦ F+ ①tstt ♠ss♦♥stt t F+ ♥tr ①t t♦ r♦♠♥t♦♥ t r tr♦♥ r♦♠t ♦♥t♦♥ ♥ ♦t t ♥ts ♦r r♦♠ t t♦ rt ♦♥ t t♠s ❬❪

s♦r♣t♦♥ ♣r♦ss ♥♦s ♥♠ ♣♦t♦♥ tt s s♦r t t r♦♥stt ♦ t F+ ♥tr ♥ ♣r♦♠♦t t♦ t ①tstt ♥tr ♠② q② tr♠③ rt② t♦ t ♠ss♦♥stt ♥ ♠t t ♣♦t♦♥ ♦r ♦♠ s♦rt② tr♣♣ ♦r ts r①t♦♥ rsts ♥ ② ♠ss♦♥♦r t tt♦♥ ♥r② s ♠ s♠r t♥ tt ♦ t t♦ ♠♥t♦♥♣r♦sss t ♠② tr♠② ♦♥③ r♦♠ ts ①t stt ♥ rs t tr♦♥t♦ t ♦♥t♦♥ ♥ ♥ t r F 2+ ♥tr rs tr♦♥ ♥ t♥♥tr♦ t s♦ tr♣s ② tr♠②♥ tr♣♣♥ ♥ rs♥ ♥t②t tr♦♥ r♦♠♥s t t F 2+ ♥tr rst♥ ♥ ♦r♠t♦♥ ♦ t ①t F+

♥tr ♥ tr♥ r①s t♦ ts r♥ ♦r♠ ♥ ♠ts ♣♦t♦♥ s ♠ss♦♥♦ ♦sr ♥ t t♠rs♦ s♣tr♦s♦♣② t♥ t ♠s♦♥ t♠s

qt♦♥ sr♥ t s♦r♣t♦♥ ♥ ♦ ♥ts ♦♥ t t rst♥♠tt ♣♦t♦♥ ♥rs ♦r t F+ ♥tr s♦r♣t♦♥ ♦r s♥r♦s ♥ ♠② rtt♥ s ♥ t ①t stt ♦ t rs♣t ♥tr

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F+ + hν(250nm) → F+∗

F+∗ → F+ + hν(390nm)

❲rs ♦r t r s♥r♦ ♥ t tr♦♥ s rs t♦ t ♦♥t♦♥♥

F+ + hν(250nm) → F+∗

F+∗ + kT → F 2+ + e−

F 2+ + e− → F+∗

F+∗ → F+ + hν(390nm)

tr s♥r♦s t♦ ♠ss♦♥ ♦ t ♥♠ ♣♦t♦♥ s♠r s♠ ♣♣s t♦ s♦r♣t♦♥ ♦♥ t F ♥tr t ♥♦ ♠ss♦♥ t♥

t ♥st♦µs t♠ r♦♥ s ♦sr ssts tt ♠♦st ♦ t ①t F♥trs s② ♦♥③ ② ♣r♦♠♦t♥ ♥ tr♦♥ t♦ t ♦♥t♦♥ ♥ t♦ r②s♠ tr♠ tt♦♥ ♥r② ts ♦♠♥ F+ ♥trs

qt♦♥ sr♥ t F ♠♥s♥ ♥ rtt♥ s ♦♦s

F + hν(250nm) → F ∗

F ∗ + kT → F+ + e−kbT≈0

F+ + e− → F ∗

F ∗ → F + hν(≈ 500nm)

♠ss♦♥ ♣ ♦ t ♣♦t♦♥ rst♥ r♦♠ t s♦r♣t♦♥ ♦♥ t F ♥trs r♣♦rt t♥ ♥♠ ❱ ♥ ♥♠ ❱ ❬❪

F+ ♥trs ♠② ♦♥sr s s♦ tr♦♥ tr♣s s ♥ rrs ♦♥③t♦♥ ♦ t F+ ♥tr rsts ♥ rt♦♥ ♦ t F ∗ ♥tr t ①ttr♦♥ ♠② ♣r♦♠♦t t♦ t ♦♥t♦♥ ♥ ♥ t♦ t r② s♠ ♥r②♥ ❯♥ ♥ ❯♥♦ ♦♥ tt ② ♦♣ s♥♥② F t②♣♥tr ♣rs ♠♥♥ ♥♦t F2 ♦r F+

2 t rtr F F+ F+F F+F+ ♣rs♠② ♦♥trt t♦ tr♠② ssst t♥♥♥ t t sts ♥ t ♦tr♥ t F+

2 ♥ F 2+2 ♥trs r ♦♥sr t♦ s ♣ tr♦♥ tr♣s s

t ♥rs ♦ t rts ♦ t ①t ♥s t♥ t♦ ♦r ❬❪♦s♥tt t s♦ tt t ①t tr♦♥s ♠② s♦ tr♣♣ t s♦

②r ♦♥s − ♦s t♦ t ♦♥t♦♥ ♥ ♠♥♠♠ s − ♥trs rstr♦♠ t s♥ ②r♦♥ tr♣♣ ② t F ♥trs ♠r② t♦ tr♣♣♥ t tsts ♠♥t♦♥ ♦r t ② ♥ t ♠♥s♥ ♣r♦♣♦rt♦♥ t♦ t♦♥♥trt♦♥ ♦ t♦s tr♣s t♥ t rrr t♦rs s♦ s♦ tt t

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♠♥s♥ s t♦♥② ♥♥ ② ♥ tr♦♥ ①tt♦♥ r♦♠ t ♥♥ ♥t♦ t ♠♣t② r♦♥ F 2+ ♦r ①t F+ ♥trs rst♥ rs♣t② ♥r♦♥ F+ ♥ ①t F ♥trs ♦t ♦ ♥t② r♦♠♥ t♦ F ♥trs②♥ t F t②♣ ♠♥s♥ ❬❪

t♣ t♦rt sts sr t ♥r② s ♦ r♥t t②♣s ♦ ts♥♦t② F2 ♦r M ♥tr ♥ r ♥trs ❬❪ ♦r ♠♥s♠ ♥s V♥trs ❬❪ sts ♦ ts t♦♥s r s♠t② s♦♥ ♦♥

tr♦♥t♠ tt♥t

♣t sts ♦ r②sts r sr t♦ ♣r♦r♠ t♦ t ♦r ♥♣ ♦❱ ❬❪ t②♥ ♠tr t ♣♦t♦♥ ♥r② ♦r t♥ ❱ ♦s t♦♦ ♣ tr♦t s♦r♣t♦♥ ② r s tt t ①♣r♠♥t st♣ s rt②s♠♣ ♥ ts s♥s r②sts r ♠♦r ♦♣t② ss

t s ♥♦♥ tt ♣r♦♣rts ♦ r3 str♦♥② ♣♥ ♦♥ ts st♦♦♠tr② s♣② ♦♥ t ♦①②♥ s♣s ♦①②♥ ♥② s r tr♠♥ t♦ ♦r♠t ❱ ♦ t ♦♥t♦♥ ♥ ❬❪ s♦ r② tt ♥r② s ♥ ♥ ♦rrt♦ ♦♥③ s sts ♥ ♣r♦♠♦t t tr♦♥ t♦ t ♦♥t♦♥ ♥ ♦r♦r t♥② ♥ ♥ t ♦tr r ♦r ♥s ♦r♠♥ t strs ❬❪s ts ♦♠♥ t t ♦ ♥♣ rst ♥ ♠ ♠♦r ♥♥t♣♦t♦♠♥s♥ ♦♠♣r♥ t♦

r ♠t ♣tr ♦ t ♠♥s♥ tr s♦r♣t♦♥ ♦ ♣♦t♦♥r♣♣♥ ♦ tr♦♥♦ ♣♦r♦♥ ♦r♠t♦♥ ② ♦r♠t♦♥ ♦ str♣♣ ①t♦♥ tr♥t rt ♦r♠t♦♥ ❬❪

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t♠rs♦s♣tr♦s♦♣②s ♠♦ sr♥ t ♠♥s♥ r♦♠ s ♣rs♥t ② ♦♥ ♥ r♥r t s s♦♥ tt t♦ ♣♦t♦♥ s♦r♣t♦♥ ♥ tr♦♥ ♠② ♣r♦♠♦t r♦♠ t ♥ ♥ t♦ t♦♥t♦♥ ♥ ♥ ♦r♠ s♠ ♣♦r♦♥ ♦ tt ♣♦r③t♦♥ ♥ ♦r♠t♦♥ r♦♥ t r rrr ♣♦r♦♥ ♥trts t ♦ tr♣♣ ♥r r②st t ♦r ♥ ♠♣rt② ♥ ♦r♠s str♣♣ ①t♦♥ ♦s tr♦♠♥t♦♥ rsts ♥ ② ♠♥s♥ s ♣♦t♦♠♥s♥♠♥s♠ s ♦t♥ ♦sr r♦♠ ♦♠♣♦♥s ♦♥t♥♥ tt♥t ♦tr ❬❪

r ♠t r♣rs♥tt♦♥ ♦ r♦♠♥t♦♥ ♣r♦sss t♥ ♦♥t♦♥ tr♦♥s ♥ ①t ♦s r♦♦♠ t♠♣rtr ♠♥s♥ ①t ♦s♥ tr♦♥s ♥ t str♣♣ ①t stt ♦♣ ♦r ①t tr♦♥s ♥ ①t ♦s tr♦ t s♦ t r♥ ♥ ♥s ♣t t ♣♥ ♥ ♦♥t♦♥ ♥s rs♣t② ❲t ♥ r② rs st♥rs♣t② ♦r ①t ♦s ①t tr♦♥s ♥ ♦♣ tr♦♥s ♥ t ♥❬❪

♥ ♦ t ♠♦r ♣r♦♠♥♥t rsts s ♣s ② ♥ t ❬❪ ♦ rt♦①②♥♥t s♠♣s s♥ t r+ rrt♦♥ ♥ ♦♠♣r tr ♣r♦♣rts t t ♣r str♦♥t♠ tt♥t r②sts ② ♦♥ tt t r3 ♠t♦r ♣♣rs ♥ tr rt② s♠ ♦s ♦ rt♦♥ t② ttrtt♦ t rt♦♥ ♦ ♦①②♥ ♥s ♦♥tt② tt ♣♣rs strts t♦strt s t rrt♦♥ t♠ ♥rss t s ♦♠♣♥ ② t rs♣t ♣♣r♥ ♥ strt♦♥ ♦ t ♥♠ ❱ ♠♥s♥ ♣ ♦sr tr♦♦♠ t♠♣rtr s♠ ♣ s ♦sr ♥ ♦r♥② ♦①②♥♥t r3

②rs rts t ♣♦t♦♠♥s♥ tr rt② t♦ t ♦①②♥ ♥ss ♠♥s♥ rsts r♦♠ r♦♠♥t♦♥ ♦ ♦♥t♦♥ tr♦♥s t ①t

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r ♠♣rtr ♣♥♥ ♦ t ♣♦t♦♠♥s♥ s♣tr ♦t♥ r♦♠r+ rrt r3 r②sts tr ♥♠ sr ♠ ①tt♦♥ ❬❪

♦s ♠♣rtr♣♥♥t ♣♦t♦♠♥s♥ ♠sr♠♥ts ♦♥ t r+ rrt

r3 s♦ tt t t♠♣rtr rss t ♥t♥st② ♦ t ♥♠ ♥r② ♥rss r♥ ts ♠①♠♠ t tr t strts t♦ s♣♣r♥ t♦ ♣s t ♥♠ ❱ ♥ ♥♠ ❱ ♥ t♦ rs

r♥ ♥♠ ♣ rsts r♦♠ t ♦r♠♥t♦♥ r♦♠♥t♦♥ ♦ ①t♦s ♥ tr♦♥s ♥ str♣♣ ①t♦♥ stts ♥ s ♦♠♠♦♥② ♦sr ♥ ♥t st♦♦♠tr r②sts ❬❪

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♥rr♦ t ♥t♥s ♥♠ ❱ ♣ s ♥♦t ♦sr ♥ t st♦♦♠trr3 s♦ t s s♣♣♦s t♦ rt t♦ t ♦①②♥ ♥② sts s ts ♥r②s ss t♥ ❱ ♦r t♥ t ♥ ♣ ♦ t t s♦ rst r♦♠ tr♦♠♥t♦♥ ♦ tr♦♥s t ♦s tr♦ r② s♦ t s

t♥♠ ♦①

❨t ♥♦tr st ♦ ts r ♦sr t♥ t 2 r②sts s♣t ①t♥sst② ♦ ♣r♦♣rts t ♠tr qrs ♣♦♥ ♦♣♥ ❬❪ rsr ♦♥ ts♥ ts ♥♦♣ ♠tr① r♠♥ rt② sr ♥r r♥t ♣♣r♦①♠t♦♥t♦♥s ♣r♦r♠ ② s♦r♦♥ t ❬❪ ♦♥ ♥ts 2r tt♥tr ♥s ♦ ♦t tt♥♠ ♥ ♦①②♥ ♥tr♦s ♣ stts ♥ t ♣ t♦ ❱ ♦ t ♦♥t♦♥ ♥ tt ♥♥♦t ♦♥③ s②

r t ♦ ♥st② ♦ stts ♦r ♥tr ♥s ♦ ♦①②♥ tt♥♠ ❬❪

♥tr sss

♦t ♦♥② ts ♥ ♠♣♦rt♥t ♠♣t ♦♥ t s♣♥♣♦r③ tr♥s♣♦rts s♦♥ ♥ t ♣r♦s ♣tr ♣rt r♦♠ t ② rts ♦r s♣ tr♦♥s②♠♠trs t♥ t rrr r ♥♥ ② t stts t s♥ ♥ r②st♥ t♥♥♥ s②st♠s ♣♥s ♦♥ ♦♥ ♠♦r t♦r t t②♣♦ s②♠♠tr② stts t♥ t tr♦ tt r ♥t ♥t♦ t ♥st♦r ♥

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t t② ♦ t ♦♥trtr♦ t♦ ♦t t♠ rs t♥ t strtrtt ♥sr t ♦rrt ♠t♥ ♦ t tr♦♥ s②♠♠trs r♦♠ t ♦♥t♦♥r♠ t♥ t tr♦ t♦ t t♥♥♥ r♠ r♦ss t trt♥ trr t ♥trs ♦r♠r ♣tr sr ♠♥s ♥ ts ♣r♦sss♥ s②st♠s s st♦♥ ♣rs♥ts ♠♣t ♦ ♥tr ♠♣rt♦♥s ♦♥ ts♣♥♣♦r③ tr♥s♣♦rt

①t♦♥

ts ♦♥♥trt ♦♥ t rrr s sr ♥ st♦♥ ♥①t♥s② st ♥ tr♠s ♦ ts ♥tr sss ts ♥tr tt ♠t♥s r ♦r t ♦r♥t tr♦♥s ♥t♦♥ ♥t♦ t rrr s ①♣♥t♥ t ①♣r♠♥t st♦♥ ♦ ts tss t ♣rt ♥tr s ♥♦ts② t♦ ♦t♥ t♦ rs ♦ ♦①t♦♥ s s ♣rtr② tr ♦r t ♦r ♥tr ①♣♦s♥ t ♦r tr♦ t♦ ♥② ♦①②♥ ss t♦♣♠♦st ♠♦♥♦②rs t♦ ♦①③ ♥ ♦r♠ t r♦♥ ♦① ②r t t ♥tr rst♥ ♥t s②st♠ ♥♦tr rs♦♥ ♦r t ②r ♣♣r♥ s t♦①②♥ ♥trs♦♥ r♦♠ ♥t♦ ♥tr ②rs ♦ t tr♦

r ♥tr ∆1 s②♠♠tr② t t r♠ ♥ t ♠♦rt② s♣♥♥♥ ♦r ♥tr t♦t t ♥ t rt t ②r ♦r♠t♦♥ t♦ t ♦①t♦♥ ❬❪

s t ② ❩♥ t ❬❪ t t ♥tr t ∆1 sttst② ♦♣ t♦ t ∆1 ♥s♥ stts ♥ t k‖ = 0 rt♦♥ rst♥♥ ♦r♥t t♥♥♥ ♦ ts stts tr♦ t rrr ♦r ♥ t♣rs♥ ♦ ♥ ♦♥ ♠♦♥♦②r t ♥st② ♦ stts t t ♥tr r♦♥s rst② r rst♥ ♥ t ∆1 t♦ ♥t♦♥ ②r③t♦♥tt s ♠ ss t t♦ t 2p ♦rt ♥tr ♦①②♥sts ♦♠♥t t t♥♥♥ ♥st② ♦ stts t♥ ♥ ♦① ❬❪ ♦r s

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r ♦r k‖ ♥ t♦t t ♥ t rt r♦♥ ♦①②r t t ♦r ♥tr ♣♥ sqrs ♦rrs♣♦♥ t♦ t ♠♥s♠ ♦r r♦♥s♣rs ♥ t ♦r rs♣t② r♦sss r② s ♦s t♦ t rs♦♥♥t t t ♥ r ♦♥trt♦♥s r♦♠ t s♣rs rs ♦♥♥tt t ♥ r s♠♠ ♣ ♦♥trt♦♥s r♦♠ ♦t ❬❪

t ♦①②♥ st ♥t♦♥ s②♠♠tr② ♦ t ②r s r② r♥t r♦♠ tt♦ t 3d ♥t♦♥♥ ♥tr ♦ ♦♥t♦♥ ♥ ♥ tr♥st♦♥ ♠t ♦①s❬❪ ♦r♥t tr♥s♣♦rt r♦ss t rrr s rst② s♣♣rss

r rst♣r♥♣ st② ♦ t♥♥♥ ♥st② ♦ stts ♥ ♣r ♦♥rt♦♥ ♦ s②st♠ ♦r k‖ t ♠♦♥♦②r ♥srt ♥ ♦r♠t♦♥ t t ♥tr ❬❪

♥ ♣♦sst② ♦ ♦♥ t ♣♣r♥ ♦ t ♥sr ♥tr ②rs t ♥tr♦t♦♥ ♦ t ②r t♦♣ t ♦r tr♦ ❬❪ ♥♣♥ tt s ① ♦♥ t r♦♥ tr♦ tt ♦♥st♥t ♥sr♥♣t① ♠t♥ ♦ t ②rs ♥s♠ s st ♦①③♥ ♠♥t ♠② s♦r♦①②♥ ♥ ♦r♠ ♥ t♦♥ ②r s ♦ ♦ t ♦①②♥ s♦♥♥t♦ t r♦♥ ♥ ♣r♥t t ♦r♠t♦♥ ♦ t r♦♥ ♦① s s♦♥ ② ❲♥ t

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t ♣rs♥ ♦ t ♥tr ②r ♦①③ ♦r ♥♦t ♦s ♥♦t tr t♥t♦♥ rsst♥ s♥♥t② t t ♠② ♥♥ t tr♥s♣♦rt ♣r♦♣rts s t♣rsrs t ∆1 tr♥s♠ss♦♥ ♥ t P ♦♥rt♦♥ t ♥♦♥♣rrr ∆2′

♥ ∆5 s②♠♠trs ①st ♦r ♦t P ♥ P ♦♥rt♦♥s ② t♥t ♠♥s♠ ②r r♣②

♦♥sq♥s ♦ ♥♥♥

♥tr ♦① ②r ♦r♠t♦♥

t s ♥♦♥ tt ♣♣r♥ ♦ t ♥tr ♦① rrr ♠② s ♦♥sq♥ ♦ ♥♥♥ ♦ t st s t t♠♣rtr ♦♦sts t ♦①②♥ ♠rt♦♥r♦♠ t rrr t♦rs t tr♦s sts r s♦ ♣r♦r♠ t♥t t♠r♠ ♦ ts tss ♥ t ♥♥♥ ♠♣t ♦♥ ♣r♦♣rts ♣rs♥t ♥ st♦♥ ♣rs♥ ♦ s♣ ♦①s s rt② rt t♦ tr♦r♠t♦♥ ♥t♣② s t ♦r ♥ t♦ ♥♥♥ s rr s trr ♦r t ♥tr ♦① ♦r♠t♦♥ sts ♣r♦r♠ ② ♥♠r t s♦ tt ♥ s♦♠ ss r t ♦ t ♥♥♥ ♣r♦ss ♠②r t ♥tr r♦♥ ♦① ②r ② t s♦♥ t♦rs t ♦ ttr♦ ❬❪

① ♦r♠t♦♥ ♥t♣② ♠♦23 2 r ♦

♦r♠t♦♥ ♥t♣② ♦ st ♦①s ❬❪

s♦♥ ♦ ♠trs ♠♦♥ t ②rs

t♥♦♦② rqr ♣rs♥ ♦ ♦r♦♥ ♥ ♦ tr♦s ♥ t ♥♦ tr ♥♥♥ s rs t♦ ♥ t♦♥ ♥trrt qst♦♥ r r♦♥trt♥ ①♣r♠♥t r♣♦rts tr r♥ ♥♥♥ ♦ t st t ♦r♦♥t♦♠s s t♦rs t ♦ t tr♦ ♦r ♥ t rt♦♥ ♦ t ♥tr❬❪ rt♦♥ t s ♥t♦ t♦♥s t♦ s♦ tt t s t ttr s tts rs t♦ t s♠r ♥♥ ♦ t ♥t♦♥ ②r③t♦♥ s ♥ s ♦ t ♣♣r♥ ♦♠♣r t ♥ t ♦tr ♥ s♦♠ r♦♣ss♦ tt t ♦r♦♥ s♦♥ ♥t♦ t rrr rsts ♥ t ♦r♠t♦♥ ♦s ♥♦t s♣♣rss t rt♦ s♥♥t② ❬❪ ♦r ①♠♣ ♥ t

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r ②r ♣r♦t ♣r♦t② ♥st② ♦r ∆1 s②♠♠tr② ♥ t ♠♦rt②s♣♥t F ♦r t ♦ tr♠♥t ♥tr ❲t ♥ rs ♥♦t s♥ ♥♣rs♥ ♦ ♦r♦♥ rs♣t② ♥tr ♦r♦♥ ♦r s ♦r t♦♥ss s♣r ♦s♥ s ♠♦♥♦②rs ♦r ♥ ♦ ❬❪

s♦ tt ♦r♦♥ s♦♥ ♥t♦ t rrr r♥ ♥♥♥ ♦r♠s t st♦♦♠tr23 ♦s ♥♦t rt ♥② ♠♣ stts ♥ t rrr t rs t rrrt t ♥rs♥ ♦♥♥trt♦♥ ♦ ❬❪

♥♥♥ t♠♣rtr s t ② ♣r♠tr t♦ ♦t♥ ♦rrt② r②st③ ②♥ ♥t♦♥s s s♦♥ ② rt t ❬❪ ♥♥♥ ♦ s t♦ t s♦♥ ♦ t♦♠s r♦♠ ♦tr ②rs ♥t♦ t rrr ♥ ♦ss ♦ t♦ t①tr strtr ♥ t ♦tt♦♠ ♦ tr♦ ♦r♦r s t♠♣rtr ♥♥♥ s t♦ t s♦♥ ♦ ♠tr r♦♠ t ②r ♠♦st②♥ ♥t♦ t rrr rsts ♥ sst♦♦♠tr② ♦ t ♦r♠r ②♥ tsr ♣♥♥♥ str♥t ♣♣r♥ ♦ t s ♠tr t♥ t rrrs♦ s♥♥t② ts t rt♦ ❬❪ ♥ t ♦tr ♥ r♥t①♣r♠♥ts ② rs♦♥ t s♦ tt ♥♥♥ t ♣ t♦ ♦s ♥♦t s t♥ s♦♥ r♦♠ t ②r ♥t♦ t rrr t rtr ts srt♦♥ t t♥tr ♦s ♥♦t tr t s♥ rt② ❬❪

❯♥rt♥ ♥tr tr♠♥t♦♥

trs ♦♠♣♦s ♦ tr♥t♥ ♣♥s ♣rs♥t ②t ♥♦tr ♥ rr♥t ♥tr qt② ♥ s ♦ r3 t ♥tr 2 tr♠♥t♦♥ st t♦ ♠♦r ♥rt② ♦r t♥ t ♦♥ ♦ t r ❬❪ ♦r

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r ♥♥♥ ♠♣t ♦♥ t rt♦ ♦ ♥♥♥ t ♦r r♥t t♠ rt♦♥s ♥ r♥t t♠♣rtrs ♥ t♠s ♦ ♥♥♥ strtr st s♦r♥♦♦♦ ♦r③♦♥t ♥ ♦♥ r t ♠rs t rt♦ ♣t ♦r ♣rt♣♣t♦♥s ❬❪

r rss ♣♣ ♦t t ♦r 2 t ♥ r rt tr♠♥t ♦ ♥tr ♥ ♦ ♥t♦♥s ♦ tr♥s r♣rs♥tt r♦♠ ❱ rs ♦♣♥ rs rr t♦ ♠♥t s♣s t ♥ s r r♣ s♦s t ♦r t♦ r♥t ♥t♦♥s ❬❪

t ♥rt♥t② ♦ ts ②r s r ♠♣t ♦♥ t ♦r ♦ t s②st♠ts ♣r♦r♠ ♦♥ ♦ s②st♠s ② ❱r r♥ t s♦ tt♣♥♥ ♦♥ t tr♠♥t♦♥ ②r t ♠♥t♦rsst♥ ♠② ♥ stts s♥ sst♥ tt t ♠① 2 ♥ r ♥tr ♦ ② t♦t ♥ ♥ r ♦ ♦t ♣♦st ♥ ♥t ♦♠♣♦♥♥ts ♦♦s②

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♠ ♦r t♥ ①♣t ② s♦ ♥ tt t t s str♦♥② t ② t♥tr ♦①②♥ ♦♥♥trt♦♥ ❬❪

tr♦♠rt♦♥ ♥ srt♥

♥ s ♦ ♣rt ♣t① s②st♠s t ♠♦♠♥t♠ tr♥sr t♥ ♣r♦♣t♥tr♦♥s ♥ t♦♠s ♦r♠♥ t r②st ♥t♦r s ♥ s tt t tr♦♥♥t♦♥ s②♠♠tr② s ♦♥sr ♦r t s②♠♠tr② s ♥♦t ♦♥sr tr♥ ♦♥rs ♥ ts t♥ tts ♦ ♦t ♠t ♥ ♥st♦r t s tts ♣s tt t ♦♥♥ ♥r② ♦ t♦♠s s ♠ ♦r t♥ ♥ t ♣rtr②st rsts ♥ t tr♥sr ♦ ♠♦♠♥t♠ ♦ ♣r♦♣t♥ tr♦♥ t♦♥ ♦♥ ♥ tr♥ ②s ♦r t♥ t ♥ t rt♦♥ ♦ tr♦♥ ♦s ts ♦r rss t♦ t ♦♠r♠♥t ② tr♦♥s t ♠② ♦♠ s♥t♥♦ t♦ ♦r♦♠ t ♦♥♥ ♥r② ♦ t ♦♥ ♥ r♦t t s rt ♦t♦♠s t♥ t ♠tr s tr♦♠rt♦♥ ♣♥♦♠♥♦♥ s s♣②♣r♦♥♦♥ ♥ rr♥t ♥sts ♦ tr♦ t ♠tr s tr ♥s ♦ ♠r♦♠trs③ ♠♥t t♥♥ ♥t♦♥s tr♥s♣♦rt ♦ t ♠trs r ♦r ♦t ♥ ♥tr r♦♥s ♦ ♥t♦♥s ♦r ①♠♣ t s♥♦♥ tt t tr♦♠rt♦♥ ss rstrt♦♥ ♦ ♦①②♥ ♥s t♥♣r♦sts ❬❪

tr♠ ♠♠rst♦r s ♦♥ t♦ sr ♦s rsst♥ ♥ss t ♦♥sq♥ ♦ ♥ ♣♣ rr♥t ♥ ♣rssts tr t rr♥t ♦ st♦♣str♦ t sr Pt2♥♠Pt ♥ ♦ t trrr s ♥t② ♦①②♥♥t ❬❪ ①②♥ ♥s t s r rrrs♠♥♥ tt t ♣t ②r s ♠ ♦r rsst♥ t♥ t st♦♦♠tr♦♥ ❲♥ ♥ tr s ♣♣ ♦①②♥ ♥s ♥ t♦ rt ♥♥t ♦♥r② t♥ ♦t 2 ②rs ♥ ts tr♠s t ♠♠rst♥ t sts

♦♥ t st ♦1−xrx ♥t♦♥s t ① ♥ t♥ ♥ ♥t♦♥s r tr② ♥st ♥ t ♦ t♠♣rtr ♥ sss ♦t ②♥ t♦ rrs ♥ ♥ ♠♣t ♥ s♥ ♦ t t♦rs ♥ ♥ ♥ ♦ r srt♦♥ t♦ t ♦r ♥tr ♥ ts♦①t♦♥ ❬❪ ♥tr ♠♦t♦♥ s sst t♦ t rs♦♥ ♦ ♦ t s♥ ♥rs♦♥ t ♦r s②st♠ rsst♥ ♠② rst r♦♠t ♦r♠t♦♥ ♦ ♥s s ssts ♥ ♣♣r♥ ♦ ♦♥t♥ ♠♥tt♥ t rrr ♦ rst r♦♠ t tr♦♥s tr♣♣♥ t ♦①②♥♥tsts ❬ ❪ ♦sr t s rrs s♦ t srt♥ ♦ ♥t♦♥s② ♣♣②♥ rr rr♥ts ♥ ♦♠ t♦♦ t♦ ♥♥r ♣r♦♣rts ♦ s♦r♦r ts rsts r t rst t♦ ♠♦♥strt t ♣♦sst② ♦ ♥♦r♣♦rt♥♠♠rst♥ ♥ ♠♥t♦rsst♥ t♥ s♥

rsr ♦ ♠♠rst♥ s ♦♣♥ st ♥ s ♠♥② ♥trst♥

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r ♠sr♠♥ts ♦♥ ♦80r20 ♥ ♥ ts r♥stt ♥ tr ssq♥t s rt♥ t♦rs t ♥t ♥ ♣♦strr♥ts ❬❪

rsts ❬❪ ♦ ♦ ♠♥ r ♣r♦r♠ ♥ ①t♥s st② ♦♥rsst st♥ ♥ s s t r ❬ ❪ ♥ ❱ ❬❪ t♥trs ♦r ♥ t ♦ t rrr s r♦♣ ss♠ ♥ ♥trst♥ ②♣♦tsstt t ♠♠rst♥ ♥ ts s②st♠s s ♥ t ♦ r♥ rtr t♥ ♦ ttr♦♠rt♦♥ ❬❪

t♥ ♠♥ts♠

♥t sts s♦ tt t ♣rs♥ ♦ ♥s t♥ r②st♥ ♥st♦rs ♦rs♠♦♥t♦rs ♠② rst ♥ t ♣♣r♥ ♦ ②t ♥♦tr ♣♥♦♠♥♦♥ ♠♥ts♠ s s ♣r♦s② ttrt ①s② t♦ ♥ ①♣t ♦♣♥ ♦ ♠trs ♥ t ss♦t rsr s ♦ t ♠♥t s♠♦♥t♦rs ♥♦①s rt ♥ rs♣t② ❬❪ rst ♦♥ ♠r ♦♥t ♦t♠♣rtr ♥tr♣② t♥ ♠♥t③t♦♥ t①tr ♥ ②♥♠s trrr ♣♦♣t♦♥ ♥ rr♥ts r s♦r ♥ ♥s ♣♥ ♥s♠r strtrs ❬❪ s♦♥ s ♥r② ♥♦ t♦ strt♥ t rst r♣♦rt ♦ t r♦♦♠t♠♣rtr ♠♥ts♠ ♦♥ ♦♦♣ 2 s♣s ② ts♠♦t♦ t ❬❪

♥ r♥t ①♣r♠♥t rt♥③♦t t ♦sr ♥♠ ❱ ♠ss♦♥r♦♠ ♥t r②sts ♦s ② rsts r♦♠ tr♣♣♥ ♦ ♦s t ♠♥s♠ ♥s ❬ ❪ ♠♣s r♦♠ t ♠ss♦♥ ♦rs s♦ ①t

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r Pr♦t♦♥ ♦ P s♠t♦♥ r♦♥ ♥② ♦r ts ♦①②♥ ♥rst ♥♦r t♦♣ ♠♥s♠ ♥rst ♥♦r ♠ ♥ ♦①②♥ ♥①t♥rst ♥♦r ♦tt♦♠ s♦♥ s ♦♥t♥♦s ♥s ♦♠♣♦s ♥ ♠♦r ♣♦st ♥ ♠♥♦r ♥t ♦♠♣♦♥♥ts s ♥s s♦ rs♣t ♥♦♥s♣♥ ♦♠♣♦s P ♥ s♥ ♦ t ♥② ♥t ♠♦♠♥t ♠♠ ♦ rs♣tt♦♠ s ♥ ♥ ♦r ♠♥t♦♥s Q st♥s ♦r ♣rt t♦♠ r ♥♣♦♣t♦♥ ♥ ♥ |e| ♥ s ♦♠♣r t♦ ts s ♥ ♣r♥tss ❬❪

r♦♦♠t♠♣rtr rr♦♠♥t ♦r ♥ tr♥ rss r♦♠ t s♣♥ ♣♦r③t♦♥ ♦ 2p tr♦♥s ♦ ♦①②♥ t♦♠s r♦♥ ♠♥s♠ ♥s rr♦♠♥t ♦rr♥ s ♠♦st ♥♣♥♥t ♦♥ t s♠♣ t♥ss t♥t ♥♠ r♥ ♦r♦r s♣t t ♠♥t ♣r♦♣rts t r♠♥s tr♥s♣r♥t ♥ t s r♦♥ ♠s t ♥ ♥trst♥ ♥t ♦r♠♥t♦♦♣t ♣♣t♦♥s

♦♥s♦♥s

r♦strtr trs r ♦ r ♠♣♦rt♥ ♦r ♥♦♥♥t♦♥ ♠♥t ♣r♦♣rts ♦ ♦t ♠♥t t♥♥ ♥t♦♥s ♥ tr r②sts s♣t ♠t♣♦♣♥ ①♣r♠♥ts ②♥ ①♥t rsts ♦♥ t ♠♥t s♠♦♥t♦rs♥ ♦①s t ♦♠s r tt t t② t♦ rt ♦♥tr♦ ♥ ♥♥r tstts t♥ t ♦① rrr s ♦ t♠♦st ♠♣♦rt♥ ♦r rtr ♣r♦rss t♥t ♦ s♣♥tr♥ r♦ss ♥♦r♥ ♦①s s s tss ♠s

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r ♦ ♠♥ ♥ r♦♦♠ t♠♣rtr t♦♣t ♥st ♠♥t③t♦♥ ♠sr♠♥ts ♦♥ t♥ ♠s ♦ r♥t t♥ss r♦♥ t♦♣ t r3

sstrts ♥t s ♣♣ ♥ t ♠ ♣♥ t r ♦rrt ♦r♦♥trt♦♥ ♦ t sstrt ♦tt♦♠rt ♥st ♣tr s♦s tt t s♠♣ r♠♥s tr♥s♣r♥t ♥ t s r♦♥ ❬❪

t♦ s♥ t♦♥ t ♦♥ trt sss ♥ ♠♥t t♥♥ ♥t♦♥s ♥♠trs ♦♥ t② r s t t ♦♣ tt t ♠② r ②t s s♣ts ♦ ts strtrs ♥ ♣ t ①t♥s ♦r sts t♦ ♠ rtrst♣

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P

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Prt

①♣r♠♥t r③t♦♥

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♣tr

♠♣ r♦t t♥qs ♥

♦♣♠♥t

s ♣tr srs r♥t r♦t t♥qs s ♥ ♦rr t♦ rt s♠♣sst t♥ t t♠r♠ ♦ ts tss rst st♦♥ r② ♥tr♦st ♣♠♣♥ s②st♠s s ♥ ♦rr t♦ rt ♥ ♠♥t♥ t tr ♠rqr ♦r t sr r♦t ♦ t strtrs s♦♥ st♦♥ srs t♣r♦r ♥ rsts ♦ sstrt ♣r♣rt♦♥ ♦r ②r ②st♠ ♣♦st♦♥t t P s q♣♣ s s②st♠ s ♦♠♣♦s ♦ r♥t ♣♦st♦♥♠rs s♣ttr♥ ♣♦rt♦♥ ♥ ♦r♥ ♠♦r ♠ ♣t①② s♣ttr♥ ♣♦st♦♥ ♠r ♦ ②r ②st♠ s ①t♥s② s ♦rt rt♦♥ ♥ ♦♣t♠③t♦♥ ♦ t r♦t ♦♥t♦♥s ♥ t ♦♥tr♦ ♦ s ♥t♦♥s r r♦♥ t t ♥sttt ♥ ♠♦r ♥ ♥② s rst♦ ♦♦rt♦♥ t ♥ ♦t ♦ ts s♣ttr♥ ♣r♦t♦♦s r ♣rs♥t♥ t tr st♦♥ ♣♦rt♦♥ ♠r ♦ t ②r ②st♠ s t♦ ssr①t♥t s ♦r t s♠♣ ♣♣♥ s♦ ts t♥ ♠ ♣♦st♦♥ s sr ♥ st♦♥♦r r♥ ts tss ♠♥t t♥♥ ♥t♦♥s ♦♥t♥♥ r3 ♥ 2

rrrs r s♦ st s r strtrs ♥♥ 0.7r0.3♥3 tr♦s ♣♦st ② ♣s sr ♣♦st♦♥ P tr♦ ♥ ♥tr♥ P ♦♦rt♦♥t ♦s r♦♠ t ♣rt♠♥t ♠ t s tr① ♥♦r♥qs P ♣♦st♦♥ s sr ♥ t t st♦♥ ♦ ts ♣tr

❯tr ♠ ♣♠♣♥ s②st♠s

♥ ♦rr t♦ rt trt♥ strtrs ♦ qt② t ♣♦st♦♥ s t♦ ♣r♦r♠ ♥ t tr ♠ ❯❱ r♥ ♣rr② ♦ t st −9 ♠r♦rr r♥t♥ ♠♥♠♠ ♣rs♥ ♦ ♥sr ♣rts ♥ t ♠r r♥t r♦t ♦♥ t t st♥r ♠♥ r♦tr② ♣♠♣s tt ② ♣rssrs♦♥ t♦ −3 ♠r ♥♠r ♦ s♣③ ❯❱ t ♣♠♣♥ t♥qsr s t♥ t t♠r♠ ♦ ts tss

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P P ❲ ❯ ❱P

r♦♠♦r ♣♠♣s ♦♥t♥ r② r♣② ♣ t♦ ③ s♣♥♥♥ r♦t♦rst ♠♦s ♥ ♣rts r♦♠ t ♥t s ♦ t ♣♠♣ ♦ ts r♥ ♠♦♠♥t♠ ♥ rt♦♥ ♦ t ①st s ♣♠♣s r s② s♥ t♦♦♣rt ♦ −2 ♠r ♥ r ♣ t♦ r ♣rssr ♥ t ♠r ♦♥t♦ −9 ♠r r♥

♦♥ ♣♠♣s s tr ♣♦t♥t ♠♦r t♥ ❱ ♥ ♦rr t♦ ♦♥③ss str♦♥ ♠♥t ♥ ② ♣r♠♥♥t ♠♥ts t♥ t s ♦t ♣♠♣ t♥ rts t ♦♥③ s♣s ♥ ♠s t♠ ♥t♦ t s ♦t ♣♠♣ ♦♥ ♣♠♣s ♦ ♥♦t rqr ♥tr ♠♦♥ ♣rts ♥♦r ♦ ts t② r♥♦t ♦♥② r② t rt♦♥r s ❯♥r ♦♥t♦♥s ♦♥ ♣♠♣s r♣ ♦ r♥ ♣rssrs ♥ ♦♥ t♦ −13 ♠r r♥

t♥♠ s♠t♦♥ ♣♠♣s ♦♥t♥ tt♥♠ ♠♥ts r♦♠ t♦♠ss♠t ♦♥ ♣ t♦ rr♥t s ♣♣ t♦ t♠ ♠t tt♥♠s t♥ ♣♦st ♦♥ ♥tr♥ srs ♦ t ♠r ♥ strts t♦ ttrt ♥ tr♣♣rts ♠♦st ♦♠♠♦♥ rt♦♥ s t ttrt♦♥ ♦ ♦①②♥ ♥ t ♦r♠t♦♥♦ s♦ 2 ♥ t♦ t ♣rssr rt♦♥ ♦s② strt♦♥ s r tr rt♥ t♠ s♦ r♣tt tt♥♠ s♠t♦♥s t♦ ♣r♦r♠ ♥ ♦rrt♦ ♥sr ♣rs♥ ♦ ♥ ♥ t ttr ♦♥ ♥tr♥ s ♦ t ♠r r ♦ t tt♥♠ s♠t♦♥ s tt t ♥♥♦t ♣r♦r♠ ♥ rt♥t② ♦ t s♠♣ s ♦ t♦ s♦ ♦ s t t♦♠s t♦ ♥♦r♣♦rt ♥t♦t s♠♣ ♥ r♦♥

♦t ♦ t ♥tr s②st♠ s ♣r♦r♠ t♠ t ♠r s ♦♣♥ ♥①♣♦s t♦ ①tr♥ t♠♦s♣r ♦r♠② ♦♥t♠♥t♦♥ ♥ ♣rts r t♦srs ♥ s ♦r ①t♥ ♣r♦ ♦ t♠ s ♦tss♥ s ♠ str ♥r t♠♣rtr t ♠r ♥s t♦ r♣♣ ♣ t rsst♥ trr ♥ ♦t ♦r ♦ ②s t t♠♣rtr s s r♥t tss s♦ s t♦ rss t ♠♥ ♦♥t♠♥♥t tr t♦♥ ①tr♥♠♥♠ ②r ♦r♥ t ♣rts ♥ ♦t s r♦♠♠♥ ♥ ♦rr t♦♣r♥t t t r♦♠ ss♣t♦♥ ♥t♦ t ♥r♦♥♠♥t

strt ♣r♣rt♦♥

♦ ♥② ♣♦st♦♥ r♦s ♦r♥ ♥ ♥♦r♥ ♦♥t♠♥♥ts s♦ r♠♦ r♦♠ t sr ♦♥ t strtr s t♦ r♦♥ s s♦ ♦♥ s♣② s tt♥ t sstrt t♦ t sr s③ ♦ s t t♠tr t♦ r♣♦st ♦♥ t♦♣ sstrts r ♥t② ♥ ♥ssq♥t t♦♥ t♥ t♥♦ ts t st ♠♥ts ♦t ♥♥ ②trs♦♥ rt♦♥s

①t♥ st② ♦ sstrts s t♥ ②r ②st♠ s♦tt s s ♦r♠ ♦ ♥♥ s ♥♦t s♥t t♦ r♥t ♣rt sr trt ♥t ♥♥ ♥ ♥srt♦♥ ♥t♦ t ②r s②st♠ t sstrts r rst

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r t♦♠ ♦r r♦s♦♣② t♦♣♦r♣ ♠♣s ♦ t r t♦♣ ♥♥♥tr ♥ t t♥ ♥♥ ♦tt♦♠ sstrt t♦♠ st♣s r s♦♥ t ttr t♦

♥st r+ t ♦r ♠♥ts r♥ ts ♣r♦r t s♠♣ s r♦tt ♥

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♦rr t♦ ♥sr ♥♦r♠t② ♦ t t♥ s s ♦♦ ② ssq♥t ♣r ♥ ♥♥♥ ♥② rst♥ ♥ ♦♥t♠♥t♦♥r sr ♦ ts st♣s r r② st ♥ ♦♥r♠ ② t♦♠ ♦r r♦s♦♣② ♠sr♠♥ts s s♦♥ ♦♥ t ♥♥♥ ♦♥ s ♥♦t s♥tt♦ r♠♦ t sr ♦♥t♠♥t♦♥ ♥ t ♦tr ♥ t t♥ ♣r♦r♥rss ♦♥♥trt♦♥ ♦ ♣ t♦ ♥♠ ♣ ♦s t♥ t r②st t♦ r ♦t t t r ②r s sr ♥ st♦♥

♣ttr♥

♣ttr♥ s t♥ ♠ ❯❱ ♣♦st♦♥ ♠t♦ ♥ r♦♥ s rr♥ ♥ t♠r ♦♠s ♦♥③ ♥ r+ ♦♥s r rt t♦rs t trt s♦s ♦ ♣r ♠tr ♥♥t ♦♥s t t trt sr ♥ s ss ♦♦s♦♥s ♥s ①♥♥ ♠♦♠♥t♠ ♠♦♥ t ♣rts t ♥r② tt trt t♦♠ ♥s s rr t♥ ts ♥♥ ♥r② t ♥ t r♦♠ t trt♥ ♣r♦♣t t♦rs t ② ♣ s♠♣ ♦r ♥ ♣♦st ♦♥ t s♠♣♣♦♥ rr

♥tr♦♥s r s s t s♣ttr♥ ♦♥ s♦rs ♥s t s②st♠ ❬❪ ss ♦♥sst ♥ ♠♥t ♣ ♦ t trt ♥♦♠♥ r+ ♦♥s r tr♣♣♦♥ ♠♥t ♣ts ♥ t♦ ♠t♣t♦♥ ♦ s♣ttr♥ ♦s♦♥s t t trt ♠tr ♥ s ♦ ♠♥tr♦♥s ♦♥t♥♥ ♥ ♥st♥trt r♦rq♥② ♣♦r s♣♣s t♦ s ♥ ♦rr t♦ ♦ t r♠t♦♥ rt t t s t♥ t tr♦s s r s s t ts ♠♣♥♠t♥ ♥ t♦ qt② ♥st♥ ♠s ♥t ♦ t s♣ttr♥ s tt ♥ ♠trs t ♠t♥ ♣♦♥ts ♥ ♣♦st t ts ♣♦st♦♥ ♠t♦ ♦r♦r r ♥ t trt ♦♥t♥s♥ ♠♦♥t ♦ ♠tr s♥t ♦r ♦♥ ♣r♦ ♦ ♠♥t♥♥r st②

②r ②st♠ s♣ttr♥

st♦♠♠ s♣ttr♥ st♣ s t♥ t t♠r♠ ♦ ts tss s ♣♦ ♣♦st♦♥ ♦ r♦♥ ♦t ts ♦ s ♥ ♠♥s♠ ♠♦♥ ♠ts s s t ♥st♦r t♦ t ♠r s♥ ♦♥② tr s♣ttr♥ s♦rs♠② ♥st ♥ t ♠r t t s♠ t♠ ♠♣s tt ss t♦♠♣s♦r② ♥ trts ♦♥② ♦♥ ♦t ♦ ♦r ♦ ♦ s s ttr ♦♥ t♥ t s♠ rt♦♥ t s②st♠ s q♣♣ t t ❯❱s♠♣ tr ♥ t r+ t♥ ♥ ♦t ①t♥s② s ♦r t ♦r♠♥t♦♥♥st sstrt ♣r♣rt♦♥ ♦r t ♣♦st♦♥ s♣ttr♥ ♣♦st♦♥ rtsr rt s♥ t ♠ qrt③ ♥ ♠♦♥t♦r s②st♠ ss♦ q♣♣ t rs s ♥②③r ♦♥ t ♣rs ♦♥tr♦ ♦♣rt s ♣rssrs t♥ t ♠r s ♣rssr ♦ 2 · 10−9 ♠r s

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② s♠t♥♦s s ♦ r♦tr② tr♦♠♦r ♥ tt♥♠ s♠t♦♥♣♠♣s

tr ♣♦st♦♥ s♣ ♣♦st♦♥ ♣rssr ♥tr♦♥ ♣♦r♥♠♠ 10−3 ♠r ❲

♣t♠③ ②r ②st♠ ♣♦st♦♥ s♣s ♥ ♦♥t♦♥s ♦r s♣♠trs

♥ ♥ sstrts ♥♠ t r ②r s ♣♦st s s ♥♦rr t♦ rtr ♥sr s♠♣ t♥ss ♥ r②st♥t② t s♦ t♦ tr♣ ♥② ♣♦ssr♦♥ ♠♣rts ♥r♥t ♦ t ♣♦st♦♥s ①♥ t ♦♥s rqr♥ s♦♠s s ①♣♥ ♥ st♦♥ ♦ ♣r♦r♠ t t s♠♣ rr♦tt♥ ♥ ♦rr t♦ ♥sr ♥♦r♠t② ♦ t ♣♦st ♠tr ts ♦ t♦♣t♠③ ♣♦st♦♥ ♦♥t♦♥s ♦r ♦ t s♣ttr ♠trs r ♣rs♥t ♥t

t♦♣ t r ②r t r♦♥ ♦tt♦♠ tr♦ ♠tr s ♣♦stts ♣r♦r♠ t t P s♦ tt t s ss♥t t♦ ♥♥ t ♦rtr♦ t ts ♣♦♥t ❬❪ tt s ♦r t rrr ♣♦st♦♥ ♥s♥ t ♦r ②r r♦t s ♦ ❱♦♠r❲r t②♣ s♥ ♦r♠t♦♥ ♥st ♦②r②②r r♦t ssq♥t ♣♦st♦♥ ♥ t♦ ♦♥t ♣♥♦s♥♥♥ ♦ t s♣♦st tr♦ ♦r r♦t ♥♦t ♦♥② r♠t②♠♣r♦s t qt② ♦ t ssq♥t② ♣♦st rrr t s♦ st♦ ttr ♣t①② ♥ ttr♥ ♠♥t ②strss ♦♦♣s ♦ t ♥tr s②st♠ st② r tt t s♥t ♥♥♥ ♦♥t♦♥ ♦r t r♦♥tr♦ s t

P♦str♦t ♥♥♥ ♦ t ♦r tr♦ t♦ ♥ ♥tr qt② ♣r♦♠ ♣rssr t♥ t ♠r rss r♥ t t♠♣rtr ♥♥♥ t♦ ♦tss♥ ♦ rt♥ ♠♥ts ♥ t ♥t② ♦ t tr rsts ♥ t♦♥t♠♥t♦♥ ♦ t ①♣♦s ♥tr ♦r t rt♦♥ ♦ t ♥♥♥ s rsts♥ st♦♥ ❯♥♦rt♥t② t♦ t ♠r s♥ t tt♥♠ ♠♥trt② s t s♠♣ ♣r♥t♥ t s ♦ ts ♣♠♣ ♥ ♣rs♥ ♦ t s♠♣s t♦ ♦ s♦ ♦ ♥♦r♣♦rt t♦♠s ♥t♦ t s♠♣ strtr ❲t♥ tt♠r♠ ♦ ts tss s♦t♦♥ ♥ t ♦r♠ ♦ ♥ ♦ ①t♥s♦♥ t♦ t♠r s ♣r♦♣♦s ♦ ♦ t tt♥♠ ♣♠♣ t♦ ♥ ♦♥st♥t st♦t t rs ♦ t♦♠s ♥ ♥♦r♣♦rt ♥t♦ t s♠♣ ♦r r♥t t♠ ♦ rt♥ t s♦t♦♥ s ♥♦t ♥ ② ♠♣♠♥t ②t

s ♣r♦s② ♠♥t♦♥ t r♦♥ ♦① ②r t t ♥tr♥ rs② t t s♣♥tr♦♥ rs♣♦♥s ♦ t s②st♠ ♦♥sq♥t② s♥

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r ♦♥t t♦♠ ♦r r♦s♦♣② t♦♣♦r♣ t ♥ ♦ rr♥t rt ♠♣s ♦ ♥♦♥♥♥ t♦♣ ♥ ♥♥ ♦tt♦♠ r♦♥ ♦♥ t sstrt ♦t r♥s ♥ ss ♥ tt t ♦ rr♥t♦ts♣♦ts ♦rrs♣♦♥ t♦ t t♦♣♦r♣ s ♠sr♠♥ts r ♦♥t ♠❱ ❬❪

♣r ♥tr s ①tr♠② t t♦ r③ ①♣r♠♥t② t t t♦♠s ♥ ❲♥ t ♠♦♥strt tt ♥tr s ♠ ♠♦r ♦r t♥ t ❬❪ s♦ tt♠♣t t♦ ♥srt t ♥tr②r s t ♦①②♥ ♥trs♦♥ ♥t♦ t♦♣♠♦st ♠♦♥♦②rs ♦ t ♦rtr♦ ♦ s ts ♦①t♦♥ r♥ t rrr ♣♦st♦♥ t s t② ♦r tt t s t ♥tr tt ♦①③s ♠② ♥ rst ♥ t♦♥ ♠♦♥♦②rs rt♦♥ ♦r ts rs♦♥s ♠♦♥♦②rst ♥s♠②r s ♣♦st t♦♣ t ♦tt♦♠ tr♦

♥ t ♦tt♦♠ tr♦ s ♦♠♣t t rrr ♥ ♣♦sts s ♦♥ r♦♠ s♥ trt s♥ r♦rq♥② ♠♥tr♦♥ s♣♣t ♥ ♠♣♥♠t♥ ♦① t s ♥♦t tt t ♥t st ♣♦r

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r ♦♥♦r♦♠t ①r② rt♦♠tr ❳ ♥ tr♥t♥ r♥t ♦r ♠♥t♦♠tr ♠sr♠♥ts ♦♥ t s② ①s ♦r♦ sts t ♥♦♥♥♥ s ♥ ♥♥ rs♦ ♦r tr♦ ♥st s♦s ♠♥♦r ♠♥t③t♦♥ ♦♦♣s ❬❪

♣♦st♦♥ ss sst♦♦♠tr② ♦ t trt t ♠ ♦①②♥♥t r♦♦r ♥ rs ♣♣r ♦♥ t s s♦r ♠♦r s r♦t rtsr sts ♣♦st♦♥ ♦ t rrr r ♠♥t ♦ t s②st♠s st ①t♥s② rs♣ttr♥ ♦ t rrr s ♣r♦r♠ t ♦rt♦t t ♣rs♥ ♦ ♦①②♥ ♥ t ♠r t ♥ ♠ t♦ ♦♥tr♦ t t②♣st♥ t rrr ❲ ♣rs♥t ts rsts ♥ st♦♥

♥ t rrr s ♣♦st t ♣♣r tr♦ ♥ r♦♥ t♦♣t rrr ♣♥♥ ♦♥ t s♠♣ st ts s tr r♦♥ r♦♥ t♥♦t ♦ ♦r ♦tr♦♥ ♦② ♦ s♣t t t tt t r②st♥strtr ♦ ♦t s ①♦♥ ♦s♣ ♣ ♦ ♥ ♠♥t♥ t strtr ♣ t♦ ♦tr♦♥ rt♦ ♦ t♥ t ♦② s t♦♦♠♣♦♥♠tr s ♥♦t s♣ttr r♦♠ s♥ trt t r♦♠ s♣rt ♥ ♦ ♦♠♥s♦rs s ♠♥t♦♥ ♦r ♦ ♥ trts ♥ ♥♦t ♠♦♥t ♥ t ♠rs♠t♥♦s② t♦ t ♠t s♣ ♦ t ♠r s rqrs t♦ ♣tr s♣r t t ♥tr ♦r t♦ r♦ r♦♥ ♦♥② ♣♣r tr♦ st ♦r♠r s rtr ♥♦r t ttr s s ♦s♥ ♦r ♥ ♦rrt♦ ♥sr rr♦♠♥t ♦♣♥ t♥ t tr♦s t② t♦ r♦♥t sst♥t② r♥t t♥sss

ss♥t strtr ♦ t ♠♥t t♥♥ ♥t♦♥ s t ts ♣♦♥t ♦♥♦r t r♦♥ s r② rt ♠♥t ♦ ♦①③ st ♦ st♥s t♦ ♦r t ♥♦♥♦①③♥ ♠t ♣♣♥ ②r ♦r s♦s♥ ♥ ♦rr t♦ ♦ s♦ t s♠♣s r tr♥srr t♦ t ♣♦rt♦♥ ♠r ♦t ②r ②st♠ t♦t r♥ t ♠ s s sr ♥ st♦♥

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♥② ♣ttr♥

♠♣s ♥ t s♣r s s♥ t♥ t ♦ tr♦sr r♦♥ s t rst ♦ ♦♦rt♦♥ t ♥ r♦♠ t ♥sttt ♥♠♦r ♥ ♥② r♥ ♥② t ♥r r♦t ♣r♦r s ♣rs♥t ♥ t♠♥sr♣t ♦r ts ♣s rr t♦ ❬❪

s ♦s s②st♠s ♦ ♥♦t ♥ t♦ ♣♦st ♦♥ r②st♥ sstrt s t② r②st③ r♥ t ♣♦st♣♦st♦♥ ♥♥♥ ♣r♦ss s st♦♥ t r♦t s ♣r♦r♠ ♦♥ t ♠♦r♣♦s ♦r♥♥ ss ♥ ♦rrt♦ ssr ♥♦r♠t② ♦ t s♠♣s s♠♣s r rrs② tr♥st tr② r♥ t r♦t t♥t♠ ♥♠t ②r s s s t tt♥♥ ②r ♦♦ ② ♦♥♠ t♦ ♠♣r♦ rtr t①tr③t♦♥ t♦ ♦♦ s♦♥ ♦ ♦tt♦ t♥t♠ s s ♦♦ ② ♥ r♥♥♠ ♥trr♦♠♥t ♦s r♦ sr s♦rt② trrs t ♦♥♠♥♠♦♥♠♠♥ t♥♥♥ strtr s ♣♦st t ♠tr s♣ttr r♦♠ s♥trt ♦ ♣r♦♣♦rt♦♥s r ♦0.40.40.2 strtr s ♣♣ tt Pt ♣♣♥ ②r

s r② sr ♥ st♦♥ t ♦s s r ♥♥ ♣♦str♦t ♥ ♦rr t♦ ♦t♥ t t①tr r②st♥ rrr ♥ t ♥trrs ♦ t tr♦s ♦r t ♥♥♥ st♣ ♣②s ②t ♥♦tr r♦ st s②st♠ s ♦♣t♠③ ♦r ♣♦st♦♥ ♦ r♥ ♥trr♦♠♥t ♠tr rtrt♥ s②♥tt rr♠♥t sr ♥ st♦♥ ♣♥♥♥ ♦ t ♦r tr♦ s ② ♥♥♥ ♦ t s♠♣ ♦r t tt s ♦ t t♠♣rtr ♦ t r♥ ♥trr♦♠♥t ②t ♦ t r t♠♣rtr ♦t ♦ tr♦s t t ♦♥st♥t ♠♥t ♣♣ ♥ ♣♥ ♦t s♠♣ s ♥s t ♥♠♥t ♦ t r♥ ♥trr♦♠♥t ♥ ♦rr♦♠♥t ♦♠♥s ♣♦♥ t ssq♥t ♦♦♦♥ ♥ ts ①♥ s t♦r tr♦

s r♦t t♥q s rt♥ r ♥ ♦♠♣r t t ♦♥ ♣r♦♣♦s ② ❨s t ♥♠② t ♥ s♦♥ r♥ ♥♥♥ ♥♥t♥trr♦♠♥t s ts ♣♥♥♥ str♥t rs ts ♣♣r♥ t♥ t rrr ♥♥s t ♦r♥t tr♥s♣♦rt ♥ rs ♦ t ♠♥t♦rsst♥ t s ♠♦r ♣r♦♥♦♥ s t ♥♥♥ t♠♣rtr ♦r t♠♥rss ❬❪ ❲ sr ♥ t ♦r st② ♦♥ t ts ♥rt tt rr②st③ t♦ ts ♣♦st♥♥♥ ♣r♦ss ♥ st♦♥

♣rt r♦♠ ♠♥t t♥♥ ♥t♦♥ sts s♠♣s ♥ t t♦♣ tr♦r s♦ r♦♥ ♦r tr♦s ♦♦ ② ♦r ♥st♦r rrt ♦r ♦♣t sts ♦ t rrr r rs♣t ♦♥tr♣rts r s♦ssq♥t② ♥♥ ♥ ♦rr t♦ st② t ♥♥♥ ♠♣t ♦♥ ♦♣t ♣r♦♣rts♦ t rrr

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❱P

♣♦rt♦♥

♣♦rt♦♥ s ♥ ❯❱ t♥ ♠ ♣♦st♦♥ ♠t♦ ♥ r t s♦s♦r ♠tr s t ♣ t♦ ts ♠t♥ ♦r s♠t♦♥ t♠♣rtr ②♦♥ ♣♦rt♦♥ ♥s t♦ t tr ♠ t♥ t ♠r t♠♥ r ♣t ♦ t ♣♦rt ♣rt s ♦♥ ♥♦ t♦ r t s♠♣ t♦t♦r t r② ♦s♦♥s r♥ ts t t♥ t ♦♥♥ss ♦♥ t sr

s ♠♥t♦♥ ♦r s♠♣ tr♥sr ♠♦♥ ♠rs ♦ ②r ②st♠♦rs t♦t r♥ t ♠ s t t♦♣♠♦st ♣♣r tr♦ ②rs ♦ ♦r ♦ r ♥♦t st t♦ ♦①t♦♥ s♠♣s r t♥ ♦r t ♥♠ t ♣♣♥ ②r ♦s ♣♦rt♦♥ s rr ♦t t t♦② ♠♥ ♣♦st♦♥ rt ♠t ♥tr ♦ ts ②r s rqr ♥♦rr t♦ ♣r♦ ♥ tr ♦♥tt tr t s♠♣ ♣r♦ss♥ s st♦♥ ♦rts

♥ ♦rr t♦ rtr ♥♥ t r②st♥ qt② ♦ t st ❬❪ t s♠♣s ♣♦st♥♥ ♦r ♦♥ ♦r t ♥ t ♣♣ s♠♣ s s② t♥♦t ♦ t tr ♠

Ps sr ♣♦st♦♥

r3 ♥ 2 s s♠♣s s s t ♦♥s ♦♥t♥♥ tr♦s r rt s♥ t Ps sr ♣♦st♦♥ P t♥q ② ♦s r♦♠ t ♣rt♠♥t ♠ t s tr① ♥♦r♥qs s rst ♦♥ ♥tr♥ ♦♦rt♦♥ t♥ t P

❲ t P r♦t s rt② s② t♦ r③ t ♠t♣st♣ ♣②ss♥r♥t s ♠ ♠♦r ♦♠♣①

sr ♠ s ♦s ♦♥ trt ♣ ♥r ♠ ♥ ♠ r♦♠ t♠tr t♦ ♣♦st ♣♥♥ ♦♥ t sr ♥t ♥ t ♦♣t ♣r♦♣rtsrt♦♥ ♥ s♦r♣t♦♥ ♦ t trt ♠tr t ♠ ♣♥trts ♥♠♥t♦ t trt t sr ♥r② s ♦ rt♥ trs♦ t ♥r②tr♥srr r♦♠ t sr t♦ ♠tr t t sr ♦ t trt s r ♥♦t♦ t ♣ t sr ♥ t ♣♦r③t♦♥ ♦rs t♦♠s ♦♥s strs t rtr♦r t r♦♠ t trt ♥ t ♠tr ①♣♥s s ♣s♠ ①♣♥s♦♥ ♣r♠trs ♦ t ♣s♠ r r♥ ② ♣♦st♦♥ ♦♥t♦♥s s♣②t ♣rs♥ ♦ ss ♥ ♦r♥ ♣rssr t♥ t ♠r s♣ ♥♦♥sq♥t② ♥r② ♣rts ♥ s♣ttr ♠tr r② ♣♦st ♦♥ ts♠♣ ♠② tr ts r♦t rt ♥ ♠♦r ♠♣♦rt♥t② st♦♦♠tr② ♥♦r♠t♦♥ strtr ts s♣② ♥ s ♦ ♦①s s♦♥ ♦♥ t r♦trt ② ♥ t ♠r t ♦①②♥ ♦ ♥sr ♥♦t ♦♥② ♥♦r♠t② ♦ ts♠♣ t s♦ ts ♦①②♥ st♦♦♠tr②

sr s ♦r t P ♣♦st♦♥ r♥ ts tss s r ①♠r srt t ♥t ♦ ♥♠ rq♥② ♥ t ♥r② ♥st② r ③ ♥

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P P ❲ ❯ ❱P

1.5J/cm2 rs♣t② s ♣rssr s ♦ 5·10−8 ♠r ♦r strtrsrt ts ② r②st♥ sstrts r s ♥ ♦rr t♦ s♦rsr ♦♥t♠♥♥ts t sstrts r ♥♥ ♦r ♠♥ts t s ♣rssr ♣r♦r t♦ ♣♦st♦♥ s ♦ 2 · 10−7 ♠r ♦r t♠♣rtr♣♦st♦♥ ♥ ♦ 9 · 10−8 ♠r ♦r t ♣♦st♦♥ t r♦♦♠t♠♣rtr rt② ♣rssrs ♠② rst r♦♠ t t tt t♦ ♦ s♣rt♦♥ ♠r t r♦t ♠r s rt② ①♣♦s t♦ t t♠♦s♣r r♥t s♠♣ ♦♥ tr t s ♥♦t ♦t

♥ ♦rr t♦ ♥ ♥ r②st♥ strtr t ♦r ♠♥t tr♦ s s② ♣♦st t t♠♣rtr s ♦r t rrr t s♣♦st t r♦♦♠ ♦r t t♠♣rtr s♣② t ♦tt♦♠ tr♦ s ♥♦① t♦♣ ♠♥t tr♦ s ♣♦st t ♦ t♠♣rtr ♥ ♦rr t♦♦ s♦♥ t t ♠♥t♥♦♥♠♥t ♥trs ♥♠ ♣♣♥ ②rs r♦♥ t♦♣ t strtr ♥ ♦rr t♦ ♣rsr t r♦♠ ♥② rtr ♦①t♦♥

t♦♥ ♥r② tr♦♥ rt♦♥

P ♠r s q♣♣ t rt♦♥ ♥r② tr♦♥ rt♦♥ s②st♠ tt ♦s t♦ ♠♦♥t♦r ♥st t s♠♣ qt② ♥ ts r♦t♦♥tr♦ t♥q ♥ tr♦♥ ♥ ♥rts ♥ tr♦♥ ♠ tt ♠♣♥s ♣♦♥t s♠♣ sr t ♦♥② rs ♥ ♥ rt t tr♦♥s rt tt♦r t tr s♣ rt♦♥ ♥s r t② ♥trr ♦♥strt② ♦rstrt② ♥ rs t♦ s♣ rt♦♥ ♣ttr♥ t t tt♦r sr♥ tts rt② rt t♦ t r♣r♦ tt ♦ t ♠tr ♥②ss ♦ t ♣ttr♥ ②s ♥♦r♠t♦♥ ♦t t r♦♥ss st♦♦♠tr② ♥ r②st♥t② tt rr♥t st ♦ t r♦t sr♣♥ss ♦ ♣s ♥rss t t srr②st♥ qt②

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♣tr

r♦♠ s♠♣s t♦ s

r♥t t♥qs ♦ s♠♣ r♦t r ♣rs♥t ♥ t st ♣tr ♥♦♠♣t ts s♠♣s r ♣r♦ss ♥t♦ ♦r♥ s s ♣tr ♣rs♥tst♦ r♥t ②s ♦ ♣ttr♥ rst ♠t♦ t ♥st t②♣ s ①s② ♦r ②r ②st♠ s♣ttr s ♥ rs ♦♥ s♣ttr♣♦st♦♥ tr♦ s♦♠ss s t♥q ♦s ♥♦t rqr t s♠♣ t♦♥r♦ ♦♥ ♥ t ♣♦t♦t♦r♣② s ♣rs♥t ♥ t s♦♥ st♦♥ ttr ♠t♦ t t ♦st ♦ ts ♦♠♣①t② ②s ①♥t s♣t rs♦t♦♥ ♦s ♥t♦♥s rt ts ② t♦ ♦ ♠ s♠r s③s ♦r♦r trsts ♥ r ♥♠r ♦ s ♣r s♠♣

♥st ♣ttr♥

❲t♥ t t♠r♠ ♦ ts tss t ♥st ♣ttr♥♥ t♥q s sts♦r t ②r ②st♠ s♣ttr♥ ♣♦st♦♥ s ♥ ♠♦♥t♥ ♦ ♥ t♦♥ r♠ ♥s t ❯❱ s②st♠ t s♦♠s s②st♠ tt t♦ t s♦♠s r♠ ♥ ♣rs② ♠♦ ♦♥ tr ♠♥s♦♥s ♦♠♥ ♥ ♥♦t ♦ t ♦♥tt ♣♦st♦♥ s ♠s t ♣♦ss t♦ ♣♦st ♦♥st ♠trst sr ♣ttr♥s t♦♣ ♦tr

♥st ♣ttr♥♥ ♣r♠trs ♦ ♣♦st♦♥ r ss♥t② s♠ s ♦r tst♥r ②r ♣♦st♦♥ ①♣t tt t ♣♦st♦♥ ♦rs t s♠♣s ♥ ♦♥tt t t s♦♠s ♣r♥ts t s♠♣ r♦tt♦♥ t♦ ts②st♠ ♦♥strt♦♥ s s t♦ r ♦ s♦ ♣♦st♦♥ ♦♥ t s♦ t ♠♦t ♦r♦r s ♥ s♥ r♦♠ t s♠t r t t ♥♦ss t♥ ♥♠ ♦r tr♦ s ♥♥♦t ♥ ♣r♥♣ ♦r ♣r♦♣r② tt t♥ rrr ♠tr ♥r ♠♦r t♥ ♥♠ ♥ ♦rr t♦ ♦ s♦rtrtst♥ t♦♣ ♥ ♦tt♦♠ tr♦s ♦♥ ts s ♦ t ♦tt♦♠ tr♦ ♥t♦♥ st♣ s ♥tr♦ ♣ttr♥ ♥♠t t♥♦♦ s♣♦st st tr t rrr r♦t st♣ ♥ ♦♥② ♥ ♦♣♥♥ ♥ t ♠♦ t ♦tt♦♠ tr♦ tr♦ t t♦♣ tr♦ ♠tr ♦ ♦♥tt t

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P P ❱

r ♠t strt♦♥ ♦ t rr♥t t t tr♦ s t ♥ts ♣r♥t♦♥ ② ♥tr♦t♦♥ ♦ t t t♥♦♦ rt ♦♦rs ♣tt ♥st♥ sstrt t ♦♥t♥ tr♦s ♥ ♦t rrr ♥t♥♦♦ r② ♥s s♦ t rr♥t ♦ ♥♥s ♦r ♦t ss♦t tt t ♣tr s ♥♦t t♦ s

r ♠t strt♦♥ ♦ t ♥st ♣ttr♥♥ r♥ t ♣♦st♦♥t ♦r tr♦ ♣♦st♦♥ ♥tr t♥ rrr r♦t tr♥s♣r♥t ♦♦ ② t t♥♦♦ t ♥tr♦t♦♥ ♥ ♦rr t♦ ♦r t ♦r tr♦ s rt t♦♣ ♦♥tts rt♦♥ ♥ t t♦♥ t♥ ♣♣♥tr♥s♣r♥t r sqrs ♠r t ♥t♦♥s ♣♦st♦♥

rrr rt② ♦♥ t rrr t♥♦♦ st♣ t② ♥ t♥t♦♥ ♥t ♥ ♦♥ t t t ♦ t ♦tt♦♠ tr♦ ♦♥sq♥t② t r

♥ t ♣♦rt♦♥ ♠r ♣rs♥t② s s♦♠s s②st♠ ♣♦st♦♥ ♥ tt ♠r s ♥♦t s ♥st t s♠♣s r ♦r tt ♥st♥ ♥♠ t ♥ t ♦tr ♥ t ♥st♥ ♥tr ♦ t ♣♣♥ ②r ♥♦t ♣r♥t ss♥ t ♦♥t ♠tr ♦ rs♦♥ s tt t s♦♠s ♣ttr♥ s♠♣ ♥♦t t♦ ♣r♦ss ②t ♦♣t t♦r♣② t rt② ♥r♥t t ♦♥t♣ ♦♥♥ ♦♥♥ s r♥ ts tss s② ②♣sss t ♥♠ t♥ ♥st♥ t♦♣t ♦♥tts s st♦♥

t♦ t ♠t s t♥ss ♦ t ♦tt♦♠ tr♦ t♥♦♦ ss ts t s st t♦ 650µ♠ r ♥♦ t♦ ♥sr ♦ rsstt② Ω ♥♦t t t ♣r♦♣rts s tr t r s ♥② 50µ♠ ♦r 100µ♠ ♣♥♥ ♦♥ t ♠s ♣ttr♥ ♦♣♥♥ ♥ t t♥♦♦ ♥ t t 50µ♠ t ♦ t t♦♣ ♦♥tts t♦ t ① ♦ tt♦♣ ♦♥tts t tr ♦ rsst♥ Ω s ② ①t② ♦t♥ss ♠♥tt♦♥

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P P❨

r Ptr ♦ s♠♣ ♣ttr♥ ♥st s♥ t s♦♠s t♥q ♦♣♥♥ ♥ t t♥♦♦ ♥♥ t r 2500µm2 ♣r ss ♥ ♦r♠ ♦ t rt str♣ ♥ t ♠ ♦ t ♦tt♦♠ tr♦ tt ♥trsts ♦ t t♦♣ tr♦s

rs ♦ s rt t t s♦♠s r 2500µm2 ♦r 5000µm2 ♠ rr t♥ ♦ ts ♦t♥ t t ♦♣t t♦r♣② sr ♥ t ♥①t♣tr ♦r t ♥st ♣ttr♥♥ s♠s ♣r♦♠s♥ s t ♥t♦♥s ♥ rt t♥ rt② s♦rt t♠ s ♦♠♣r t♦ ♦♥ ♥ t ♠tst♣t♦r♣② ♣r♦ss t②♣ s♠♣ rt s♥ t s♦♠s ♣ttr♥s ♣rs♥t ♥ r

♣t t♦r♣②

♣t t♦r♣② ♦s ♠r♦♠trs ♥t♦♥ ♦ ♣ttr♥s ♦♥ t s♠♣t s ② s ♦r rt♦♥ s ♦ t r qt② ♥ s♥♦ tr♦t t sr ♦r t t♦r♣② ♣r♦ss ts st♣s r rr ♦t ♥ t ♣ t t♥♦ ♥r♦♦♠ r ♠♦st ♦ t q♣♠♥t ss♥t♦r t ♣r♦ss s ♥st

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P P ❱

t♦r♣② ♠s

r ♥ s♦tr ♠s rs r♥ ♥ r tr♥s♣r♥tt t ♦♥s ♠r t ♦♣q rr♦s ♠r ♠♦ts s r♥ ♦rrs♣♦♥♥t♦r♣② st♣s r sqrs ♠r d r t♦r♥ sqrs

♥ ♦rr t♦ st② ♥st t rsst ♥ ♦♥st② ♦t♥ sr ♣ttr♥s ♦♥ t s♠♣ t♦r♣② ♠s ♦♣ ② ♥♥ r♦♠ t ❯P②s r♦♣ s rs♥ s♥ t ♥ s♦tr ♣tt♦♥sr ♣r♣♦ss ♦ t ①♣r♠♥t ♥ ♥ t♦r♥ st♣ s♦ s t♦ ♠♣r♦rs♦t♦♥s ♦r s♠ ♣ttr♥s ♦♥ t②♣② s♠ ①♠♠ s♠♣s t♦st♣ strt② ♦ rr♥t ♥t♦♥ ♥t♦ t ♦tt♦♠ tr♦ ♦tr ♦♥t♥ ♦♥♥t♦rs ♥

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P P❨

r ♥ s♦tr ♥r s③t♦♥ ♦ t s♠♣ t ♦r ②rs♦r♣♣ ♦r t rr t♦

rs ♦♥ ♣♦ss ♦♥♥t♦♥s ♠♦♥ t tr♦s t♦♥ ♠♦ts s♦ st♦ ♥rs t rs♦t♦♥ ♦ t ♥♠♥t t♥ t♦r♣② st♣s ♥ srstrts t♦ ♦♥r ♦♣t ss t♦ ts s ❲t ts ♥s ♣r♦r♠t t ♦♥st ♦ t tss ♠♥♦r ♠♣r♦♠♥ts r ♣r♦r♠ r♥ t tss s♦s t♦ ♦♣t♠③ ♥t♦♥ s③s tst ♠s rs♦♥ t t t♠ ♦ rt♥ t♠♥sr♣t s s♦♥ ♦♥ r ♣r♣♦st♦♥ ♦ t ②rs s ♣t ♦♥ rs s ♠♥t♦♥ ♦ t ttr s♦♥ s♦♠ ♦ t ♦r♠♥t♦♥ trs ♠s ♥s t ♣ttr♥♥ ♦ st ♥t♦ r♦s ♦♥t♥♥ ♥t♦♥s ♦ t s♠ s③ ♥t♦♥ s③s r ♥

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P P ❱

r ❩♦♦♠ ♠ ② ♥ s♦tr ♦ t s♠♣ t ♦r ②rs♦r♣♣ ♦♦rs ♥ t ♦♥st ♣♦t♦t♦r♣② st♣s ② sr ♥t ♦♦♥ st♦♥ r♦♥ ②♦ ❱r♥ A ♥ rr t♦ tr♦ ♥♠r ♥ t ♠tr ♦ ♥t♦♥s ♥ t r♦ ♥ µ♠ rs♣t② r♦sss♥ ♣rs ♥ t ♦tt♦♠ ♣rt r ss♥t ♦r ♣rs ♥♠♥t ♦ st♣s rs♣② ♦r t ♠t♥ ♥♦t ss t♥ ♥♠ ♠r♥ rr♦r

µ♠ ♥ ♠tr rs♣t② t♦ rs♦t♦♥ ♣r♦♠s ♦♥r♥♥ t s♠st♥t♦♥s ♠♦t♦♥ ♦ s③s s ♣r♦♣♦s t t t♠ ♦ rt♥ s③s ♦♥t♦♥s ♣ t tr♦s ♥ ♦r ♣rt ♦ t ♠s r t s♠ s ♦ ts♥ t ♣♣r ♦♥ s ♠①♠♠ ♥♠r ♦ ♥t♦♥s rt r♦♠ ♦♥ s♠♣t♥ s♥ t♦r♣② ♣r♦ss s

♠s t t♦r♣② ♠♦ts ♣r♥t ♦♥ ts r♦♠♠ s tt ♦♠ ♥t♦♦♥tt t t s♠♣ r♥ t ❯❱ ♥st♦♥ s♠♣ ♠♣r♥t ♦♥sst ♦♠♥ts r♦♣ ♦♥ ts qrtrs qrtr ♦♥t♥♥ ♣ttr♥s ♦r t rs♣tt♦r♣② st♣ ♦ t ♠♦ts r ♠t♣ ♠♣r♥t♦♥ s♦♠♦ t♠ s♦ tr trt♦♥s ♥ rrs ♦ tr♥s♣r♥② ♦r ♣r♦ss♥♦ ♣♦t♥t ♦r♥ s st♣s ♥ ♥ ♠t♥t♦♥ ss ♣ttr♥st♣ ❱ ♦r tr ♦♣t sts t♥ t t♠r♠ ♦ ts tss s ♦♥②♦r tst♥ ♣r♣♦ss t s ♦ t ♠s ♣ttr♥s ♥ t ♣r♦ss

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P P❨

♣rs♥t ♥ t ♦♦♥ sst♦♥s

P♦t♦rssts

P♦t♦rssts P r ts♥st ♠trs ♠♦st② ♣♦②♠rs t ♦♥ str♥t♦ ♥s ♥ ①♣♦s t♦ tr♦t t s trs tr s♦t②♥ s♣ ♦♣rs s tr s ♥♦ ❯❱ ♠♥t t ♣rs♥t ♥ t t♥♦♥r♦♦♠ ♣♦t♦rssts ♦ ♥ tr ♣r♦♣rts ♦♥② ♥ ①♣♦s ♦♥ ♣r♣♦s♦ ♥r t②♣s ♦ ♣♦t♦rssts ♥ st♥s ♣♦st ♦♠♠ ♠♦r s♦ ♥ ♦♣r tr t ❯❱ ♥st♦♥ ♥ ♥t ♦♠s♦② ♦♣ tr ♥ ①♣♦s t♦ t tr♦t t rsts r♦♠str♥t♥♥ ♦ t ♦♥s ♥♠ ❯❱ ♠♣ s r♥ ts tss ②15mW/cm2 t ♦s

r ♠t r♦ssst♦♥ ♦ ♣♦st t ♥ ♥t rt♣♦t♦rssts tr tr ❯❱ ♥st♦♥ ♥ ♦♣♠♥t ♦t t ♦r♥ ♦ t♥t P

r ♥st ② t ❯❱ t s ♥ ② ♦r♥ ♣rts ♦ t ♣♦t♦rsst♦r s♠♣ t t t♦r♣② ♠s ♣♥♥ ♦♥ tr ♣♦t♦rsst s♣♦st ♦r ♥t ts s qr st♥t s♣ ♣♦♥ ♦♣♠♥t s♣② t s ♦ t ♥t rsst s r ♥ ♦rr t♦ ♦t♥ ♥ ♦r♥ tt ❲t♥ t t♠r♠ ♦ ts tss t♦ s♣ ♣♦t♦rssts r st ♣♦st ♥ t ♥t ❩

P♦st ♣♦t♦rsst

Pr♠trs ♥ ♦r ♦rrt rsst rs♦t♦♥ r st ♥st♦♥t t ❯❱ t ♦r s♦♥s ts ♦♣♠♥t ♦r s♦♥s ♥ ♦♣r ♥ rtr ♦t ♦r s♦♥s t ♥ ♦rr t♦ ♠♣r♦ tsstt②

t ♣♦t♦rsst ❩

♥ ♦rr t♦ ♦t♥ t sr ♦r♥ t t ♣♦t♦rsst tt s r ♦rt t♦ ♣r♦ss sr ♥ sst♦♥ t ♥t P ❩ ss s ♥t② ♣♦st ♣♦t♦rsst ♠② ts ♣♦rt② ♥rt ② ♦t♦ ts ♥st ♣rts ts ♣r♦ss♥ ♣r♠trs r st ♥st♦♥ tt ❯❱ t ♦r s♦♥s t♥ t ♥ ♦rr t♦ ♥rt ts ♣♦rt②

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P P ❱

♦♦ ①♣♦sr t♦ t ❯❱ t ♦r s rtr st str♥t♥♥ ♥ ♥s♦♥ ♦♣♠♥t ♥ t ❩ ♦♣r

Pr♦ss♥

♣♦t♦t♦r♣② ♣r♦ss ♦♥sst ♦ ♦r st♣s sr t♦ ssq♥t②♣ttr♥ t s♠♣ ♥t♦ ♠♦r ♦♠♣① strtr ♦ ♥② ♦r♠ t s r ssq♥t② ♥t♦♥ ♣r ♥t♦♥ ♦r tr♦ ♣ttr♥ ♣sst♦♥ ②r ♣♦st♦♥ ♥ ♥ ♠t③t♦♥ ❱ ❲t♥ t t♠r♠♦ ts tss ♥ t♦♥ t♦r♥ sst♣ s ♥tr♦ ♦ t♦r♠♦ t ♥♥t t ♣♦t♦rsst r♦♠ t s ♥ ♠♦r ♣rs ♥t♦♥♦ ♠♦ts t♦r♥ sst♣ s ♦♣t♠③ t♦ ♣r♦r♠ ♦r ♦t ♠♥ st♣s t♦ t♦ rst♥ ss s st♦♥ t s s♦♥② rqr

P♦t♦rsst ♣♦st♦♥ ♥ ts t♦r♥

P♦t♦rsst ♣♦st ♦♥ t s♠♣ ♥ r♦♣ts t♥ s♣♥♦t ♦r s♦♥s tr♣♠ ♦r ts sr ② s♣♥♥♥ t s♠♣ ② t ♥ ♥♦r♠②r ♦r s♣t ♥ ♦rrt② t ♦r t ♥tr s♠♣ sr t♣♣r t♦ ♠ tr t t s♠♣ s ♥ ♦rr t♦ rtr ♠♣r♦ ts♥♦r♠t② ♥ t ♥tr ♦ t s♠♣ t s ♦r ♠♥ts t

♦r ♦t ♣♦t♦rsst t②♣s t ♠♦♥t ♦ sst♥ ♥ t s♠♣ s st♦♦ t♦ ♣r♦ rtr ♦rrt ♦♥tt ♦ t ♥tr ♣rt ♦ t s♠♣ tt ♠s r ♦r t qt② rs♦t♦♥ ♦ ♠♦ts ♥ ♦rr t♦ ♦ ts♣r♦♠ t t♦r♥ sst♣ s ♦♣t♠③ s♦ t ♦ ♣r♦r♠ t t♥♥♥ ♦ t♦r♣② st♣ ♦♥ t ♦tr t P ♦r ♦t P t②♣s tss ♦♥ ② s ❯❱ ♥st♦♥ ♦ t ♦tr rsst ♥ t ♥tr♥ s♠♣r ♦r t t r sqr ♠♣r♥t ♦♥ t ♠s str♦♥② ♥strsst s t♥ ♦♣ ♦r s ♦r s ❩ ♥ ♦♥② t rsst♥ t s♠♣ ♥tr ♥ t r t♦♥ s t♥ t s♥ ♦r t rsst ♥ ♦rr t♦ ♣♦rt t ♦♣r ♣rts r♦♠ t t♥ s ♥♦t ♣r♦r♠ ♦♥ t ❩ rsst s ♦ ♦ s♦ ♦ ♣rt②♥rt ts ♣♦rt② ♥ t r② st

P Pr ♥t♦♥

❲ ♥ ♦♥② t t ♥ ♥♦r♠ rsst t ♦♥ t s♠♣ ♣rs♦♥tt ♦ sts t♥ t s♠♣ ♥ t t♦r♣② ♠s

♥t♦♥ ♣r ♣ttr♥ s s ♥ ♦rr t♦ ♥ t t ♥t♦♥r r ♦♥tt ♣s r ♥ ♥ ts st♣ s ② ♦ ♦t rr♥t ♦ t♦rs t ♦r tr♦ ♦ ♥ ♥ t st♣

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r ♠t t♦♣ ♥ r♦ssst♦♥ ♦ t ♣♦t♦rsst st♣ ♣ttr♥♥♦♦rs ♣t rs♣t② tr♦s r② rrr ②♦ ♠t ♣♣♥②r r ♣♦t♦rsst t s♦♠s ♦♣q r t♦r ♣♦t♦rsst ♥♦♥tt t t ♠s st ♦r ts ♥st♦♥ st ❯❱ ♥st♦♥ ♣r♦ss ♣ttr♥ ♣♦t♦rsst r♠♥♥ ♦♥ t s♠♣ sr ♦t t ♣tr s ♥♦t t♦t s

♣♦t♦rsst s st② ♥st ♥ r♠♦ ② ts ♦♣♠♥t r♦♠ t rs ①♣t ♣rs ♥ ♣s

r t♣ t♥ s♠ ♥ st r+ t♥ ♦♥ t♦ trrr s♠♣ s♠t tr t ♣♦t♦rsst r♠♦

r+ t♥ ♥ ♦rr t♦ r♠♦ ♠tr r♦♠ ♥♦♥♦r ♣rts ♦ t s♠♣t s♠♣ ♥r♥t t r+ t♥ ♣r♦r ♥ ts ❯❱ t♥q ♥trr t♦♠s r ♥t ♥t♦ t ♠r ♥ str♣♣ ♦ tr tr♦♥s t♦ rt ♣s♠ ♥ r+ ♦♥s r rt t♦rs t s♠♣ s♥ ♦s♦♥s ♥r♠♦♥ t ♠tr ♥ ♠② s tt ts ♣r♥♣ s s♠r t♦ t s♣ttr♥♣♦st♦♥ ♠t♦ t t r r♥ tt tr s ♥♦ trt r♦♠ t ♠tr s s♣ttr t s t s♠♣ r♦♠ t ♠tr s r♠♦ ♦♣r♦tt t t♥♥ rrr r♦♠ ♠ rt♦♥ ♦ ♦♥t ♠♥ts t♥

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t rrr t r+ ① ①t♥ t ♥ s ♥tr③ t♥s t♦ t tr♦♥♠tt♥ ♠♥t r t♦♥ s ② tt♥ ♦♥t t♣t♦ t s♠♣ ♦r♥rs ♦r ② ♦r♥ t♠ t s♠ ♠♦♥t ♦ t sr ♦♥t♣st ♥ ♦rr t♦ ♥sr t♥ ♥♦r♠t② t s♠♣ s r♦tt r♥ t♣r♦r

t♥ ♣r♦r s rr ♦t ♥ s♠ st♣s ♥ t r ♣♦♥t♦ t ♥t♦♥ ♣r t♥ s t♦ st♦♣ t♥ t rrr ♦r st t ts ♦r ♥tr t♥ ②♦♥ t rrr ♥ s t ♦r tr♦ ♠tr t♦ ♦rt ts t② ts t♥ss ♦ r s ♥ t ♦ttr ♦♥tt② ♥ ts ♠♥t ♦r ♦ t tr♦ ♦r♦rt t ♦♥t ♠tr ♥ r♣♦st ♦♥ t rrr s s♥ tss♦rtrt ♥♦tr ♣r♦♠ rs♥ r♦♠ t tr♦ ♦rt♥ s♣②♦r 0.7r0.3♥3 s trt♦♥ ♦ ts st♦♦♠tr② t s ♥♦♥ tt ♦①②♥♥t ♠tr ♦♠s s♠♦♥t♥ ♦r ♥ ♥st♥ ❬❪ s s② ♥♦r s t ♦st ♣♦ss ♦♥tt rsst♥s r ♥ ♥ ♦rr t♦♣r♦r♠ ♦rrt ♠sr♠♥ts ❬❪ s st♦♥

r tr♦♥ s♣tr♦s♦♣② ♥ ♦rr t♦ ♦rrt② tr♠♥ t t♥ ♣tt t♥ ♠r s q♣♣ t r tr♦♥ s♣tr♦s♦♣② s ♦r♠ ♦s♣tr♦s♦♣② s s ♦♥ t r t ♥ t t♦♠ ♣r♦ ② t tr♦♥♠ ♠② ts ♦r stt tr♦♥ r♠♦ ②♥ ♥ ♥st ♦ s stt♠② ② ♥ tr♦♥ r♦♠ ♥ ♦tr s ♥ ts tr♥st♦♥ ♥r② ♠② tr♥srr t♦ ♥♦tr ♦tr s tr♦♥ t ♥r② ♦t♥ s s♥tt♦ ♦r♦♠ ts ♦rt ♥♥ ♠② ♠tt r♦♠ t t♦♠ t rt♥ ♥t♥r②

r tr♦♥ ♣tr♦s♦♣② t t t♥ ♠r s q♣♣t③s ❱ ♥♦♠♥ tr♦♥ ♠ r tr♦♥s ♠tt r♦♠ rst ♠♦♥♦②rs ♦ t sr r st ♥ tr ♥t ♥rs ♣ t♦ ❱ ❬❪ s②st♠ ♦ t♦ ♦♥tr♦ t t♥ ♣t ♣rs② t ♥♦t rt② r♥t t♥ ♣r♦ss ♦r t♥ rs♦♥s t r ♥ ♥ tt♦r r ♠♦♥t♥ r♥t ♣♦st♦♥ t♥ t t♥ ♥ ♥ ♦rr t♦ ♣r♦r♠ t ♠sr♠♥tt s♠♣ s tr♥srr t♦ t r ♣♦st♦♥ t♦t r♥ t ♠ ss t♦ tr♥ s♠♦s t♥ st♣s ♦ s ♦♦ ② t r♠sr♠♥t ♥ ①♠♣ ♦ t t♥ sq♥ ♦r t ♦ s②st♠s s♦♥ ♦♥ tr t rst t♥ st♣ t rst ②rs ♦ tsr r ♣r② ♦t t♦♠s s♦♥ ♦♥ r ②s ♣s r♦♠ ♦t r♦♥♥ ♦t s♦ t ♦ ♥tr s ♥♦ ①♣♦s tr t♥ st♣ ♥s t♥ t t♦♣ r♦♥ ②r rs tr t ♦rt st♣ r♥ t rrr strt t♦ s t s♠ q♥tt② ♦ ♦ s♥ ♣s r♥♦t s t♥ ts ♥r② s♣♥ ♥ ♦rr t♦ tr♠♥ tr t r♦♥ ♣s

①♣r♥ s♦s tt sr s♠ t♥ ♦ss ♦t② t♦ ss t♥ t♥ ♥rt s♥st♣ t♥ ♦s

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r r s♣tr♦s♦♣② ♠sr♠♥ts rts tr ssq♥t t♥s♦ t ♦ st ♦♥st rsts r st ♣rs ♦r rt②rs♦♥s rr♦ s♦s t t♥ ♦rr r♦♠ rst t♦ st ♣ ♣♦st♦♥s rr♦♠ rst t♦ s♠st ♣r ♠♥t ♦♥♠ ♥♠♥♠ ♣s r ♥♦t s

♦♠ r♦♠ t ♦tt♦♠ ♦r t♦♣ tr♦ t s♠♣ s trt ♥ t s♠ t♥ ♦s ♣♥ s♦ ♥ s♥ ♦ t ♣s s ♠♥stt t ♦r♠r t♥ st♣ ♥t r♠♥♥ts ♦ t ♣♣r tr♦ ♥tt t s t tt s ♥♦ t s♠♣ sr ②r s sr ♦t ttt t♥ ♣r♦r ♦s ♥♦t t t s♠♣ r♦♥s r ♦r ② t♣♦t♦rsst ♥ t r ♠ s ♦s ♦♥ t t ♦ ② ♦♥② tr r♦♥ ♣ st② s ♥②② t ❱

P ♦r tr♦ ♥t♦♥

tr t ♣r t♥ t st♣ ♣♦t♦rsst s r♠♦ ♥ s t♦♥ ♥t♥♦ trs♦♥ ts t ts ♣♦♥t t ♦tt♦♠ tr♦ ♣ttr♥♥ st♣ s♣r♦r♠ s♥ t ♣♦t♦rsst s st♣ s ①♣r♠♥t② r③ ts♠ ② s t rst ♦♥ ①♣t tt t s♠♣ sr s ♦r t ts♦♥ st♣ ♦tt♦♠ tr♦ ♣♦t♦rsst ♣ttr♥ t s tr t t ts♠ r+ ♠ ♦♥ t♦ t sstrt s ♦r t rst t♥ st♣ s♦t ts ♣♦♥t t ♦rt s ♥♦t sr s s s♣② t s ♦r r3

sstrts ♦s ♦♥t♦♥ ♥ ②s ♦s t t r♠ ♥ ts♥② ♦①②♥ sst♦♦♠tr② ♠② s t sstrt t♦ ♦♥t s s ②

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r ♠t ♣tr ♦ t s♠♣ tr t st♣ t♥ ♥ t ♣♦t♦rsst r♠♦ t r♦♥ ♦♦r ♥ t t♦♣ r♣rs♥ts t ♥st♥sstrt

♥♦r s s♥♥t ♠♦♥t ♦ rr♥t ♦ ♦ tr♦ t sstrt ♥t♦♥ t♦ t ♥♦r♠ ♥t♦♥ rr♥t ♥rss t rs ♦ s♦rtrtt♥ t♦♣ ♥ ♦tt♦♠ tr♦s ♦ ♥ ♥t♦♥

P Psst♦♥ ②r ♣♦st♦♥

♥ ♦t t ♥t♦♥ ♣r ♥ t ♦tt♦♠ tr♦ r ♥ 2 ♣sst♦♥ ②r ♣♦st♦♥ s ♣r♦r♠ ♥ ♦rr t♦ ♦ s♦ t ❩ ♥♠t ♥t ♣♦t♦rsst s ♣♦st t♦♣ t rs r t 2 ♣rs♥s ♥♦t sr s r s♣② s♠ rs t♦♣ ♥t♦♥ ♣rs ♦ t♦ rt ♦♣♥♥s t♥ t 2 ②r ♥ ♦rr t♦ ♣r♦ rtr ♠t♦♥tt ♥ t ♦♦♥ st♣ ❱ s t ♣♦t♦rsst s ♥ ts st♣ s ♥tt ♦r♥ ♦♥ ts s r♠♥ tr t ♣ttr♥♥ trrs t ♥♠t 2 ♥st♦♥ ②r s r♦rq♥② s♣ttr ♦♥ t s♠♣ s♥ t♦rr ♥tr♥t♦♥ ♥ s♣ttr♥ st♣ t ♦ r♦♣♥♥ ♠ ♣♦②♠rst ♠tr① P ♦ts t t♥♦ ♥r♦♦♠ s s ♦♥ ♥ ♦♦rt♦♥ t ♦s r♦♠ t r♦♣ ②r s ♣♦st r♦♠ s♥ 2 ♥ ♠tr trt ♣ ♣r ♥ ♠ ② r♦♠ t s♠♣ trt s ♣rs♣ttr ♦r ♠♥ts ♦r ♣♦st♦♥ ♥ ♦rr t♦ r♠♦♥② ♦♥t♠♥♥ts s♠♣ s r♦tt r♥ t r♦t ♥ ♦rr t♦ ♥sr ♥♥♥ ♥♦r♠t② ♦ t ②r ♣rssr ♣r♦r t♦ t ♣♦st♦♥ s t♥t 10−6 ♠r r♥ r♥ t r♦t t s r♥ 1.1 · 10−3 ♠r ♥r♦♥ ① ♦ s♠ ♣♦st♦♥ s♣ ♦ s ♥ t t♥ss r♠sr ♥ t rt♠ t qrt③ r②st ♠r♦♥ r♥ t s♣ttr♥♣r♦ss t s♠♣ t♠♣rtr ♥rs ♣ t♦

t♦ t♦ t 2 ♠t s♦♥ t♦ s♦♠ ♠trs trs♦♥s ♦ ♥♦t♥ ♥r s t♦ r♠♦ t ♣♦t♦rsst ♥ t 2 r♦♠ t♦♣ t ♥t♦♥

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r ♠t ♣rs♥tt♦♥ ♦ t t♦r♣② st♣ ♥t ♣♦t♦rsst tr ts st ♦♣♠♥t t 2 s♣ttr♥ ♣♦st♦♥ s♠t ♦ t s♠♣ tr t t♦ ♣r♦ss ♥♦r♠② s♠tr♥s♣r♥t 2 ♦♦rs ♦♥ r tr ♥ t t♦♣ ♥ ♦rr t♦ s♦ tttr r r♥t ♠trs ♥r♥t

♣rs ♥st t s♠♣ s t ♥ t t♦♥ t ♦r t st ♦rs t♦ t ♣rs♥ ♦ t rsst ♦r♥ t t♦♥ tts t ①♣♦s ss ♦t rsst ②r tt ♥♦t ♥ ♦r ② 2♥ ss♦s t ss♦♣♦t♦rsst s t♦ r♦♠ t s♠♣ sr ♦♥ t t 2 t♦♣ tsrt♥ ♦♣♥♥s ♥ t 2 ♥st♦♥ ②r

r t ①ss t♦ ♦ t ♣sst♦♥ ②r ♦r♥t♥ r♦♠ tt♦r♥ ss ts ♥♥t r♠♦ r♦♠ t tr♦ r t ♠♣t♦ t ♣♥♦♠♥ ♦♥ t ♥ stt ♦ t s♠♣ ♦ 2 rt② t♦♣ t♥t♦♥ ♥ t ♠ ♥ t ♦♥ rt② ♦♥ ts t ss s♦rtrt♥ ♦ tss s t rr♥t ♦s rt② t♥ t t♦♣ ♥ t ♦tt♦♠ tr♦s

t♦r♥ ss ♥ s♦♠ ss t t♦ ♣r♦ss s t♦♦ s♦ ♦r ♥♦ts♥t ♥♦ t♦ r♠♦ t ♣♦t♦rsst t t 2 t♦♣ ♥♥② ♦st♥r t♦ ♣r♦ss s s ♠♦st② ② ♥♦rrt ♥t♦♥ ♦ t ♦r♥

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r♥ t ♣♦t♦t♦r♣② t t ♣r♦♠ s s♦ ♥♦t t♦ rt t♦ ♥♦ t ♣♦t♦rsst ♥ s ss ♣ t♦ ♦♥ s♦♥ s♦rt trs♦♥ ♣ss r s ♣r♦r rst② ♥rs t t♦ s♣ t s ♥ ♥sr 2

t♦ r♦♠ t s♠♣ sr s s r♠♦ s strt♥ r♦♠ t s♦ t 2 ②r s ♥♦r♠② r r♦♠ t r ♦r tt♦r♥ s ♣r♦r♠ r♥ t st♣ t t♦r♥ ♦ ♦s t♦ tt s♠♣ r♦♥ ♥ t ♠② ♦♥t♥ rsst rss t♦ r♣t♥st♦♥ t 2 s ♣rtr② r t tt ♣♦♥t ♥ t 2 t♦ ♠②ts ♣r♦ r♦♠ t s ♥ s t 2 t♦ r♠♦ r♦♠ t s♥st r ♦r ts rs♦♥ t t♦r♥ st♣ s s ♦♥② rs♦t♦♥ ♦ t ♣ttr♥ ♣♦t♦rsst ♦ ♥♦t ♦t♥ t♦t t

P ❱ t③t♦♥

r t♦r♣② st♣ ❱ s♠ t ❩ ♣♦t♦rsst trst ♦♣♠♥t ♠t ②r ♣♦st♦♥ ♥ strtr tr t t♦ ♥ t t♦♣ ♣tr t s♠tr♥s♣r♥t r ♦♦r ♦ t ♣♦t♦rsst sst② tr ♥ ♦rr t♦ s♦ tt tr r r♥t ♠trs ♥r♥t

❲t t t ♦♥tt rs ♦r ② t 2 ♥st♦r ♦tt♦♠ tr♦ss ♣s ♥ ♦♣♥♥s t♦♣ t ♥t♦♥s r♠♥ ①♣♦s ♠t③t♦♥s ♥② ♣r♦r♠ s s ♦♥ ♥ s♠r ② t♦ t ♦r♠r st♣ s♥t s♠ ❩ ♣♦t♦rsst ♦♥② ts t♠ t r♠♥♥ rsst s ♣rsr ♦r t s♠♣ sr ①♣t t rs r t ♦♥t ♦♥tt ♣s r♠♥t t♦ ♣♦st s♠♣ s t♥ ♠♦ t♦ t Pss②s ♠t ♣♦rt♦♥ s②st♠ r ♥♠♥♠ ②r s♣♦st ♥r s ♣rssr ss t♥ 9 · 10−7 ♣♦st♦♥ s♣s♦r ♥ r s ♥ s rs♣t② trrs t s♠♣ ♥r♥tt t♦ ♣r♦ss ♠ sr t ts st♣ s r ♣♦t♦rsst rs t♦ ♠♠♦r s② t♥ t s♠ ♦♥s trrs ♦♥② t ♠t ♦♥tts r♠♥

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r ♥ ♣tr ♦ ♣rt ♦ ♦rrt② ♣r♦ss s♠♣ t♠trs rs♣t ♦♦rs r strt ♦r t ♥♠ t2 t ♦tt♦♠ tr♦ ♦r t t 2 ❨♦ ♠t②r ♥t♦♥ ♣rs ♥ ♦r tr♦ ss ♣s ♥ r② s♥ ② st♦♥t♦rs ♣rss♦♥s ♥ t ②r ♦♠♣r t ♥

♦♥ t s♠♣ s ♣rs♥t ♦♥ ♠♥♠ s ♣♦st s t ♦r♠t③t♦♥ ②r t♦ ts ♦♦ s♦♥ ♣r♦♣rts t♦ t ♣sst♦♥ ②r ♦ s ♦s♥ s t ♥ t♦♣♠♦st ②r s t s r② r t♦ ♦①③ ♣tr♦ t t♦r♣② ♥ rst s s♦♥ ♦♥ t

sst♥ ♣r♦♥ ♥ ♦♥tt ♠♦s

s tr r ♥t♦♥s ♣r ♣r♦ss s♠♣ t s ss♥t t♦ ♥ ♦t ♦♥s ♦ st ♦r rtr ♠sr♠♥ts s ♥t rsst♥sts r ♣r♦r♠ t♦t ♦♥♥ t s♠♣ ♦r ♣♥ t ♥ ♠♥t s s ♦♥ s♥ r ss P ♣r♦r t ♦♥ ♥ ♣r♦r♠q ♠sr♠♥ts ♦♥ ♠♥② ♥t♦♥s

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♦♣♦♥t ♠sr♠♥t ♦ t ♦♥tts

rsst♥s ♦ t♦♣ ♦♥tts ♥ ♦tt♦♠ tr♦s r rst ♥ t st♥r t♦ ♣♦♥t ♦♥rt♦♥ ♥ ♦rr t♦ ♥sr tt tr rsst♥s r s♥t②s♠ s♦ t② ♦ ♥♦t ♦rs♦ t ♦♥s ♦ t ♥t♦♥s ♦♥r♥♥ s♠♣s♣r♦ss t t ♦♣t ♣♦t♦t♦r♣② t t♦♣ ♦♥tts rt♦♥ ♦♥t♦♥sr♥ t ♦rt st♣ r t s♠ ♦r t s♠♣s ①♣t t ♣♦st♦♥ ♣rssr ♦ tr ♥s♥♥t② s t rst t② ②s ② r♦♥10Ω rsst♥ ♦ t ♦tt♦♠ tr♦ ♣♥ rt② ♦♥ t s♠♣strtr ♥ ts t♥ ♣t tr t rst t♦r♣② st♣ t t s② ②t♥ Ω ♥ Ω ♥ s ♦ ♥st s♦♠s♣ttr♥ ②r ②st♠s♠♣s ♦t ♦tt♦♠ ♥ t♦♣ tr♦s r st♦♠♣♦st s♦ tr rsst♥sr ♠♦♥ s♠♣s t t② rr② ① Ω

♦r♣♦♥t ♥t♦♥ st②

r ♠t strt♦♥ ♦ t ♣♦♥t ♦♥tt ♠sr♠♥t ♦ts ♣♣ t♥ t♦ ♦♥tts ♦♥ ♣♣r ♥ ♦♥ ♦r ♥ t rr♥t ♦ s♠sr t♥ t ♦tr t♦ t② t rr♥t s♥s s t rr♥t ♦♥tr♦ t r♦ss♣♦♥t ♦♥② ♥ ts s t ♠♥t t♥♥ ♥t♦♥

♥ t ♦♥tt rsst♥s r ♥♦♥ t ♥t♦♥ t♠ss ♥ ♣r♦ ♥t ♣♦♥t ♦♥rt♦♥ s s ♦r♠ ♦ ♠sr♠♥t s t ♥t♦r t t♦♣♦♥t ♠♦ tt t ♠srs ♦♥② t rr♥t ♦♥ tr♦ t r♦ssst♦♥ ♦♠tt♥ t rsst♥ ♦ ♦♥tts s ♦s ♣rs ♥t♦♥ st② ♥s ②s ♣rrr rtr t♥ t t♦♣♦♥t ♠♦ ♦r ♠tt♦♥s ♦ ts♠t♦ ①st

t ♦♥tt rsst♥ s ♠ rr t♥ t rsst♥ ♦ t r♦ssst♦♥♥ ts s t ♥t♦♥ ♥t rsst♥ ♥ rtt ♠② ♠sr ❬❪t s ♦r ts rs♦♥ tt t ♦r tr♦ rsst♥ s ②s ♠ t♦ s♦ s ♣♦ss ② ♦r ♥st♥ ♥♦t ♦rt♥ t ♦r tr♦ s sr ♥st♦♥ ♦♥tt rsst♥s ♠② s♦ rst r♦♠ tr ♠♥♠ ♥ ss ♦ ♥t♦♥s ♦r t r ♦ t ♦♥tts ♦ ♥♦t ♣t② t♦ ♠sr ♥ t st♥r ♣♦♥t ♦♥tt ♦r ♥ ss ♦ ♦♥

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r strt♦♥ ♦ t ♣♦♥t ♦r ♣♦♥t ♦♥tt ♠sr♠♥t ♣r♦r♠ ♥ s ♦ t tr♦ ①ss rsst♥ ♦r ♠ s♠t② ♠rs t r rsst♥ ♦ t t♠♦st ♣rt ♦ t tr♦ ♦♥ t ts ♦♥tt r s t♦ t ♥t♦♥ rsst♥

♦♥♥t♦r ♦♥② ♥ t ♣♦♥t ♦♥rt♦♥ s♦♠t♠s rrr t♦ s t ♦r♣♦♥t ♦♥tt

sst♥r ♣r♦ts

♥t♦♥s rt r♦♠ t s♠ s♠♣ r ①♣t t♦ s♦ s♠r rtrsts r♦♠ ♥♦♠♥ r♦t st♥♣♦♥t t ♥st② ♥ q♥t③t♦♥ tss t ♦♥② r②♥ ♣r♠tr s tr r s rsst♥s ♦ ♥t♦♥s t♥t s♠ r♦ r ①♣t t♦ ♦ t s♠ ♦rr ♦ ♠♥t t♦ tr s♠s③ s♠r ♥t♦♥s s♦ s♦ ♠ r s ♦ rsst♥ ♥ ♦rr t♦ ♥♦t tr ♦sr rsst♥s r sttst② ♦rrt tr sst♥r♣r♦ts r ♦♠♣r t s ♦♦s

RA = R ∗ A[µΩm2]

♦rrt② ♣ttr♥ ♥t♦♥s s♦ ①t ♥ ♥♦r♠ ♣r♦t ♦r ts♠♣ ♦r s ♣rs♥t t♥ t s♠♣ ♥②ss s♠ ♥t♦♥st♥ t♦ s♦ tt s ♠ r t♥ ①♣t s s s ts♠st µ♠ ♥ ♠tr ♥t♦♥s r r t♦ ♦t♥ t♦ t t t♦r♣②rs♦t♦♥ ♥ tr s③ s s② s♠r t♥ ①♣t t♦ t s♠ s③ ♥st rt♦♥ ♥ t ♥t♦♥ s③ s t♦ t r ♥ ♥ t ♣r♦t ♦rrt② rt ♥t♦♥s r ss♠ t♦ t ♦♥s ♥ tr t♥ t s♠ ♦rr ♦ ♠♥t st② ♦ t♦ q② st s ts r tr s♦rt r② ♦ ♦r ♦♣♥rt t ♦♥s r♦♠ t ♣♦t♦rsst s ♥♦t r♠♦ tr♦♦t t t♦ ♣r♦ss s♥ ♥♦rr♥t ♦ ♥ s♠ ♣ttr♥s ♦ t ♣♦t♦rsst r t t♦ r♠♦ r♥♠r ♦ t s♠st ♥t♦♥s ①t t ttr ♣r♦♣rts

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♠♦♥ s t

r ♠♦♥ s tt♥ ♠♣t ♦♥ t rsst♥ r ♣r♦t ♦ sr♥t♦♥s sqrs ♥ r rs s♦ ♣r♦ts ♦ ♥t♦♥s ♦r ♥tr tt♥ t s♠♣ rs♣t②

♦r ♥② ♥ ♠sr♠♥ts t s♠♣ ♥s t♦ ♠♦♥t ♦♥ tt rt ♣ s st♦♥ ♦r ts ♥ ♦rr t♦ ♦ s♦ ts s③ t♦ r ② tt♥ s♦ t ♦ t ♦♥ t ①♠♠ s♥t ♣ r ♦ ♣r♦ttt s♠♣ sr r♦♠ ♥② ♦♥t♠♥t♦♥ rst♥ r♦♠ t tt♥ ts srs ♦r t t ❩ ♣♦t♦rsst t♦t ♥② rtr ♣r♦ss♥ ♥ ❲ ♣rs ♠♦♥ s s s ♥ ♦rr t♦ r♠♦ t ♦tr ♣rts ♦t s♠♣ r♦♥ t r t♥ t ss♥t ♣rt s t ♥ t♦ ♦♥ t ♦r③♦♥t s♣r t♥ t t♦♣ ♥ ♦tt♦♠ s ♣♦t♦rsst s t♥r♠♦ ♥ t st♥r t♦♥ ♥ t♥♦ t t♦t t trs♦♥s s♥t♦ ♦ s♦ ♦ t t 2 ♥ s♦♥ ❲ ♦♥r♠ tt ttt♥ ♣r♦r ♦s ♥♦t t t ♣r♦♣rts ♦ t ♥t♦♥s

r Ptr ♦ t t s♠♣ ♠♦♥t ♦♥ t rt ♣ t ♥t♦♥s♦♥ t ♦tt♦♠t tr♦ ♦♥ ♥ t ♦r♣♦♥t ♦♥tt ♠♦ ♦♥♥ rs♦♥♥t♥ t ♣ ♥ ♣s r s

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P ❯ ❲

♥♣ ♠♦♥t ♥ r♦♥♥

s♠♣ t ♥♦ ♦ ts ♦r♠r s③ ♠② ♥ ♦♥ t♦ t ♣ ♦♥r s t♥ t t♠r♠ ♦ ts tss s t ②♦♥ tr♠♦s♦♥ ♦♥r ♥ ts ♦♥♥ t♥q t ♠♥♠ r s t♦ ♦t s♠♣ ♥ ♣ ♦♥ ♣s ② ♣rssr ♥ trs♦♥ ♦st rt♦♥ ♠t♦ ♦s ♥♦t rqr ♥② t ♥ ♦rr t♦ rt t ts t s ♣rrr t♦ ♦♥♥ s s♦ t t t♥♦ ♥r♦♦♠ ♥ ♦rrt♦ ♦ ♥② str② rr♥ts t♥ ♦ ♠ t ♥st♥ rrr t s♠♣s tr② r♦♥ r♥ t ♣r♦ss s♠♣ ♦♥ ♦♥ t ♣ ♥ t♣♦♥t ♦♥rt♦♥ s ♣rs♥t ♥

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♣tr

st② ♣♣rts ♥

t♥qs

s ♣tr srs q♣♠♥t ♥ s♦♠ ♦ t ♠sr♠♥t t♥qs st♥ t t♠r♠ ♦ ts tss t ♦♥♥trts ♦♥ t rt st♣ ♥ tst ♣ ♣r♦♣rts rst st♦♥ ♥ ♦ t s s ♥ ♦rr t♦ ♦t♥ I rtrsts ♥ ♦tt♠♣rtr ♣♥♥② ♠♣s st♦♥s ♥ ♦rtst♦♥ ♣rs♥ts t ♦♣t st♣s s ♥ ♦rr t♦ ♦t♥ t ♣♦t♦♠♥s♥♥ s♦r♣t♦♥ s♣tr

st♣ ♣ts

♦♥strt♦♥ ♦ t rt ♣ ♣rs♥t ♦♥ ♣ ♠s t ♣♦ss t♦ ♦♥♥ ♠sr ♣ t♦ ♥t♦♥s ♥ ♣♦♥t ♠♦ ♦r ♣ t♦ ♥t♦♥s ♥ ♣♦♥t♦♥rt♦♥ ♠sr ♥t♦♥s sr t ♦r tr♦ s ♠s ♥t♦♥♥ st♦♥ s♠♣ r♠♦ r♦♠ t ♣ s s② ♥♦t ♣♦ss t♦t♠♥ t t ♣♦sst② ♦ ts ♠t♣ r♦♥♥ s rt ♥t♥ t ♥♠r ♦ ♥t♦♥s ♣r s♠♣

rt ♥ ♦s t♦ ♣r♦r♠ ♠t♣ s♠ ♦r ② t♦♠t ♠sr♠♥ts q♣♠♥t ♦s t s♠♣ t♦ ♠♦♥t t♥ t r②♦stt ♣t♥ tr♦♠♥t ♦s t♦ ② t ♠♥t ♦ ♠♦r t♥ r②♦stt ♥ t q ♠ r♦♠ ♥ ①tr♥ s♦r ♥ ♦♦♦♥ t♦ ss t♥ t♥s t♦ ts t♦♠r s♥ r♥ t t♠ ♦ tstss st♦♠♠ ♣♦r s♦tr s ♦♣ ♦s t♦ ♣r♦r♠ t♦♠t t♠♣rtr♣♥♥t ♠sr♠♥ts t st t♦♠t st♥ ♠♦♥ s ♣♣ s ♦t ♥ ♠♥t s ♥t♦tr♥s♣♦rt♠sr♠♥ts ♥ ♣r♦r♠ ♦r ♠t♣ s♠♣t♦ ♥s ♥② rr♥t♦t rtrsts r t♦r ♥rst♥♥ t t ♥r② s ♥ ♦t♥ ♦r r♥t t♠♣rtrs ♥ rt ♠♥t③t♦♥ ♦r♥tt♦♥s ♦ trr♦♠♥t tr♦s ♥t② s♠t♦♠t ♠t♣①♥ s ♣r

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P ❱ ❯❨ PP❯ ❯

t♥ t rt♦♥ ♦ ts tss t♦ t ② t♦♠t ♥t♦♥t② t ♦r ♦❯ s♠r ♦ st st♥ t♥ ♥t♦♥s r♥ t ♠sr♠♥t ♥♥ sttst ♦♠♣rs♦♥ ♦ t ♥t♦♥s ♦r ♥r ♦♥t♦♥stt ♠t ♦trs ♠♣♦ss t♦ ①t② r♣r♦

①♣r♠♥t tr♠♥t♦♥ ♦ t rrr ♣♦

t♥t ♥s♣

♦♠♣tt♦♥ t♥qs t♦ tr♠♥ rrr ts s ♦♥ t r♥♠♥s ♦r♠♠♦♥s ♦r♠s ♠♥t♦♥ ♥ st♦♥ sr r♦♠ sr♦s r trt② ♦♥② ♦r t rrrs Prs♥ ♦ ♠t♣ t②♣s ♦ ts s st♦♥ t♦♥ ♥tr ♦① sts ♦r ♥ tt♥ ♣r♠trs sss ♥ rs t♦ sr♣♥② t♥ rsts ♦ t♦♥s ♥ rt②

rt ❱ rtrsts ♥②ss

♥ rr♥t♦t rtrsts r ♥♦r♠t♦♥ rr♥ ♦t t ♦♥t♥ rss s♥♥t② t V/e s t ♥r② ♦ t ♦♥t♦♥ ♥ ♦r t rt② t♦ t r♠ e ♥ t tr♦♥ ♠sss ♣♣r♦ s s ♥ ♥②ss ♦ rrrs ♥ st♦♥

g ♠t♦

♦tt♥r t ♣r♦♣♦s t♦ ①♣r♠♥t t♥qs t♦ ♠sr t rrr t♦♥ s ♦♥ t ♦rt♠ rt ♦ ❱ rs ♥ ♦♥ s ♦♥ t t♠♣rtr ♣♥♥ ♦ ts rs ❬❪

r ♠t r♣rs♥tt♦♥ ♦ t rrr ♦r ♣♦♥ ♣♣②♥ s s ♦r ♥ r t♥ t rrr t rs ♣t t r♥♠♥stt♥ t② ❬❪

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P ❯

r s♠t② s♦s t ♦r ♦ ♣♦t♥t rrr t qts t ♥tr tt s ♦ts t t♦ r♥t ①tr♥ ♦tr♥ ss t ♣♣ ♦t V +dV s ♦r t♥ t rrr t t rrrr t rss ♦♥ t t dV ♦t ♥rs t ts t r♠♥s♦♥st♥t ♦r t V + dV ①s t rrr t t dV s ♦t♥r♠♥t ss ♥♦t ♦♥② rs ♦ t t r rrr t t ♦ tst s ♥ t♦ ♥ t♦♥ ♠♦r ♣r♦♠♥♥t rs ♥ ♥t♦♥ ♦♥t♥

I ♠t♦

s♦♥ ♠t♦ ♣r♦♣♦s ② ♦tt♥r t s ①t♥s② s t♥ tt♠r♠ ♦ ts tss t rqrs ♣r♦r♠♥ rr♥t♦t rtrsts tt♦ r♥t t♠♣rtrs s t r♠ strts t♦ s♠r ♦t t t ♥rs♥ t♠♣rtr t rr♥t t♥♥s ♠♦st ♥t② ♦r ♦ts st ♦t rrr t ♦ t ♣♦st② s tr♦ ♥♦r♠③ t♠♣rtr♣♥♥ ②s ♥rs s r♦♥ t rrr t ♦ t ♣♦st②s tr♦

I(V ) =I(V, T2)− I(V, T1)

I(V, T1)

♠sr♠♥ts ♦♥ ♣r♦r♠ ♦♥ r♥ ♦ t♠♣rtrs IT1−T2

IT2−T3 IT3−T4

♥ s♦ ♦♥ ♥ ② ♥st ♥t♦ t tt♦♥ t♠♣rtr ♥♦t ♦ rt♥ ♠♥t♦tr♥s♣♦rt trs ② r rt I ♦r Irel s♦♣♣♦s t♦ s♦t I ♦r Iabs srs ♥ t t s ♣♦tt ♥ rr♥ t♦ ① s② ♦ t♠♣rtr

❱♦tt♠♣rtr ♣♥♥② ♠♣s

ts tt ♥♥ t ♠♥t♦rsst rtrsts ♦ t st s②st♠s rstr♦♥② ♣♥♥t ♦♥ ♦t ♥ t♠♣rtr rt♦♥s ♥ ♥ ♦rr t♦ ♥rst♥ ts ♣♥♥s ♦♥ ♥s t♦ ♥②③ t♠ t♦r♦② ♥s t♦ t♣rt t♦♠t♦♥ ♦ t rt st♣ ♠sr♠♥ts r♥ t ♥ ♣rt ♦ tt♠r♠ ♦ ts tss ♠t♣ ♥t♦♥s ♦ st ♣♦♥ s♥ srs♦ ♦t ♥ t♠♣rtr s♣ s ♦ t♦ rt t♦ ♠♥s♦♥ ♦tt♠♣rtr ♣♥♥② ♠♣s ♦ rsst♥ ♠♥t♦rsst♥ ♥ ♦t s♦t♥ rt I s

♣t sts

♦♣t sts ♦ ts r ♣r♦r♠ ♥ ♦r r♦♣ t♥s t♦ ② ♠rr s s ② t ♦t r♦♣ t♥ ♣rt♠♥t ♣tq trr♣ t

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P ❱ ❯❨ PP❯ ❯

♥♦♣♦t♦♥q r♦♣ s rst ♦ ♥ ♥tr♥ ♦♦rt♦♥ t♥ tP ♦t r♦♣s ♦♣rt st♥t t②♣s ♦ ♦♣t st♣s t r♥t ♣ts st♣ ♦♣rt ② ♠rr ♦♥sst ♦ ♥♠ ①tt♦♥ ♥t ❨ ♥♦②♠♠ ♦♣ ❨3512 sr t ♠❲ ♣♦r r ♦t ♦♣t sts r ♣r♦r♠ ② tt rt r♦♠ t ♦t r♦♣ s♥t ♥♠ sr st♣ ♣ ♦ ♣r♦r♠♥ t♠♣rtr ♣♥♥t sts② ♣♥ s♠♣s ♥ t r②♦stt ♥ ♥ t t t q ♠ ♦r♦r s♦r♣t♦♥ s♣tr st♦♥ r ♦t♥ t ❯❱❱s Pr♥♠r♠ s♣tr♦♣♦t♦♠tr ② ❲ ♦ r♦♠ ♦ t♦♥ ❯♥rst② s rst ♦ ♥ ①tr♥ ♦♦rt♦♥

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Prt

st②

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♣tr

r♥st♦♥ ♠t ♦①s

r♥st♦♥ ♠t ♦①s r ♦ rt ♥trst t♥ t ♦ s♣♥tr♦♥s t♦tr ♣♦t♥t ♠t ♣r♦♣rts s t ♦♥s r♣♦rt ♥ 0.7r0.3♥3♦r♦r t♦ ♦ ♥♣ ♦ r3 ♥ 2 r②sts r♦♥ ❱ t②r ♥♦t s t t♦ st② ♦♣t② s tr ♦♥tr♣rts ♦r ♣ ❯❱ sr s ♥ ❯s♥ rq♥s ♥♦ t♦ ♦r♦♠ t ❱ ♣ ss s♦r♣t♦♥ ♥ ♠♥s♥ r♦♠ srr♦♥♥ ♠♥ts ♥ t s ♦tr♥st♦♥ ♠t ♦① rrrs st② t ss s ♣rs♥t t♦ ♠ ssr ①t♥t

♥ s ♦ ①♣r♠♥ts ♣r♦r♠ ♦♥ tr♥st♦♥ ♠t ♦①s s♦♥ s♠♣ ♦ ♥ s r♦♥ t♥ ♣r♦ss t t st♥r t♦r♣②♣r♦rs sr ♥ st♦♥ ts ②♥ ♣ t♦ s s sr st ♥ tr♠s ♦ tr ♣r♦ts ♥ ♠♦♥ t♠ rt♥ ♥♠r s♦s♥ ♦r ①t♥s sts

tr♦♥t♠ tt♥t

s ♠♥t♦♥ ♥ st♦♥ rrr ♦♠♥ t tr♦s s♦t st s s♦ r ♦r t qst♦♥ r♠♥s tr t s ♣♦ss t♦ ♦t♥ tr♥st♦♥ ♠t ♦① s ♠♥t t♥♥ ♥t♦♥s t s♠♣tr♦s s♦ tt ♦♥ ♠② ♦♠♣r t t♦r② ♠♦r s② ❬❪

♦♣t tt②

♥ ♦rr t♦ ♣ t ② ♦r tr sts ♦♥ t t♠t s♣♥ ♣♦r③tr♥s♣♦rt ♥ ts ♣r♦♣rts ♣♦♥ ♠♥t♦♥ ② sr t sr ♠sr♠♥ts r ♣r♦r♠ s♦s t ♣♦t♦♠♥s♥ ♦ ♥♦♥rrt ♥r+ rrt r3 r②sts ♠♥t t ♥♠ sr ♥♠ ♣ ♦ ♥♦♥rrt r②st s ♦♠♠♦♥② ♦sr ♥ st♦♦♠tr r3 ♥ rts r♦♠♥t♦♥ ♣r♦ss ♦ ①t ♦s ♥ tr♦♥s t str♣♣ ①t♦♥s ❬ ❪ ♥

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P ❳

r ♠♣t ♦ r+ rrt♦♥ ♦ r②sts ♦♥ t ♣♦t♦♠♥s♥s♣tr t s ♦t tr ♠♥t♦♥ t t ♥♠ sr

r P♦t♦♠♥s♥ s♣tr ♦t r♦♠ r②st t ♦r ♠♥ts ♥ ♣♣ t ♥♠ ♦r ♥♠ s ♥s r♣rs♥t ♣♦st♦♥s♦ ♣s ♣♣r♥ ♦r s♠♣s ♣rs♥t ♦♥

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t ♦tr ♥ t ♥♠ ♣ ♦ t rrt r②st ♦rrs♣♦♥s t♦ t r♦♠♥t♦♥ t♥ ♦♥t♦♥ tr♦♥s ♥ ①t ♦s ♦♥t♦♥ tr♦♥♥st② ♥rss t ♥rs♥ ♦①②♥ ♥② s t♦ r ♥♠♠♥s♥ ♥t♥st② ❬❪

♥ t♦♥ st② s ♣r♦r♠ ♦♥ s♠♣ rrt ♦r ♠♥ts s♠♦rt② t s♠♣ s♦s ♣rt trs ♦ ♦t t r♥ ♦♥ ♥ t♦♥ ♥♥ ♦r ♠♥ts ♥ ♣rt ♦ t s♠♣ s ♣♣ t♣♦rt ②r ♦ ♥♠ rs t ♦tr s ♣♣ t ♥♠ ss♦♥ ♦♥ t t P s♥ ♥ r ♥ tr♦ t rt② t♥♠ ②r ♦ ♦

r ♠♣rtr♣♥♥t ♣♦t♦♠♥s♥ s♣tr ♦ r②st rrt ♦r ♠♥ts ♥ ♣♣ t ♥♠ ②r t s ♦t trt ①tt♦♥ t t ♥♠ sr

①♣r♠♥t ♦ t♦ st♠t t t♥ss ♦ t t♦♣ tr♦ s ss♥t ♦r ♣♥♥ tr ①♣r♠♥ts ♥♦♥ ♠♣t ♦ t sr t ♠♥t♦♥ ♦ ♥t♦♥s ♦♥ tr tr♥ s♣♥♣♦r③ tr♥s♣♦rt ♥ ♦rr t♦tr♠♥ tr t♠♣rtr♣♥♥t ♦♣t ♣r♦♣rts ♦ t ♣♣ r②st♦ ♠sr sts t ♦ t♠♣rtr r ♣r♦r♠ ♦♥ s♠♣ rrt ♦r ♠♥ts ♥ ♣♣ t ♥♠ ②r s♣tr♠s♦s ♣ t ♥♠ ♣♦♥ ♦♦♥ ♦♥ t♦ s♣ts ♥t♦ ♥♠ ♥♥♠ ♣s ♦r♦r t ♣♦st♦♥ ♦ t ♠♥ ♣ t s ♥♠ rsttr s ttrt t♦ t r♦♠♥t♦♥ ♣r♦ss t♥ ♦♣ ♦r ①t

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tr♦♥s ♥ ①t ♦s tr♦ t rs t s♦♥ ♦♥ ♦rrs♣♦♥st♦ r♦♠♥t♦♥ ♦ ①t ♦s ♥ tr♦♥s ♥ str♣♣ ①t♦♥ s st♦♥

♦2r3♦2

r ♥ st ♠s t♥ ♦♥ t ♦ s♠♣ tr t ♦2♥♠ ♥ ssq♥t r3♥♠ r♦t ♣trs r t♥♦♥ t ❬❪ sstrt ③♠t ❬❪

♥ ♦rr t♦ st② t t♠♣rtr ♥♥ ♦♥ ts ♦r♠t♦♥ ♥ t ❬❪ s s ts ♥♥ ♦♥ t ♦2r3 ♥tr st t t♦2♥♠r3♥♠♦2♥♠♥♠♥♠ strtr s r♦♥♦♥ t sstrt ② t ♣s sr ♣♦st♦♥ t♥q ♥ ♦♥t♦♥ssr t♥ st♦♥ ♦r ♦2 ②r s r♦♥ t rst r3 rrr s r♦♥ t ♦ s♠♣ ♥ s♠♣ ♦2 t♦♣ ♠♥t ②r s r♦♥ t ♥ ♣♣ t r♦♥ t♥t♠ ②r ♥ ♦rr t♦ ♣r♦tt t s♠♣ r♦♠ ♦①t♦♥ ♣♦st♦♥♣rssr s ♠♥t♥ t 2 · 10−7 ♠r ♠sr♠♥ts ♣r♦r♠ ♦♥t ♦ s♠♣ ♦t tr t ♦r ♦2 ♥ t r3 rrr r♦t s♦♦rrt r②st♥ strtr ♦ ♥trs

♠r♦r②st♥t② ♦ ②rs ♥ tr rs♣t ♦r♥tt♦♥ r tr♦ rs♦t♦♥ tr♥s♠ss♦♥ tr♦♥ ♠r♦s♦♣② ♠sr♠♥ts rs t ♦r♠t♦♥ ♦ r② ♥♦r♠ ♥ strtr② sr♣ ♥trs ♦ ♥♦ t r3 rrr rrr t♥ss st♠t r♦♠ t ♣tr

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r rs♦t♦♥ r♦ssst♦♥ ♦ t♦2♥♠r3♥♠♦2♥♠♥♠ ♦ st t♦♣♠♦st ②r s ♥♦t s♦♥ ♣tr s t♥ tt ♦ s t t ♣♦♥t rs♦t♦♥ ♦ ❬❪

s 3.1± 0.2♥♠ t♦♠ strtr ♦ ♦t t ♦tt♦♠ tr♦ ♥ t rrrs ♠♦♥♦r②st♥ s ♦sr ♦♥ t s♣tr ♥ t ♦tr ♥ tt♦♣ ♦2 tr♦ s ♣♦②r②st♥ t t t♦♠ ♣♥s ♥♦t ♥ ❲ttrt ts t♦ t ♦ r♦t t♠♣rtr ♦ ts tr♦

♦♦♠t♠♣rtr tr♥t♥ r♥t ♠♥t♦♠tr ♠sr♠♥ts ♣r♦r♠ ♦♥ ♦t s♠♣s s♦ sr♣ rrs ♦ tr♦s ♠♥t③t♦♥s♥ ♦r s ♦ ♥ ♦r t ♦ st ♥ ♥ ♦r t st ♠♥t s ♣♣ ♦♥ t sstrtrt♦♥ s♠r ♥ rr ♦r s ♦rrs♣♦♥ t♦ t ♠♥t③t♦♥ st♥ ♦ t ♦tt♦♠ ♥ t t♦♣ tr♦ rs♣t② st rs ♦ts s ♦r t s♠♣ ♠② ttrt t♦ t ♥tr ♦①t♦♥

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r r♦♦♠t♠♣rtr ♠sr♠♥t ♦ t♦2♥♠r3♥♠♦2♥♠♥♠ ♦ ♥ ♠t②rs ♦♥ t ❬❪ ①s ❬❪

♦r t s♠ rs♦♥ t ♦ ♣♦st♦♥ rsts ♥ st② sr♣r r r♦♦♠ t♠♣rtr s ♥♦t ♦sr ♦r t s♠♣ t

♦ ♦♥ ② ♣♦st rsst♥ r ♣r♦t ♦ts ♥t♦♥s s ♦ 105µΩm2 r♥ st♥ s r ♥ r♠♥t tt ②strss rs ♦t♥ r♦♠ ♠sr♠♥ts

r r sr rs♦♥s ttrt t♦ t ♦ ♦ t t♥♥ ♠♥t♦rsst♥ rt♦ ♦r t s♠♣ ♥ t r3 rrr s r♦♥ t t ♦rt♠♣rtr ♦♥ ♥②③s t rrr ♥ strtr t s s② t♦ s tttr♦♥s tt ♦♠♥♥t② t♥♥ r♦ss t rrr r ♠♦st② ♦ t ∆2′ ♥ ∆5

s②♠♠tr② ♥ t s ♦ r♦♥ tr♦s ♥s ♦ ts s②♠♠trs r♦sst r♠ ♦r ♦t ♠♥♦rt② ♥ ♠♦rt② tr♦♥s ♣♦♣t♦♥s rst♥ ♥♣♦♦r tr♥ ♥ t ♦tr ♥ ♥ ♦t ♥s ♦ t ∆2′ ♥ ∆5 s②♠♠tr② ①st♦♥② ♥ t ♠♥♦rt② s♣♥ ♥♥ ♦ ♥ strtr ♦rs ♥s♥t② ♦tr ♦ ❬❪ ♠② ♥♦t t s ♥ ♦r ♦2 strtrs♦x1−x x = 0.5

♥♦tr t♦r tt ♠② r ♠♣t ♦♥ t ♦ rt♦ s t rrr strtr t t ♥tr s sr ♥ t t♦rt ♣rt t r3

♠♦♥♦r②st♥ rrr ♦♥sst ♦ tr♥t♥ r ♥ 2 ♣♥s s st♦♥

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r ♦♦♠ t♠♣rtr r ♠sr ♦♥t 20µ♠ ♥ ♠tr ♥t♦♥ ♣r♦ss r♦♠ t ♦♦2♥♠r3♥♠♦2♥♠♥♠ st❬❪

t♦ ♥ ①♣r♠♥ts ♦♥r♠ t ♣t① strtr ♦ t rrr t ♥tr t♦♠ st♣s r ①tr♠② r t♦ ♦ ♥t rs♦t♦♥ ♠r♦s♦♣② ♠ ♥♥♦t ♥t ♥sr s trtr s ♦♥② ♦♥ t②♣ ♦ t ♥tr tr♠♥t♦♥ ②r ♦r ♥♦t s s♦♥ ② ❱rr♥ t t s♥ ♠② ♣♥ ♦♥ t tr♠♥t♦♥ ②r ❬❪ s♠② t s ♥ t st s②st♠ ♥ t ♥tr ♠② ♦♥sst ♦ tr ♥ 2 ♠①tr ♦s ♣♦st ♥ ♥t s♣♥ ♣♦r③t♦♥s r ♦t♥ rst ♥ rt② ♦

rs♦♥ ♦r t t♥♥ ♠♥t♦rsst♥ s ♥♦t ♦sr ♥ t s♠♣ ♦ t rrr ♣♦st♦♥ t♠♣rtr ts ♦r t r ♥r②♦ t♦♠s r♥ t r♦t ♦rs t ♦① ♦r♠t♦♥ t t ♦tt♦♠ ♥tr♥♦t② t r♦♥ ♦① s ②♣♦tss s s♣♣♦rt ② s♦♠t rr ♦rs ♦sr ♦♥ t s♠♣ ♥ t ♦tr ♥ t ♦ s♥♦sr ♥ t ♦ s♠♣ ♠② rst r♦♠ t s♠ ♦①t♦♥ ss s t s♣rssr ♥ t P ♠r ♣r♦r t♦ t ♣♦st♦♥ s t♥ t 10−8 ♠r r♥s st♦♥

♥ ♦rr t♦ rtr ♦♥r♠ t ♦①t♦♥ ②♣♦tss t rr♥t♦t rtrst s ♣rs♥t rrr ts t ♦t ♥trs r t s♥ t

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r ♦♦♠ t♠♣rtr ❱ ♠sr♠♥ts ♦♥ ♥t 20µ♠ ♥ ♠tr♥t♦♥s r♦♠ t ♦ ♥ sts t ♥ ♦rrs♣♦♥♥ ♦♥ ♦t♣♥♥ ♦r t ♦ ♥t♦♥ rt ♦ ♠♥t♦rsst♥ s ♣rs♥t ♦♥ t ♥t♦♥ ♥♦t s♦♥ ❬❪

r♥♠♥ ♠♦ ❬❪ s t♠♣rtr♣♥♥t I ♠sr♠♥ts r ♥♦t t t t♠ r♥♠♥ t ♦ t t♦♣ ♥tr rrr t ♦r ♦t ♥ ♦ s♠♣s s♦ ❱ ♥t s ①♣t ♦r ♦ts♠♣s s tr ♣♣r ♥trs r rt ♥ t s♠ ♣♦st♦♥ ♦♥t♦♥s♥ t ♦tr ♥ rrr ts ♦ ♦r ♥trs r ❱ ♥ ❱ ♦rt ♥ ♦ ♥t♦♥s rs♣t② s s♦s t ♠♣t ♦ ♦①t♦♥♦♥ t ♦r ♥tr s rtr ♥♥ ♦r t t♠♣rtr rrr♣♦st♦♥ t t♥ss tr♠♥ ② t r♥♠♥ t ♦r ♦t s♠♣st s ♥♠ ♦s t♦ t ♦♥ ♦sr ② t ♥♠

s♣t t rt② ♦ s♥ ♦sr ♦♥ tt t s t rstt♠ tt t s♥ s r♣♦rt r♦ss r3 s ♥t♦♥s t s♠♣tr♥st♦♥ ♠t tr♦s ♥②ss ♦ t rsts ssts tt s♥♥t ♠♣r♦♠♥t ♥ ♣r♦♣rts ♦ ♥t♦♥s ♦ ♥ t♦ ②s ② ♦♥tr♦♥ t♦♠♣♦st♦♥ ♦ ♥tr r3 ②rs ♦♥ ♠② ♥sr t t♦♠ tr♠♥t♦♥ ♦t rrr ♥ ♠♥t t s♠t♥♦s ♣rs♥ ♦ r♥t s②♠♠tr② tr♥♥♥s rst ♥ r♥ ♦ ♣♦st ♥ ♥t ♠♥t♦rsst♥ rt♦s sttt♦♥ ♦ r3 t 2 ♥ ♦♠♣s ts ♥tr r♦♥♦① ♦r♠t♦♥ ♠② ♦ ② ♠♦♥ st♦①③♥ ♠♥ts ② ♥tr♦t♦♥ ♦ t♥ ♦t t ♦t ♥trs ♠② s♦ ♠♣r♦ t s②♠♠tr② tr♥ s t♦ r♠♦ ♥s ♦ t ∆2′ ♥ ∆5 s②♠♠tr② r♦♠ t r♠ ♦ tr♦s ♦t ♦ ts s♥r♦s r tt♠♣t

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t♥♠ ♦①

s st♦♥ ♣rs♥ts rsts ♦t♥ ♦♥ s s ♦♥ t tt♥♠ ♦① rrr s ♦ 2 ♥st ♦ str♦♥t♠ tt♥t s ♠♥② ♠♦tt ② t ♥ t♦♠t ♣♦ssts ♦ ♥ ♠♥② r♥t ♠ ♥r♦♥♠♥ts t ♠♥t♥♦♥♠♥t ♥trs t♦ ♣r♦st tr♠♥t♦♥ sss ♦ t②♣s ♦ s s♦♥ t 2 rrr r r♦♥ ♥ ♣r♣r t ♦♣t t♦r♣② t ♦2♥ ♦ ♥tr ②rs rs♣t②

♦22♦2

r ♦♦♠ t♠♣rtr ♠sr♠♥ts ♣r♦r♠ ♦♥ t♦2♥♠2♥♠♦2♥♠♥♠♥♠ s♠♣ ♦♥ tss② ①s

strtr ♦2♥♠2♥♠♦2♥♠♥♠ s r♦♥♥ t P ♠r ♦♥ sstrt ♥ ♣♣ t ♥♠ s♥♣♦st♦♥ ♦♥t♦♥s sr ♥ st♦♥ 2 ♣♦st♦♥ t♠♣rtr s♣t t sq♥t r♦♦♠t♠♣rtr ♠sr♠♥ts s♦ tt tst ①ts rs♦♥② ♥ ♥t♣r ♠♥t③t♦♥ stt rs♦♥ ♦r t ♣t s ♥♦t ♣rt② ♥ s t♥tt② ttrt t♦ 2 · 10−7 ♠r ♣rssr r♥ t ♦r ♦2 ♣♦st♦♥ t t t

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t♠♣rtr s♠r② t♦ t s ♦ s s sr ♥ t♦r♠r st♦♥

r ♠♣ ♦ ♦2♥♠2♥♠♦2♥♠♥♠s②st♠ ♥t♦♥s ♥② ♦r♥ ♥t♦♥s ♦t ♦ r s♦♥ t ♥ rtss ♦rrs♣♦♥ t♦ t t♦♣ ♥ ♦tt♦♠ ♣rts ♦ t s♠♣ rs♣t② ♦ tttr s tr ♥♥

st ♥r♥t t st♥r t♦r♣② ♥ tt♥ ♣r♦r tr rsst♥r ♣r♦ts r ♠sr s♥ t rss P ♣r♦r s♥ ♠❱ s ♥ t ♣♦♥t ♦♥tt ♠♦ ♣r♦t s r t♥ ts♠ ♦rr ♦ ♠♥t 105− 106µΩm2 ♥rs♦r♥ t tr ♦♠♦♥t②♦ t s rt② ♦ ♥♠r ♦ ♦r♥ ♥t♦♥s s ♦t♥♠♦♥ t s♠st ♦♥s t♦ µ♠ ♥ ♠tr t♦ t t t♦ ♣r♦ss♥ t ♦tr ♥ s♠ ♦r♥ ♥t♦♥s s♦ ♥s② ♣r♦t ttrsts r♦♠ t ♠t t♦r♣② rs♦t♦♥ ②♥ ♠♥s t r♦t sss sr ♥ st♦♥

s♠♣ s t♥ t ♥ ♦♥ ♦ t ♥t s s ssq♥t② ♥♥ t ♥ r ♦r ♥ ♦rr t♦ tr♠♥ t ♥♥♥ ♠♣t ♦♥ s②st♠♣r♦♣rts s s♦♥ ♦♥ t ♣♦st♥♥♥ ♥rs tr rsst♥s ② ♦rrs ♦ ♠♥t ♥ tr♥ ♥rs ② ♣ t♦ ♦♥ ♦rr ♠♦r ♦♦♥♦♥ t♦ t rsst♥ ♦ t ♥t♦♥s ♥rss st ♣♦♥ ♦♦♦♥ t♦

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r t ♥♥♥ ♥ ssq♥t ♦♦♦♥ ♠♣t ♦♥ t ♣r♦t ♦sr ♦2♥♠2♥♠♦2♥♠♥♠ ♥t♦♥s ♣r♦t ♥ t r♥ stt ♦ ♥t♦♥s ♥ tr ♥♥♥ t ♠srt r♦♦♠ t♠♣rtr r ♥ t r♥ t ♠♣rtr ♣♥♥ ♦ t②♣ ♥♥ ♥t♦♥ t 10µ♠ ♠tr ♠sr t ♠❱

tr t st③s ssts tr♠ tt♦♥ ♦ ♦♥t♥s♦ t s sr ♥ st♦♥

rrr ts ♦ s r tr♠♥ ② st②♥ tr rr♥t♦trtrsts t r♦♦♠ ♥ q ♠ t♠♣rtrs ♥ ♣♣②♥ t I ♠t♦♦r rsts r ♠♦♥ ♥t♦♥s ②♥ ♣♦♦r②♣r♦♥♦♥ s♣s ♦rrs♣♦♥♥ t♦ t ♥tr rrr ts r♥♥ t♥ ♥ ♠❱ rrs♣t t♦ tr t ♥ ♥♥ ♦r ♥♦t ♦♥② ♥♥ ♥t♦♥s s♦♥ ♦♥ t r I s♣s t s ♦ ♥rs r ♥♦t r♣♦rt♥ tr 2s ♥t♦♥s r t tr♦♥ rrr t s rtr st♠t t♦ ❱ ❬❪ ♥ t ♦tr ♥ t♦rt t♦♥s ♣rt t♣rs♥ ♦ ♦t ♦①②♥ ♥ tt♥♠ ♥s ♥ t r②sts t♥ ♥ ❱ ♦ t ♦♥t♥ ♥ ♠♥♠♠ ss♠♥ tt t rrr t♦ t♥ ♠ ♠② r ❬❪ t s♣s ♦sr ♠② rst r♦♠ ts♥s t s t♦ ♥♦t tt t ♦ r② ♣r♦♥♦♥ trs ♥ rsts♦ t I ♠t♦ s t②♣ ♦r ♥t♦♥s ②♥ ♦ s♥ ❬❪

♥t♦♥s r♦♠ t ♦22♦2 strtr s♦ ♥♦ t r♦♦♠ t♠♣rtr ♥ ♥ t ♥♦ s♥ ♥ t r♥ stt s ♦sr ♦rt ssq♥t srt♥ s st♦♥ t t ♦ t♠♣rtr ② ♥s

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r ♦r♠③ s♦t I ♠sr♠♥ts t♥ ♥ ♦♥ sr♥♥ ♦2♥♠2♥♠♦2♥♠♥♠ ♥t♦♥s t ♠trs ♦ 20µ♠ ♥ 30µ♠

♥ rsst♥s ♦♠♣♥ ② ♣♣r♥ ♦ t s♥ s rst s ♥♦tr♣r♦ ♥ ♦t t rsst stt ♥ t s♥ s♠ t♦ ♥♣♥♥t ♦ t ♣♣ s s♦s ♥ ①♠♣ ♦ tt tr s♦♥s ♦♥ s♥ t ♠❱ s♦ rsst♥ ♥rs ♦♠♣♥ ② t♣♣r♥ ♦ ♥t rs tr ssq♥t rt♥ t ts♠ ♥ s♥ ♦ s ts rsst♥ r♦♣♣ ♦♥ ♥ t ♠ ♣♦st rtr rt♥ t t s♠ r t♥ ♣♦st ss ♥ ts♦rr rst ♥ r♥♦♠ rsst♥ st♥ ♥ ♥♦ t s♥ s r②st♥s r♦♠ t ♥♦s ♦r s ♦sr ♦♥ s ♣r♦ssr♦♠ t s♠♣ ♦r t st ♠♥t♦rsst♥ s♥ ♠sr ♦♥ t♥♥ ♥t♦♥s s s♥♥t② ♦r ♣ t♦ ♥♦t s♦♥ t♥ t ♦♥♦sr r♦♠ tr ♥♦♥♥♥ ♦♥tr♣rts

♠r② t♦ t s ♦ r3s s t♦ t st ♦ ♦r ♥♦ ts♣r♠♥r② rst ♦♥sttts t ♦♥② ♥ ♦ rs♦♥② r r♦ss 2s ♥t♦♥s t tr♥st♦♥ ♠t tr♦s

♥ s ♦ ♦t ♥♦♥♥♥ ♥ ♥♥ s♠♣s ♦ t rrr tsr♦♠ ❱ ♥ ♦ ♦ts t tr♦♠rt♦♥ ♥ trr r♦♠

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r ♠sr ♦♥ s♥ ♥♦♥♥♥ ♦22♦2 ♥t♦♥t 20µ♠ ♥ ♠tr r♥ s♦ R = 14.7kΩ ♥ ♥♦s② rtrsts t ♥♦ s♥ ♥♦t s♦♥ srt♥ t ♦♥st②rs♥ s ♥ t ♦tt♦♠t♦t♦♣ rt♦♥ ♦ t tr♦♥s ♦ rst ♥ r♥♦♠rsst♥ ♥s t ♥♦ s♥ ♥t ♠❱ rt♥ ♥ t ♥t s ♦sr r sq♥t rt♥ t t s♠ ♠❱♦t ♦♥ ♥ ② r♥♦♠ rsst♥ ♠♣s ♥ ♥♦s② rtrsts♥♦t s♦♥ ♥t ♥①♣t ♣♦st r r rtr srt♥ ♥♦t rst ♥ ♥② r s♥

♠❱ sst tt ts 2 rrrs ①t ts r strtr② s♦rr ♠② ttrt t♦ t 2 ♣♦st♦♥ t♠♣rtr ♥s s②st♠s t s♦rr ♣②s r r♦ ♥ t s♣♥♣♦r③ tr♥s♣♦rt s ts ♥♦t strt ♦♠♦♥♦s② t rtr ♦s tr♦ ♦ t ♦♥rt♦♥s tt sr s ♦♥t♥ ♥♥s s②♠ t s♦s tt ts ♥♥sr rtr③ ② ♦ t ♣♦t♥t rrrs❬❪ s t s ♥ ♦r①♣r♠♥t s♠ t♦rs s♦ sr t ♣♥♥ ♦ t s♥ ♦♥t ♥rt ♣♦st♦♥ ♦ ♦♥t ♠♣rts rt② t♦ t r♠ ♥s ♦③ stt ♣♣rs t♥ t F ♥ F+eV r♥ t ♦♥trt♦♥ ♦tr♦♥s t♥♥♥ tr♦ t ♠② ♥rt t t♥♥ ♠♥t♦rsst♥ ❬❪ ss ♣♦ss ②♣♦tss ♥ t ♣r♦r♠ ①♣r♠♥t r t srt♥ trst ♦♣t♦♥ ♦ t stts t♦ ♥ ♥ ♥♦♥tr♦ ②

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♦2♦

r t ♥ ♦t rt ♣♥♥s ♦ t rt♦ ♥ tst ♦2♦ strtr

♥ t♦♥ tt♠♣t t♦ ♠♣r♦ t s♣♥♣♦r③ tr♥s♣♦rt r♦ss tr♥st♦♥♠t ♦①s s t♦ ♥tr♦ t♥ ♦t ②rs t 2 ♥trs ♥ ♦rr t♦ r t ♥tr ♦①t♦♥ s st♦♥ ♥ ♦ s♦ ♠ t♥tr sr t♦ ♥rst♥ ♥ tr♠s ♦ ts ♥ strtr ♥ t P ♠rt ♦2♦2♦ strtr s r♦♥♥t③t♦♥ rtrsts r ♦♥ t♦ s♠r t♦ ts ♦ t ♣r♦s②st ♦22♦2 s♠♣ ♦r s♣t t ♦rrt t♦r♣② ♣r♦ss♥ ♥ rt② r ♥♠r ♦ ♥t♦♥s s♦♥ ♦rrt s ♦t ♣r♦ts r②♥ t♥ 105Ωµm2 ♥ 106Ωµm2 s ♣r♦r♠ ♣♦♦r②r♦♠ s♣♥tr♦♥ st♥♣♦♥t r t♠♣rtr ♣♥♥ s s♦ s♠r t♦ tt♦ t ♦22♦2 ♥t♦♥s ♥ ♥♦♥ ♦ ♥t♦♥s s♦ t s♥ ♥ tr r♥ stt srt♥ t t♠♣rtr rst ♥ r♥♦♠ s♥ rrss t st ♦sr ♥ ♥ ♥♠♦s ♦♥ ♥♦♥♥♥ ♦ ♠tr 10µm2 ♥ ♥ s ♦t♥ ♥trt r♦♦♠ t♠♣rtr ♥♦r r♦♠ ♥♥ s ♥ t s ♣♦♦r ♣r♦r♠♥s r ttrt t♦ t s♠ rrr st♦rt♦♥s s ♥ t ♦22♦2s

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❯ ❱ ❲

♦♥s♦♥s ♥ ♠♦ t♦rs

♥ t ♦♥st sts ♦ r3 ♥ 2s s tt♠♣t t♦ rs♦ sr sss ♥tr tr♠♥t♦♥ ♦ r3 r ♥ 2 ♠①♥ ts ♥t♦♥ ②r③t♦♥ t t ♥tr ♥ ♥tr ♦①t♦♥ t♦ ♦①t♦♥ ♥t♣② ♦ t ♠tr ♦ s ♦2 ss ♦r s ♦♦♥t♠♥♥ts ♥ t ♠r t t ♥ ♣rssr ttr ♦♥ rts trt s ♣rssr ♥ t ♠r ♦r t t♦♥ ♦♠♣♦♥♥ t tt t♦r tr♦ s ♥♥ ♦r t rrr ♣♦st♦♥ ♥ t♦ ♥ r♣rssr rst♥ r♦♠ ①ss ♦tss♥ t♦ t rt ①♣♦st♦♥ ♦ t P♠r r♥ t ♦♥ ♦ s♠♣s tr t s ♥♦t ♦t s♣t t♥r♠♥t ♠♣r♦♠♥ts ♥ t strtr ♦ s♠♣s ♣rs♥t t s sst ttt s♥ ♦ t ♠r ♣rs t st② ♦ s t ♦r tr♦ ♦♥sst♥ ♦ tr♥st♦♥ ♠t ♥ ♦t s t ♦♥sq♥ rsr s rtt♦rs 0.7r0.3♥3 ❯s ♦ s t ♦tt♦♠ tr♦ ♦ rst ♥♥♦ ♦①t♦♥ ♦ t ♦r ♥tr ♦r♦r t 2♦ strtr ♦♣rs♥t ♥♦ sss ♦♥♥t t♦ t ♥rt♥t② ♦ t rrr tr♠♥t♦♥

r ♦♦♠ t♠♣rtr t ♥ ❯ rt ♠sr♠♥ts ♦♥♥♠ strtr rt t t P st♣ ♥ ❩ ♥♦t♦♦ ♥ ③r♦ ♦♦ ❯ ♠sr♠♥ts rs♣t②

♠s r♦♥ ② t r♦♣ s♥ t P st♣ r stst♦r②r♦♠ t ♠♥t st♥♣♦♥t ② ①t ♦ ♦r rrs ♥ r t♠♣rtr ♦ ♦t ♦r♦r t ♦♦ ♥ ③r♦♦♦ s♣r♦♥t♥ q♥t♠ ♥trr♥ ❯ ♠sr♠♥ts ♥♦t s♦ ♥② r♥ ♠♥s tt t r②st s r ♦ ♠♣rts

♦r s ♦♥t♥♥ ♦r♥ tr♦ r r② t t♦ ♦t♥ ss♥t② t♦ ♦①②♥ ♦♥t♥t sss t♥ t ♥♦♠♥② r♦♥ ♠tr

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♥ t ♦①②♥♥② ♦ ♠s strs t ♦①♥ tr♦♥tr♥sr ♠♥s♠ rsts ♥ rst② r ♦♥t♥ ♦ t ♠tr♥ s rs t♦ ts ♥st♥ ♥tr ❬❪ s tr♦r ♠♣s tt t s rtt ts ♠s s♥t② ♦①②♥t r♥ t r♦t ♥ r♠♥ s♥t②♦①②♥t r♦♠ t r♦t st t♦ t ♠sr♠♥t st ♥ t P♠r t ♠r ♦ ♦①②♥ r♥ t r♦t ♣r♦ t♦ ♥♦t ♥♦♥ ♦rr t♦ ts st♦♦♠tr②

s t rst t②♣ rsst♥ ♦ t ♥♠ t ♦tt♦♠ tr♦rst♥ r♦♠ t st♥r t♦r♣② ♣r♦ss♥ s ♦ Ω ♦rr ❱st♦♥t♥ s♣♣rs ♣♦♥ ♦♦♦♥ r♥ ♠♦r t♥ Ω r② t ♦ t s ♥♠sr t♦ s♥s♥ ♣ts ♦ t st♣♦s② s rsst♥s ♥♦t ♦ ♥② st② ♦ s

r ①♣r♠♥ts r ♣r♦r♠ ♥ ♦rr t♦ tr♠♥ tr t sst♦♦♠tr② ♦ t ♠tr ♦ ♣r♥t t t rst st♣ ♥rs♥ t♦①②♥ ♦♥t♥t r♥ t ♣♦st♦♥ s tt♠♣t ❬❪ ♦r trsst t♥ s②st♠ s ♥ ♦rr t♦ ♠♥t♥ t sstrt t♠♣rtr t r♥ t r♦t ♦t ♦①③ ♥t② t♦ ts r♦♥ ♣♦♥♥♠r♦s tt♠♣ts

tr♦ t②♣♥♥♥ ♦rrt② t②

t♠ t ♦rt Ω Ω Ω Ω Ω Ω

♥♥ ♦ ♥t♠♦s♣r ♥♥♥ t♠ ♦ sst♦♦♠tr0.7r0.3♥3 ♦r tr♦s t

♥♦tr ② t♦ ♥ t ♣r♦♠ s t♦ ♣r♦r♠ ♥ t♦♥ ♥♥♥ ♦t ♦r tr♦ ♦♦♥ t s♦♥ t♦r♣② st♣ ♥♥♥ s ♦♥t ♥ r ♥ ♦rr t♦ r♦①②♥t t st② s ♣r♦r♠ ♦♥ t♦t②♣s ♦ s♠♣s t ♦rrt② st♦♣♣ ♥ t rrr ♦r st② ♦rtrr♥ t♦ t tr ♥ ♥♥♥ ♦t♥ rsst♥ s ♦rt ♦r tr♦ ♦ t♥ss ♥ s♣ tt r s♠r t♦ s r r♣♦rt t♦ ② ♦rrt rsts ❬❪ ♦r t ♦r tr♦ rsst♥r♠t② ♥rs ♦♥ t 2 ♥♣st♦♥ s ♣r♦r♠ s ♦ trrt ①♣♦sr ♦ t ②r t♦ t ♠ ♦r ♦①②♥ ♣♠♣♥ ♦ ② t sst♦♦♠tr 2 rst s ♦ ♠♣② tt s♥♦t ♠♥t♥♥ ts ♦①②♥ st♦♦♠tr② tr ♥♦♠♥② ♦t♥ tr♦ t♣♦st♦♥ ♦r tr♦ t ssq♥t ♥♥♥ ♥ r r♦t ♦♥t♦♥s ♦ ♦ t♥ rs♣♦♥s ♦r ts t♥♦♦ s♦rt♦♠♥ t ♣♦♦r

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♣r♦r♠♥ rsts r♦♠ t s♦♥ s ♠♦r st 2 ♦r ♥ t s♦♥♥tr 34 ♣sst♦♥ ②r ♠② ♥ ♦r s s

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Page 139: Impact of structural defects on spin-polarized transport ... · Impact of structural defects on spin-polarized transport across magnetic tunnel junctions par FILIP SCHLEICHER Soutenue

♣tr

♥s♠ ♦①

s ♣tr srs sts ♣r♦r♠ ♦♥ s strtrs sts♥ ♥t♦ t♦ st♦♥s sts ♦♥ ♠♥s♠ ♦① ♠s rr♦♥ s♥ t ②r ②st♠ t♥ st tr② ♥ ♦♣t② r♦♠ trt st♥♣♦♥t st② ♦ s ♠♥t t♥♥ ♥t♦♥s s tttr st♦♥ srs t♦ r♥t ♣♣r♦s t♦ t♥♥♥ s t s s♦ s♣t♥ t♦ ♣r♠♥r② rsts ♦ t ♥st ♣r♦ss♥ ♦ s r♦♥ t t ②r ②st♠ ♥s sss♦♥ ♦♥ sss rt♥ t♦ t s♣ttr ♠r♣rssr ♥ st② ♦ ♦s strtrs r♦♥ ② ♥ t t ♥sttt♥ ♠♦r ♥ ♥②

rrr sts

s t s ② ♣t t rrr qt② s r ♠♣t ♦♥ t ♣r♦♣rts ❲t♥ t t♠r♠ ♦ ts tss ①t♥s sts r ♣r♦r♠♦♥ t ♠♥s♠ ♦① r♦t ♦♥t♦♥s tt str♦♥② t t qt② ♦ tstr

♣t tt②

s ♠♥t♦♥ ♥ st♦♥ ♦①②♥ ts ♣② ♥ ♠♣♦rt♥t r♦ ♥ t rrr♦r ♥ ♦rr t♦ tr t ♥st② ♦ t ts r♥ t ②r ②r②st♠ ♣♦st♦♥ ♦①②♥ s ♥tr♦ ♥ t♦♥ t♦ t r♦♥ ♦ rqr② ♠♥tr♦♥s t♦ ♠♥t♥ t ♣s♠ ♦r♥ ♣rssr r♠♥ ♥♥1 · 10−3 ♠r t ♦①②♥t♦r♦♥ rt♦ s r r♦♠ t♦ ♦rs♣ ♣♦st♦♥ r♥s

r ♥♠ s♠♣s t r♥tO2/Ar rt♦s r r♦♥② ♥r♥t ♦♣t tr♥s♠ss♦♥ s♣tr ♠sr♠♥ts s♥ t ❯❱❱sPr♥♠r ♠ s♣tr♦♣♦t♦♠tr tr tr ♦♣t s♦r♣t♦♥s t rsts r s♦♥ ♦♥

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r ♣t s♦r♣t♦♥ s♣tr ♦ ♥♠ s♠♣s rt♥r t s♠ ♣rssr t t r♥t O2/Ar rt♦s strtrt trsr strt ❬❪

r r tr s♥♥t s♦r♣t♦♥ ♣s ♦r t s♠♣ r♦♥ ♥ t ♣rr♦♥ ♦♥t♦♥s ♣ ♣♦st♦♥s r ss♠ t♦ r♣rs♥t s♦r♣t♦♥s ♦♥ t♦ ♦①②♥ ♥② F2 ♦r ♥tr t ❱ ❬❪ ♥ t ♦①②♥ ♥tr ♥s♥② r ♥② F ♥ F+ ♥trs rs♣t② t ❱ ❬ ❪ ♣♦st♦♥ ♦ ts ts ♥ t ♥r② ♣ s s♠t② s♦♥♦♥ ♥ rtr♥ t♦ ts ♣tr sr t♠s tr♦♦t t ♥②ss♦r♦r ♣ tt ♥ ss♦t t ♦② r ♦①②♥ ♥②F 2+ ♥tr s s t ❱ ❬ ❪ t t ♥♦t ♣② s♥♥t r♦ ♥t ♥tr♣rtt♦♥ ♦ rsts t s ♥t tt ② ♥rs♥ t ♦①②♥ ♦♥t♥tr♥ t r♦t t s♣tr t ♦ ♣s rss s♣② tt ♦ t ♦♥ttrt t♦ t F ♥ F+ ♥trs t ❱ s♣♣rs ♥r② ♥tr②

tr ♠sr♠♥ts

♥ ♦rr t♦ tr♠♥ t ♠♣t ♦ ts ♦♥ t t♥♥♥ tr♥s♣♦rt ♦♥tt♦♠ ♦r ♠r♦s♦♣② s ♣r♦r♠ s♥ t rr ♥♦♦s ♥ ♦♦rt♦♥ t ❲ ♦ t ♦ t♦♥ ❯♥rst② ♦♥ ♥♠t ②rs r♦♥ t♦♣ ♥♠♥♠ sts ②rs r r♦♥♥ ♥ O2/Ar rt♦ s♥ st♥r ②r ②st♠ ♦♥t♦♥s ♥ t ttrs t rst ♠♦♥♦②r s s♣ttr t♦t ♦①②♥ ♥tr♦ ♥ t

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r ♠t r♣rs♥tt♦♥ ♦ ♦①②♥ t s ♥ t rrrt ♥ ♣ s ss♠ t♦ ❱ ♥ F t♦ ♥ t ♥tr ♦ t rrr♠rs ♥♦t s♦t ♥r② r♥s ♥ ❱ t♥ t F♥ t ♦t ♦rrs♣♦♥♥ t st ♦ rr♦s ♣t ♦♣t s♦r♣t♦♥ ♥ ♠ss♦♥♣r♦sss ss♦t t ♦rrs♣♦♥♥ t sts tr s ♦♥tr♣rts♠r ♣♦♥♦♥ssst r①t♦♥ r♦♠ ①t stt t♦ r♦♥ stt ts r ♥♦t r♣rs♥t ♦r rt②

♠r ♥ ♦rr t♦ ♦ t r♦♥ ♦① ♦r♠t♦♥ t t ♥trs♣t t t tt t r♦♦t ♠♥ sqr r♦♥ss r♠♥s ♠♦st② ♥♥

tr♦♦t t st② t ♥st② ♥ ♥t♥st② ♦ t ♦ rr♥t ♦ts♣♦ts sr② ♦♥ s ts ♦ rr♥t ♥♦♠♦♥t② s ♥♦t t♦♣♦r♣②rt t s t♦ rst r♦♠ t ♥st♦r rrr t♥ss ♦r ts t t♦♥sr♥ t ♣♦t♦♠♥s♥♥rr rs ♥ t ♦①②♥ ♥② ♥st②t ♥rs♥ ♦①②♥ ♦♥t♥t ♥ t r ♣s♠ ss♠ tt ts ♦ rr♥t♠♦t♦♥s r ss♦t t ♦①②♥ ♥s ❬❪ tt♥ ♦ t t rs t r rr♥ts ♦ ♣ ♥ ♣ ♦r t ♥ 2

rrrs rs♣t② ♠♣s t t qtt s♥♥t ♠♣r♦♠♥t♥ t rrr t

s ♦♥t ♦ts♣♦ts ♦♥ t ♦ t♥♥♥ ♠♣s ♦r♥t r♦♠ ts ♥t rrr rr♥t♦t ♠sr♠♥ts r ♣r♦r♠ t ♥ ② r♦♠ t

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r ♦♣♦r♣ ♠♣ ♦ t rrr ♣♦st t♦t ♦①②♥ ♣rs♥t♥ t ♠r r♥ t r♦t rst s s♠r t♦ tt ♦r t 2 ②r ♦ t♥♥♥ ♠♣ t ❱ s ♦ t 2 ②r ♠ ♦r t 2

②r ♦♠♣rs♦♥ ♦ t♦♣♦r♣ strt♦♥ t♦♥ r♦♠ t ♥♦♠♥t♥ss ♦r ♦t s♠♣s ♦ rr♥t strt♦♥ ♦♠♣rs♦♥ r♦♠ rs ♥ ❬❪

♦ts♣♦ts ♥ ♦rr t♦ st② tr ♠♣t ♦♥ t rrr t s s ♦♥ ♦♥♦t s♠♣s s♥ t ♦r♠♥t♦♥ ♦♥t♥ ②♣ ♥ r♣r♦❱ rs r s♦♥ ♦♥ ❲ ss♠ r tt t tr♥♦♥ ♦ t ❱ rr♣rs♥ts qtt st♠t ♦ t t rrr t ❬❪ ♥ ♦rr t♦tt ♥ ♥rst♥♥ ♦ t ❱ r t s♠t s r♥ ♥ st rst ♠♦♥♦②r ♦ t rrr s ♣♦st t♦t ♥② ♦①②♥ t♥t ♠r t ♦r ♥tr ♦ t 2 s♠♣ ♠② rs♠ t ♦♥ ♦ t

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r ❱ rtrsts ♠sr t ② ♦♥t t♣ ♦♥ ♥ 2 s♠♣s ♦t t ♥ ② r♦♠ t ♦ t♥♥♥ ♦ts♣♦ts ❬❪

s♠♣ r♦♥ ♥ t ♣r r♦♥ s t s t ♦r ♥tr s ♣r♦ tt ♥t s t♥ rs ♠sr ♥ t r♦♥ ♦♦ ♦r ♦ts♠♣s ❲t♥ t ♣♦st ♦t r♥ ♦♥ r♦♠ t♦ 2 trrr t rss r♦♠ ❱ ♣ t♦ ❱ ♥ t r♦♥ ♥ r♦♠ ❱ t♦❱ ♦♥ ♦ts♣♦ts 2 r♦♥ ♥ 2 ♦ts♣♦t rtrsts rs♠r ssts tt t ♥rs ♥ ♦①②♥ ♦♥t♥t r♥ t r♦t rsts♥ t s♣♣r♥ ♦ t ts ♥ t♦ t ❱ rrr t ♦r♦rt t♥ ❱ rrr ♣rs♥t ♥ t r♦♥ ♦ t 2 s♠♣①st ♦♥② ♦② ♦♥ ♦ts♣♦ts t♥ t ♦♥ t♦ t ♠♣r♦♠♥t ♦t rrr strtr ss♠ tt t r♠ s ♥ t ♠ ♦ t ♥ ♣ ❬❪ ♠② ttrt t rrr t ♦ ❱ t♦ rstr♦♠ t ♣rs♥ ♦ t sts ♦ t F2 t②♣ r rrr t ♦r♦♥ ❱ ♦rrs♣♦♥s t♦ F ♥ F+♥trs tr♥♦♥ t r♦♥ ❱ ♥ tr♦♥ ♦ t s♠♣ s ss♠ t♦ t ♥tr♥s rrr t ♦ t ♥st♦r

♦♠♥♥ rsts ♦ ❱ rtrsts t ts ♦ t s♦r♣t♦♥ s♣tr ♦♥♠② s tt F ♥ F+ ♥trs ❱ ♦ t ♦♥t♦♥ ♥ ♥ rrs♣♦♥s ♦r t ♦♣t s♦r♣t♦♥ t ❱ ♥ t t rrr tt r♦♥ ❱ r ♠♦st t♦t s♣♣r♥ r♦♠ t s♦r♣t♦♥s♣tr ♦ t 2 s♠♣ s ♦♦ ② t s♥♥t ♥rs ♦ t rrrt ♥ t r♦♥ r♦♠ r♦♥ ❱ t♦ ♣ t♦ ❱ s ssts tt F ♥

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r ♠t r♣rs♥tt♦♥ ♦ t rt♥ ♣rt ♦ t ♦r③♦♥t s ♦rrs♣♦♥s t♦ ②♣♦tt tr ♠sr♠♥t ♥♦♥tr♥ s♥ ♦ts♣♦t rt s s♦s t②♣ ♦t ♦ t ♦♥t♥tt♦♥ ② ♦♥t ♦ts♣♦ts ♦ t s♠♣ r ♠♥t ♥ t s♠♣ ❱ ♦ r♦♥ ♦♥t♥ ♦ t s♠♣ s r♣♦rt ♦♥ t s♠♣ ♦ts♣♦ts r♦♥ ♦♥t♥ ♦ t s s♥♥t② ♦r t♥ ♥t s

F+ ♥trs ♣rs♥t tr♠♥ t t rrr t r♦♥ ❱ ♥ rt②r t tr qt② ♦ rrr

♦♠♥♥ rsts ♦ ❱ rtrsts t t♦s ♦ t s♦r♣t♦♥ s♣tr ♦♥♠② s tt F ♥ F+ ♥trs ❱ ♦ t ♦♥t♦♥ ♥ ♥ rrs♣♦♥s ♦r t ♦♣t s♦r♣t♦♥ t ❱ ♥ t t rrr tt r♦♥ ❱ r ♠♦st t♦t s♣♣r♥ r♦♠ t s♦r♣t♦♥s♣tr ♦ t 2 s♠♣ s ♦♦ ② t s♥♥t ♥rs ♦ t rrrt ♥ t r♦♥ r♦♠ r♦♥ ❱ t♦ ♣ t♦ ❱ s ssts tt F ♥F+ ♥trs ♣rs♥t tr♠♥ t t rrr t r♦♥ ❱ ♥ rt②r t tr qt② ♦ rrr

♥ ♦♥s♦♥ ♦r ①♣r♠♥ts s♦ tt t ♥st② ♦ ♦①②♥ ♥s ♥ ♦♥tr♦ r♥ t r♦t ② tr♥ t ♦①②♥ ♦♥t♥t r♥ t ♣♦st♦♥ ♥ tt t ♣rs♥ ♦ rt♥ t②♣s ♦ ts ts ♥ t♦ rt♥①t♥t s♣♣rss s rsts ♥ s♥♥t ♠♣r♦♠♥t ♦ t rrr t♥ rt♦♥ ♦ ♣♦ss ♥sr ♦ts♣♦tr♥ ♠♥tr② rr♥t ♥♥s

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s st♦♥ sr rsts ♦t♥ ♦♥ s rt t t s♦♠st♥q sts ♦♥r♥♥ t s♣♥♣♦r③ tr♥s♣♦rt r rtr ♣r♠♥r②s ♠♦st ♦ t rt ♦r ♦♥♥trt ♦♥ t r♦t ♦♣t♠③t♦♥

s♥♥t ♣rt ♦ ts tss ♦♥♥trt ♦♥ rt♦♥ ♦ s s s♥ t ②r ②st♠s s♣ttr♥ ♠r t t s♦♠s ♣♦st♦♥st♦♥ t♦ t♥ s♣ts t s ♥♦t ♣♦ss t♦ r♦tt t s♠♣ r♥ t ♣♦st♦♥ ♠♥t♥♥ ♣rs ♣♦st♦♥♥ s♦ s t♦ ♣r♦r♠t ♦rrt ♥♠♥t ♦ t t♥♦♦ st♣ Pr♦♦♠tr ♥ tsts♣r♦r♠ ♦♥ s♠♣s r♦♥ ♥ t s♥ ♦ t r♦tt♦♥ s♦ t♦♣♦r♣ ♥♦r♠t② ♦ s♠♣s ❨t t rsst♥ s ♥♦t ♥♦r♠ r♦ss ♥ s♠♣♥ s ♦ t s♠♣ ♣rs♥t ♦♥ r µm2 rsst♥s ♦ ♥t♦♥sr Ω Ω Ω ♥ Ω ♥ tt ♦rr s s ♦rrs♣♦♥ t♦ ♣r♦ts ♥ µΩ♠2 ♥ rs♣t② r s♦s t ♦srrsst♥s ♦♥ ♦rt♠ s s ♥t♦♥ ♦ t ♥② s♣ ♥t♦♥ ♣♦st♦♥ r ♥t♦♥s s♦ ①♣♦♥♥t ♣♥♥ ♦ rsst♥ ♦♥ t ♥t♦♥♣♦st♦♥ ssts ♥r t♥ss rs ♠♦♥ t♠ ♥ ♦ t s♥trs ♦ t♥♥♥ r♠ ♥ t ♦r♠ ♦ ♥♦♥♥r rr♥t♦t rtrsts❬❪ s ♦sr ♦♥ ♦r ♥t♦♥s s ♥tr rrr ts t s♥ r♥♠♥s ♦r♠ r ❱ ♥ ❱ ♦r t ♦tt♦♠ ♥ tt♦♣ ♥tr rs♣t② r♥ ♦ rt ♦①t♦♥ sss t t ♦r♥tr

r ♣♦♥t rsst♥s ♦ µm2 ♥♠♥♠ ♥t♦♥sr♦♥ ♥ s♥ t s♥ t s♦♠s t♥q

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r rr♥t♦t ♠sr♠♥t ♣r♦r♠ ♦♥ µm2

♥t♦♥ r♦♥ ♥ s♥ t s♥ t s♦♠st♥q ♣♦♥t ♥t♦♥ rsst♥ t ♠❱ s Ω

♦♠♣r ♣r♦ts ♦ ♦r ♥t♦♥s t t ♦♥s r♣♦rt ♦♥ s♠♣s ♥ t trtr ♠② s tt t♥ ts r♥ t s♥ ♦ ♠♦r t♥ s ♦sr ♦r ♥♦ s♥ s ♦sr ♦♥♠♥t t♥♥ ♥t♦♥s r♦♥ t ♦r ②r s♣ttr♥ s②st♠ ♥ t ♦t♠♣rtrs

t♦ s♥♥t rsts ♦♥r♥♥ t t ♥♥ ♦♥ ♣r♦♣rts ♦ t r②st r ♦t♥ s r♦♥ t t ②r ②st♠s s♣ttr♥ r♥♦t stst♦r② r♦♠ t s♣♥tr♦♥ st♥♣♦♥t s ♠♥t♦♥ t♥ t st♦♥ t r ss rt t♦ t ♣♦♦r s♣♥tr♦♥ ♣r♦r♠♥ ♦ t srt t t ②r s②st♠ s ss♠ t♦ t ①ss ♣rssr r♥♥♥♥ ♦ t ♦r tr♦

tr ♠♦♥t ♦r♥② t♥ t s♣ttr♥ ♠r s r♠♦♦①♥t t t♥ ♠♥ts ♦r ♥ 23 ♦ t♦ r t ♥♥♥ s ♣r♦r♠ ♥ ♦①②♥ ♦r t♦ ①ss ♦tss♥ ♦r ♥ ♠♥ts t s r♣ t ♣t♥♠ r♦ tr ♦r ♥ ♥ts s t st♥ss st ♦r s ♦tss♥ ♦ r♦♠♠ rst♥ ♣rssrs ♦ 10−6 ♠r r♥ t r♥ t t♠ ♦ rt♥ t rr♥ts♦t♦♥ ♦r t ♥♥♥ ♣rssr s t tr ♠♣r♦ t ♥♥♥♣rssr ♦♥ t♦ 10−7 ♠r t t t ♥ s ♦♥② ♦ ♠r ❯♥♦rt♥t② ♥②ss ♦ t rsts ssts tt ts ♣rssr r♠♥s ♥♦♠♣tt ♦①t♦♥r ♥trs

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♦♦

s tss s t♥ ♣ t ②r s②st♠ s ♥ ♦♥st♥t② ♦♣♥ ♠♣r♦ ❲t♥ t t♠r♠ ♦ ts ♠♥sr♣t ♣t♦♥ r♥t ♣r ♦ t st♣ ♥ t ♦r♠ ♦ tt♥♠ s♠t♦♥ ♠♦t♦♥ s ♥r②♣r♦♠s♥ s♥♥t② ♦r ♣rssr r♥ t s♠♣ ♥♥♥ ♦r t s♦t♦♥ ♣r♦s ♥sss s ♦♠tt♥ t ♦r tr♦ ♥♥♥ st♣s ♦♥sr ♥ s ♠♦ ♦ rst ♥ ❱♦♠r❲r s♥ r♦tt s ♣♦ss tt ♠♦♥ t♦ ♦ tr♦s ♠② rqr

♦♦

s st♦♥ ♥♦♠♣sss rsts ♦t♥ ♦♥ ♦s strtrs r♦♥ ② ♥ r♦♠ t ♥sttt ♥ ♠♦r ♥ ♥② r tr ♣r♦ss♥ t P ts rt t♦ ts s s r ♣r♦r♠ t♦rs t♥ ♦ t tss ❲ sr ♦r ♣rs♥t ♥rst♥♥ ♦ ♦r rsts ♥ ♥ttr rt♦♥s ♠♣ ② ts rsts

♥♠♦♥♠r♥♥♠♦♥♠♥♠♦♥♠strtrs r r♦♥ ♦♥ ♠♦r♣♦s ♦r♥♥ ss s♥ r♦t ♦♥t♦♥ssr ♥ st♦♥ s ♠♥s tt ♦♥ ♦ tr tr♦s s ♠♥t②♣♥♥ ♥ t rt♦♥ ♦♦♥ t ♠♥t③t♦♥ rt♦♥ ♦ t ♥trr♦♠♥t strtrs r ♣♣ t ♥♠Pt♥♠ ②r ♠r strtrst t♦t t t♦♣ ♦Pt tr②r r s♦ r♦♥ ♥ ♦rr t♦ st② t♥♠ ②r ♦♣t② ♦ ♦ t st② s t♦ tr♠♥ t ♠♣t♦ ♥♥♥ t ♦♥ tr ♠♥t♦rsst ♥ ♦♣t ♣r♦♣rts ♦rs ♦t s♠♣ t②♣s r ♥♦t ♣♦st ♥ t s♠ t t s♣rt② t s♣♦ss tt ♦srt♦♥s ♦ ♦r ①♣r♠♥t ♠② ♥♦t ♥♠♦s② ①♣♥s t♦ ♥♥♥ ♥t t♥♥ ♥t♦♥s r ♣ttr♥ s♥ t st♥r♦♣t t♦r♣② ♥ r t rst t♦ st t t rt st♣ tr tt♦♠t③t♦♥ ♦ ♠sr♠♥ts

♥r ♣r♦♣rts

P♦t♦♠♥s♥ ①♣r♠♥ts ♣r♦r♠ t ♥♠ ♥ ♥♠ ♥t sr♦♥ strtr tr♠♥t t t ♥♠ ②r ♥♦♠♣ss♥ t ♦rtr♦ ♥ t♥♥ rrr t ♥♦t t t♦♣ tr♦ st s♦ ♣s t ♥♠❱ ♥♠ ❱ ♥ ♥♠ ❱ tr ♦♥♦t♦♥ t♦t ♣♦t♦♥ ♥r② s ♥ ♦r ①♣r♠♥t s ♥♦t s♥t t♦ ①t F ♥ F+

♥trs s♦ t ♠♥s♥ rst♥ r♦♠ ts sts ♥♥♦t ♦sr rt② ttrt t ♣ t ♥♠ t♦ t rrs ♦♥③t♦♥ ♦ F ♥ F+ ♥trs ♥r♦♠♥t♦♥ ♦ tr♦♥s t♦ t t♦♣ ♦ t ♥ ♥ ♦tr t♦ ♣s♥♠ ♥ ♥♠ ttrt t♦ ♣♦t♦♥ ♠ss♦♥ ss♦t t r①t♦♥ ♦F ∗ ♥ F+∗ ♥trs t♦ tr rs♣t r♦♥ stts ♠r rsts ♥♦t s♦♥

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r t ②♣ r♦♦♠t♠♣rtr ♣♦t♦♠♥s♥ s♣tr r♦♠ ♥ ♥♥ ♦r♥♦ st r♦♥ ♦♥ ♦r♥♥ ss ♥ ♥♥ ♦r t r ♦t tr t ♥♠ sr ①tt♦♥P♦st♦♥ ♦ t ♠♥ ♣ tr ♦♥♦t♦♥ s ♥♠ P♦st♦♥s ♦ t ♠♥♦r ♣sr ♥♠ ♥ ❱ ♠r rsts r ♦t♥ r♦♠ ♥♦♥♥♥ s ♥tr ♥♠ t ①tt♦♥ ♥♦t s♦♥ t ♠t r♣rs♥tt♦♥ ♦ t♦sr ♠♥s♥

r ♦t♥ ♦r t ♥♥ s s s ♣♦♥ ♥♠ t ①tt♦♥r♦r ♦♥r♠ ♣rs♥ ♦ t ♠♥t♦♥ t sts ♥ t rrrs st

❲♥ t♥ ♥t♦ ♦♥t ♣r♦ss♥ sss ♦ t sts s st♦♥ ♠♥t t♥♥ ♥t♦♥s r rtr③ ② r② ♥♦r♠ ♣r♦ts ♣rs♠♣ ♥ t ♣rtr s ♣rs♥t ♣r♦ts ♦ ♥♥ sr s♥♥t② ♦r t♥ tr ♥♦♥♥♥ ♦♥tr♣rts ♦r sts ♣r♦r♠ ♦♥ ♥♠r ♦ s♠♣s s♦ tt t r♥ ♥ ♣r♦ts ♦s ♥♦trst r♦♠ t ♥♥♥ ♣r♦ss t rtr r♦♠ st rt♦♥ ♥ t s♠♣ r♦t ♦♥t♦♥s ♦r ♣r♦ss♥ sss s♣② r♦♠ t rrr ♦rt♥r♥ t st♣ ♦ t ♣♦t♦t♦r♣② s st♦♥ ♦r ts

r ♥t♦♥s ♦ t②♣ r st ♥ ♦rr t♦ ♣r♦r♠ t ♠sr♠♥ts ♥ s♦ r♣r♦ rtrsts ♥ r ♣♦t t②♣Iabs r♣ ♦r ♦t ♥ ♥♥ ♥ ♥ ♥♦♥♥♥ s ♠t♦ ♠♦♥

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♦♦

r sst♥r ♣r♦ts ♦ ♥♥ ♥ ♥♦♥♥♥♦♦ s♠♣s t ♦r s♦rt ♥ ♦♣♥rt s r s♦♥ s ③r♦

♦trs ♠♥t♦♥ ♥ st♦♥ s sts s t♦♦ t♦ ①trt t trrr t ♦ ♠♥t t♥♥ ♥t♦♥ ♥ s ♦ t ♥♦♥♥♥ t t rrr t s ❱ ♦r ♦t P ♥ P ♦♥rt♦♥s ❲ ♥♦ttt ♥♥ t s♠ ♦r ♦t P ♥ P ♦♥rt♦♥s s ♥ t ①♣t♦r ♣r♠♥t rrr ❬❪ ♦r t rrr t ♦ t ♥♥ s♦s ❱ ♥ t P s ♥ ♠♦r t♥ ❱ ♥ t P s rtr♠♦r tsrrr t s ♦♦s② ♦r t♥ tt ①♣t ≈❱ t rt ♥♦r ♦♥t♦♥ ♥ t s tr♦r ttrt t♦ ts ♥ tr♥ ts sststt ts ts ♥ ♠♣t ♦♥ t s♣♥ ♥♦r s②♠♠tr②♣♦r③ tr♥s♣♦rt♥ t s②st♠ s s rtr

♥t③t♦♥ rs ♦ ♦t s♠♣s ♠sr t r♦♦♠ t♠♣rtr t t

♦♦♠ t♠♣rtr ♠sr♠♥ts ♥ ♦t r t♥ ❱ r ♥♦t ♣r♦r♠ t♦t ①♣r♠♥t ♣r♦t♦♦ tt s ♠♣♠♥t ♥ ♦rr t♦ ♠tt t rs ♦ t trr♦♥ ♦r ♥ t r♥ t Iabs ♣ ♦rr t ❱ s t ♦♦♥♥②ss s♦ t ♣ s ①♣t t♦ t♥ ❱❱ r♥

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r Iabsolute rs ♦r ♥ ♥♥ t♦♣ ♥ ♥♦♥♥♥ ♦tt♦♠ ♥ t P ♥ P r rt ♠♥t③t♦♥ stt ♠sr t♥ ♥ ♠tr ♦ ♥t♦♥s s µ♠ ♥ µ♠ rs♣t②

❯ st♣ r s♦♥ ♦♥ rs ♥ ♥♦♥♥♥ s♠♣s♦s ♥♦t t ♥♦t ♣rt② ♥ ♣ ♦ t ♠♥t③t♦♥ t t♣♣ ts ♥♥ ♦♥tr♣rt ①ts ♥ ♠♣r♦ P ♥♠♥t t♥st♦ t ♣♥♥♥ ♣r♦ ② t r♥♦ ♦r tr♦ ①♥ s ♥② ♥♥♥ ♥t③t♦♥ ♣♣♥ ♦ s♣ ②rs ♦ t ♥♥ s♠♣ s♠r ♦♥ t r♣ ♦r rt♦♥

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♦♦

r ♦♦♠ t♠♣rtr ❯ ♠♥t③t♦♥ ♥ rsst♥ s ♣♣ ♠sr♠♥ts ♦♥ t ♥♥♦r♥♦♦ s♠♣ rr♦s ♥♦trt ♠♥t③t♦♥ ♦ tr♦s ♣♣♥ ♦ s♣ ②rs s s♦♥

❲ ♥♦ ♣rs♥t ♠♥t♦tr♥s♣♦rt rsts ❲ ♠♣s③ tt ts rsts rsttst② r♥t s t② r r♣rs♥tt ♦ s ♠sr ♦♥ t ♥♥st ♥ s ♠sr ♦♥ t ♥♦♥♥♥ st

t r♦♦♠ t♠♣rtr ♥♦♥♥♥ ♥ ♥♥ s s♦ ♥ s♥ rs♣t② rs ♥ s♦ t rs ♦ ♦t t②♣s ♣♦tt t rs♣t t♦ tr ♠♥t③t♦♥ rtrsts t s ♥♦tsr tr t ♦ ♦ t ♥♦♥♥♥ s s t♦ t P stt♥ ♥♦t ② ♦r ♥♦t ♥ ♦rr t♦ t ♥♥♥ ♦ ♥♦♥♥♥♥t♦♥s t ♦♥st② ♥ s ♣r♦♣♦s ♥ ♦rr t♦ s♣rtt rr②st③t♦♥ ♥ t P stt ♦r♠t♦♥ ①♣♥t♦♥s ♦r t ♦ ♦sr r♦♠ t ♥♦♥♥♥ s♠♣ r r♥ ♠② s♦ rst r♦♠ tt①tr③t♦♥ ♣r♦ss tt ts ♣ r♥ t ♥♥♥ ♥ t r②st♥t②♦ t rrr s ♠♣r♦ ♥ t tt ♠♣r♥t♥ ♦ ♦♥t♦ ♦ ts♣ rst♥ ♥ s♥♥t ♥♥♠♥t ♦ t s②♠♠tr② tr♥ r♦♠ s♣♥tr♦♥ st♥♣♦♥t s ♠♣r♦♠♥t s ♠ ♠♦r ♠♣♦rt♥t ♦♥sq♥s t♥

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r ♦♦♠ t♠♣rtr ❯ ♠♥t③t♦♥ ♥ rsst♥ s ♣♣ rs ♦ t ♥♦♥♥♥♦r♥♦♦ s♠♣

t ♠tr s♦♥ ♦r t ♦r♠t♦♥ r♥ t ♥♥♥♥ ♦rr t♦ rtr ♥rst♥ t ♠♣t ♦ ♥♥♥♥ ts ♦♥ ♠

♥t♦tr♥s♣♦rt r t ♣r♠tr ♦ t♠♣rtr rr♥ t♦ t rsst♥ ♣♥♥ ♦♥ t♠♣rtr ♦ ♥ ♥♥ ♠sr t ♠❱s♦s st ♥rs r♦♠ Ω t♦ Ω ♥ t ♣r stt ♥ rt② ststrt♦♥ t ♥ t ♦tr ♥ t rsst♥ ♥ t ♥t♣r s ♣s♥rs♥ ♣♦♥ ♦♦♦♥ r♦♠ Ω t♦ Ω ♥t t t♠♣rtr rs r♦♥ ♦r ♥ qtt② ♥rst♦♦ ♦♥ ♦♦s t t ♥ strtr♦ ♦ tr♦s P s ♦r ♦ rt r ♥t♦♥ ♦ t♠t ♠①♥ ♦ s②♠♠tr②♣♦r③ tr♥s♣♦rt ♥♥s ♦ tr♦♥s ♦ t ♥t② ∆1↑ s②♠♠tr② t♦ t♥♥ ♥t♦ ∆2′,5↓ stts ♥ t ♦♥trtr♦ s♥r♦ s ♣r♦t ♥ s♥ ♦ t ♠①♥ s ♥t ♦tr ♥ t P s t♥♥♥ ♦ tr♦♥s t t ∆1 s②♠♠tr② s ②s

s ♣ t♦ ♦r st ♥♦ t♦♥s ♦ t ♦ ♥ strtr ♥♦t ♥ ♣r♦r♠ r ♥r② s ♦ rs♣t ♥s ♦ ♥ ♦ ♦0.40.40.2 ♦♠♣♦st♦♥t t ♥♥ ♦ ♦r♦♥ ♥t s ♦r ♥②ss s♦ ts r st ss♠♣t♦♥ ②s♦r♥t rsts

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♦♦

r ♠♣rtr ♣♥♥ ♦ rsst♥s ♥ ♣r ♥ ♥t♣rstt ♦ t ♥♥ r ♥ t rs♣t② ♦ t s ♥t♦♥ ♦ t♠♣rtr ❱rt ♥s ♠r t♠♣rtrs t t t♠♣rtr ♣♥♥ ♦ t rt♦ ♥s ts ♦r ♠sr♠♥t s♣r♦r♠ t ♠❱

♦ rsts ♥ t rt② q strt♦♥ ♦ t rsst♥ ♥ t ♣r ♦♥rt♦♥ r♦♥♥ ♦ P ♥ P rsst♥s ♦♦s② s t♦ s♥♥t ♥rs ♥ t

t♠♣rtr ♣♥♥ ♦ ♥♦♥♥♥ s ♣rs♥t ♥ r s♣ ♠sr♠♥t s♦♥ s ♣r♦r♠ ♥ t ♣♦♥t ♦♥tt ♠♦ t ts♦s s♠ ♣r♦♣rts s ts ♦ t ♣♦♥t t②♣ t♦ ♠ ♦r rsst♥ ♦♦♥tts t♥ t ♦♥ ♦ t ♥t♦♥ Ω ♥ Ω ♦r ♦tt♦♠ ♥ t♦♣ tr♦srs♣t② s st♦♥ ♦t② ♦♠♣r t♦ ♥♥ s tr s ♥♦rsst♥ strt♦♥ t♥ t ♠sr t♠♣rtr r♥ ❲ r tt tsrts ♦ t tr♥s♣♦rt r♦ss t ♥♦♥♥♥ rrr ♦rs r♦ss t sts♥ t ♦ s ♦ t♠♣rtr

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r ♥ ♥♠♥t ♥ s♠t ♦ tr♦s ♥♦♦ s②st♠ ♥ P↑−↑ t P↓−↓ ♥tr ♥ P↑−↓ rt♦♥t♥ ♥♥s s♠ts r r♥ ♦r tr♦♥s ♦♥ r♦♠ tt♦ rt ♦r ♦s ♦♥ t ♦♣♣♦st ② ttrs r q rr♥st♦ rs♣t trs sss ♥ t t①t ♦♥ t ♥t♦♥s tr t②♦♥t ♦r ♠①♠ ♦r ♠♥♠ t t I s♣tr P↓−↑ ♥♥ ♥♦t s♦♥ st ♠rr♦r ♠ ♦ t P↑−↓ ♦♥ t♦ t ♦s ♥♦t ♣r♦ ♥② rr♥t ♦①♣t t♠t s t①t

♥②ss ♦ t ❱ ♣r♠tr s♣

♦r ♥rst♥♥ ts r♥ tr♥s♣♦rt t♥ ♥♥ ♥ ♥♦♥♥♥s♠♣s ①♣♦r s♣♥♣♦r③ tr♥s♣♦rt t♥ t ❱ ♣r♠trs♣ ♥ ♥r tr♠s t♠♣rtr♣♥♥t ❱ rtrsts s♦ r②♦♦ r♣r♦t② ♠♦♥ ♥t♦♥s ♥ t s♥ ♦ t♦ tr♠♥rrr ts s♥ t I ♠t♦ tr r♦♥ ♦rr r♦♥ ❱ t ♥ t r♦♥ s trs♦ rs t ♥rs♥ t♠♣rtr s♠♣ ♣rt♦♥r② ♠sr♠♥t ♣r♦t♦♦ s ♠♦st ♦ t t♠♣rtrs ♠sr♠♥ts r ♣r♦r♠ t♥ ❱ t♦ ❱ ♣♥♥ ♦♥ t s♣♥t♦♥ ♦r ♥t♦♥ t②♣ ♥♥ ♥ ♥♦♥♥♥ sr s rst s♦♥ r♣r♦ Irel rtrsts

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♦♦

r ♠♣rtr ♣♥♥ ♦ rsst♥s ♥ t ♣r ♥ ♥t♣r♠♥t③t♦♥ stt ♦ t ♥♦♥♥♥ r ♥ t rs♣t② ♦ t s ♥t♦♥ ♦ t♠♣rtr ♠sr♠♥t s ♣r♦r♠t ♠❱ ♥ t ♣♦♥t ♦♥tt ♠♦

♥ ❱ s♣

♥ r ♣♦t ♣♥♥ s t♠♣rtr ♥ ♣♣ s ♦r ♦t♥♥ ♥ ♥♦♥♥♥ ❨♦ ♥ t ♦♦rs r♦② ♦rrs♣♦♥t♦ ♥ r♦♣ r♦♠ t ♥t rs♣t② t s r② s tt t rt♦ rss ♠ str ♥ t s ♦ t ♥♦♥♥♥ s♠♣ ♦♠♣rt♦ ts ♥♥ ♦♥tr♣rt s ♥t♦♥ ♦ ♦t t♠♣rtr ♥ t ♣♣ ss r♥ s ①♣t s t tr♥s♣♦rt r♦ss t rrr s ♠♦r ♥♦r♥t ♥t ♥♦♥♥♥ s♠♣ ♦r♦r t rst ssts tt t♥♥♥ t

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r ❱ ♦ t ♥♥ t♦♣ ♥ ♥♦♥♥♥ ♦tt♦♠♦♦ ♠♣rtr ♥ ♦t s♣♥ s ♥ ♠❱rs♣t②

sts s tt t ♠ r s ♦ ❱ ♥ s ♥ r♠♥t t ♦rsts ♦ t t♠♣rtr ♣♥♥ ♦ rsst♥s ♣rs♥t ♦♥ rs ♥

♥ r ♣rs♥t t t♠♣rtr♣♥♥t ♦t♦♥ ♦ ♥ t♥♥ s ♥t♦♥ ♦ t ♦t ♣♣ ♥♦r♠③ t rs♣t t♦t ♠sr t ♠❱ s ♦r tt t♠♣rtr ♦r tr♥ s ttrrss ♦ t♠♣rtr t rss t ♣♣ s s ssts tt

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r ❱ ♦ t ♥♥ ♦♦ ♥♦r♠③t♦ ❱0 t ❱0♠❱ ♠♣rtr ♥ ♦t s♣♥ s ♥ ♠❱rs♣t② t♥ ♥s r s t♦ t ② t ♦♥s s♣rt qr♥tssr ♥ t t①t

tr tt♦♥ ♦♠♥ts tr♠ tt♦♥ s ♥♦t sr♣rs♥ ♥ trt ♥rs ♥♦ ❯♣♦♥ ♦sr ♥s♣t♦♥ s s t♦ t ② ♠②s♣t ❱ ♣r♠tr s♣ ♥t♦ ♦r qr♥ts ♥t ② ♥ t♥ <❱< ❱ s r♥ ♥ qr♥ts ♥ ❱ s ♣♥♥ ♦ tt♠♣rtr ♦t♦♥ ♦ rt s ♥♦t ♥ qr♥ts ♥ t sss♥t② s♥♣♥♥t ❲ r st ♦r♥ ♦♥ ♥rst♥♥ ts s♦♥♦rr s♣ts t t t♠ ♦ ts rt♥

❲ ♥♦ ♦♥sr tr tt♦♥ ①♣t② ② ♣♦tt♥ s♠r r♣ ♥❱ ♣r♠tr s♣ t ts t♠ t ♥♦r♠③ t ♥ ♦♣♣ s t♦ tt ♦♥ t ♦ t♠♣rtr s r ❲ t♥ss trtrs t r② ♦ s ±♠❱ t t rs st rs t♦t ③r♦ s ♥♦♠② s r♦♠ ts tr t♥ss t♥ ≈ ±♠❱ rtr t t♠♣rtr ♣♥♥ ♣ t♦ ♦t t r t♠♣rtr ♥s t♦ r♦♣ s♥♥t② ❲ ttrt ts s♦♥ tr t♦ t ♦♥st ♦tr♠② ssst t♥♥♥ s tr tr s tt strt♥ t ♦t tr s r rt r♦♣ tt s s♣tr② ♥tr r♦♥ ±❱

❱ st② ♣rs♥t ♥ t s ♦ ♥♥ s ♦ ♥♦t ♦t♥ ♥ stst♦r② ② ♦r ♥♦♥♥♥ s t♦ s♠ r♥s t♥

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r ♦ t ♥♥ ♦♦ ♥♦r♠③ t♦ t t s ♥t♦♥ ♦ t♠♣rtr ♥ t ♣♣ s ♠♣rtr ♥♦t s♣♥ s ♥ ♠❱ rs♣t②

s♠ s s r st♦rt♦♥ ♥ ❱ tsts ♦r ♥t ♦♦s ♦♦ ②♦♥ ♥ ♥stt ❱ ♣r♠tr s♣ ♦r ttr♥s♣♦rt ♥♥s ♥ ♦ t P ♥ P ♦♥rt♦♥s ♣② s st I ♠t♦♦♦② t♦ ♥♦r tr ♥ tr♠ tt♦♥s ♦ rr♥t t♥❱ s♣ ♦r P ♥ P ♥t♦♥ stts

♥♥ s②st♠

♥ ♦ t rst ♥ ♠♦st ♦♠♣t Irel rsts ♦t♥ ♦♥ ♥ ♥♥ µ♠♥ ♠tr s ♣rs♥t ♦r P ♥ P ♦♥rt♦♥s ♦♥ r ♦♥st ♠sr♠♥ts r st ♣rs ♦r rt② rs♦♥s ♦r ♦ t♠r♠♥ ♥ s s♥♥t r♥ t♥ t ♦r ♦ I rs ♦r ♦t♠♥t③t♦♥ ♦♥rt♦♥s ♥ s♣ ♦ts ♥ t♠♣rtrs ♠② s♥ rs ①t r ♣ t♥ t ♠❱ r♥ s tr s ttrt

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♦♦

r Irel rs ♦r t ♥♥ ♥ t P t♦♣ ♥ P ♦tt♦♠rt ♠♥t③t♦♥ stt t♥ t r♥t t♠♣rtrs t♥ ♥ ♥ ♣♦tt ♥ rs♣t t♦ t t ♦t♥ r♦♠ t ♣r♥ ♠sr♠♥t t t♦r t♠♣rtr

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t♦ t ③r♦ s ♥♦♠② ❩ tt s ♦♠♠♦♥② ♦sr ♥ ts ♦t r♥♥ tt rsts r♦♠ ♠♥♦♥ ①tt♦♥s st♦♥ ♦r ♦r♥ t♦r♥t ①♣r♠♥ts ❬❪ t ♠② s♦ rst r♦♠ tr♦♥tr♦♥ ♥trt♦♥s ♥ tr♥ ♦r♥t r♦♠ t ♦ tr♦♥ strtr ♠♦t♦♥ t♦ t ♠t♥st♦r tr♥st♦♥ ♦ tr♦s ♣ s ♥t② ♠♦r ♣r♦♥♦♥ ♥ t P♦♥rt♦♥ t♥ ♥ t P ♦♥ s t ❩ ♦♥trt♦♥ t♦ t ♦r ♦♥t♥t♥ t ♠♥t♦♥ ♦t r♥ rt② t♦ t st♥r t♥♥♥ s r♥ t P stt t♥ ♥ t P ♦♥ t♦ ♠ r t♦t ♦♥t♥ ♦ tttr

♥ ♥r tr♠s ♥ ①tr♠♠ ♥ ♥ I ♣rs♥t t ♥ s ❱ ♥ rtt ♦♦♥ ♣♦ss ♣♥♦♠♥ ♥ ①tr♥s ♣♥♦♠♥♦♥ t♦ s♣♥ ♣ tt♥ ♥rt ② ♠♥♦♥s t♦ t r①t♦♥ ♦ tr♦♥s t ♥r② ❱ ♦F t♦ F s ♥t ♦rs ♦r t ♥tr ♣r♠tr s♣ ♦♥sr r ts ♦♥♥ t♦ ❱±♠❱ ♥ ①tr♥s ♣♥♦♠♥♦♥ t♦ ♦♣♣♥ ♣♦♥ ts♦ tr♦♥s ♦s tt r ♦♥t♥ t t ♥r② dF❱ t tt s ♦t ss♠♥ tt tr s ♥ ss t♠♣rtr r♥ ♦r ts ♥t ♥ r♦③♥ ♦t t♥ ts ♥t ♥ ♣r♥♣ sts ♥ t t ♦♥st ♦tr♠② ssst ♦♣♣♥ s② r♦♥ > ♥ ♥tr♥s ♣♥♦♠♥♦♥ t♦ ♥s ♥ t ♥st② ♦ stts ♦ t tr♦ tt s ♦t♥ t tr♦♥ ♦r♦ t r②st strtr t r ♥st② ♥ t②♣ ♦ ts ♦ t♥t♦♥ ♣r♠ts s②♠♠tr②♦♥sr♥ tr♥s♣♦rt t♥ ♥ t s♥ ♦ tr♠②ssst ♦♣♣♥ ♦♥ ♥ ♦♥sr s②♠♠tr②♦♥sr ♥♥s ♦ ♦♥t♦♥ ♥ > ♦♥ s♦ t ♥t♦ ♦♥t t ♣♦ss ♠①♥ ♦ s②♠♠tr② ♥♥s♥ t ♥tr♣rtt♦♥ ♦ ①♣r♠♥t rsts ♥ tr s ♥ss stt t♦t ♦♠♣① ♥ strtr ♦ ♠♦st② ♦♥sr t ♥t t♥♥♥♦ ∆1 stts r♦♠ t ♠tt♥ tr♦ s ♠♣s ♦r ∆1→∆1 s②♠♠tr②♥♥ ♠♥t ♥ t s ♦ ② ♥ t♦♥ ∆1→∆5 ♥♥

♦ ①♣♦r t ❱ ♣r♠tr s♣ ♥ ② rstrt♥ ♦rss t♦ t t♠♣rtr r♥ ♦r tr♠② ssst ♦♣♣♥ tr♥s♣♦rt s s♥t ❯s♥ ts rstrt♦♥ tr♦r ♥stt t ♠♣t ♦ s♥tr tt♦♥ ♦♥ ♦♥t♥ ♥ t t♦ stts ♦ ♠♥t③t♦♥ ♥ ♦♥sq♥t② ♦♥

❲ rst ♦s ♦♥ t P s t ♦ t♠♣rtrs r♥ t r ♥ t ♥tr♥s r♠ ♦ tr♥s♣♦rt rr♥ t♦ r ♣s ♦sr t ❱ ♥ t P ♦♥rt♦♥ t ♥♦t ♥ t P ♦♥rt♦♥ ♥ r t ♦ t♠♣rtr ♠② rs♦♥② ① ①tr♥s ♣♥♦♠♥ s s t ♣♥♦♠♥♦♥ ♦ s②♠♠tr②♥♥ ♠①♥ ❲ tr♦r ttrt ts♦♥t♥ rs t♦ ♥ ♥tr♥s s②st♠ ♣r♦♣rt② ♥♠② r♥ t ♦tt♦♠ ♦ t∆1↓ ♥ trrs t t♥♥♥ ♦ s♣♥♣ tr♦♥s ♦ t ∆1 s②♠♠tr② t♦tr rs♣t s♣♥♦♥ stts ♥ t ♦♥trtr♦ ❬❪ tr C t ♦♥sst♥t② t ts ♥tr♣rtt♦♥ ♥ ♦ ♥♦t ♦sr t ♣ ♥ t Ps

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♦♦

❲ ♥♦ tr♥ t♦ t P s t♦ t tst s♦♥ ♥ ♥s ♣ t ❱❱ ts tr s ♥tr r♣r♦ t ♣♦st ❱ ♥♦r ♥ ♦tr♥t♦♥s s♦ ♦♥t sss t rtr ❲ ♦sr ♠♥♠♠ ♦r ♣t t ❱r ♥ t♥tt② ttrt ts ♣ t♦ r♥ t ♦tt♦♠ ♦ t ∆1 ♥♥ t s♣♥♣ ♥♥ t♥s t♦ r♥ t ♦tt♦♠ ♦ t∆1↑ ♥ ♥ ♦ts ♦t t t♥♥♥ rt r♦ss t ♥t♦♥ s ①♣t t♦ rs t Atr ❲ ♥♦t tt s♠r tr ♦rs ♥ t P s t♥ ❱ ♦ tt♥ t P s tr ♥ t P s ♥♥♦t ①♣♥ s♥ ♥ ♥tr♥s♣♥♦♠♥♦♥ t ♦ rt t t tt ts ♦ P I ♠♥♠♠ s tr②t rst ♦ ♥ s♣tr② ♦t t♥ t♦ ♠①♠ ♥♥ ♦♥ ②♦♥±❱

♦ ♦♥ ts ♣rt ♦♥ ♥tr♥s ♣♥♦♠♥ tt r rt♥ t♦ ♦r t♥t ♦ t♠♣rtr r♥ ♦♥sr t♥ss trs ♥ t P s tt ♠② ♦♥♥t② sr t♦ ♥ strtr ts t♦s ♥ t P s r ♠♦rt t♦ ♥♠♦s② ttrt

❲ ♥♦ ♦♥sr t t♠♣rtr r♥ ♦r ①tr♥s ♣♥♦♠♥ ♠② t ♣ ♥♦t② ♥♦♥ ts ♦ ttr ♦♦ t ♥②ss r♣r♦ ♦♥ ♥ ♥ ♥s ♥s♣ ♦ ♥rt ♣♦st♦♥ ♦ s♣ ts♥ t rrr s s ♦♥ ♥♦r♠t♦♥ ♣r♦ ♥ st♦♥ ♦♦♥ ♥②ss ♦ rsts ♣r♦s ♦♥ t ♠♣♦rt♥t ②♣♦tss tt s s♦♥♥ t r♠ s t t ♥tr ♦ t ♦♣t ♥ ♣ t♦r ♥trt② ♦♥srt♦♥s ♦r t ♣♥♥♥ str♥t ♦ t r ♥trt② ♣♥s ♦♥ t t t②♣ ♥st② ♦ ts t♥ t rrr s s tr s♣t ♦t♦♥ ♦s t♦ ♦♥ ♥tr ♦r t ♦tr ♦r ♥ t ♠ st t ♣♦st♦♥ ♦ F ♠② r♥t ♥ t♥ ♥♦♥♥♥ ♥ ♥♥♥t♦♥s t ♦♥ ♥ ♦♠♣r t sts ♣r♦r♠ ② ♦tr r♦♣s tr♥♠♥t ①r② ♣♦t♦tr♦♥ s♣tr♦s♦♣② ♦r s ♥ t ♦♦s ♣r♦ ts ♥tr♣rtt♦♥ ♦ ♦r rsts tt s ♦♥sst♥t tts rs♦♥ ♥rt ♣♦st♦♥♥ ♦ t r♠ ♥ ♦r s

❲rs t rt I P t t r r r♠♥s s♠r t♦t ♦♥ t ♦r t♠♣rtr t ♦♥t♥ ♥ t P ♥♥ ♦♠s♦♠♥t ② ❱ tr tt t ♥rs♥ t♠♣rtr ♦♠♥t t♦♥t♥ rs t t♠♣rtr ♥trs s tr s♦ ♣♣rs strt♥r♦♠ ♥ t P ♦♥rt♦♥ t r♥ r ♥ t ♣♣r♥ ♦ tstrs s ♦♥② tr♠② rt ss♦t t ♣ t t ♦ t♥♥♥ F ♥ F+ ♥trs tt ❱ ♦ t ♦tt♦♠ ♦ t ♦♥t♦♥ ♥ ♠♥♥

♥ ♣r♥♣ t t s♦ ♦♥r♥s s♣♥♦♥ tr♦♥s ♦ t ∆2′,5 s②♠♠tr② s t ♦tt♦♠t♦♣ ♦ ts ♥ s r ♥ t P ♦♥rt♦♥ t ❱ ❱ s ♦rrs♣♦♥s t♦ t B

E tr t ♦r ♦ ♥♦t ♦sr ts trs t♥ t t♠♣rtr r♥♦rrs♣♦♥♥ t♦ ♥tr♥s tr♥s♣♦rt ❲ s♣♣♦s tt t♦ ② rt ♦ tr♦♥s ♦ tss②♠♠trs tr ♦rrs♣♦♥♥ ♣s r ♥♦t s ♥ t t

tr r♦♥ ♦ ♥t♦♥s t r ♦ts ♣r♥t rt♦♥ ♦ ts ♣♦♥t

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r ♦s ♥r② ♥s♣ ♦ ts ♥ t rrr s♠r t♦tt ♣rs♥t ♦♥ rs ♥ trs ♥♦t ♦sr ♥ t ①♣r♠♥t rr② ♦t ♦r rt② rs♦♥s ♥ ♣ ♦ t ♦ rrr s ss♠ t♦ ❱ ♥ t r♠ t♦ ♥ ts ♠

❱ ♦ t r♠ s s♥ ♥ ❲ t♥ tt t rs♦♥ ♦r t ❱ tr s ♥♦t s t ♥

t P ♥♥ s ttrt t♦ ts ♦rs♦♥ ② t ♦r♠♥t♦♥ ♥tr♥str tt s s♣tr② ♦s t t♠♣rtrs ♥ r t s t ♥tr♥st tt ♦♠s ♦rs♦ ② t t♠t t♥♥♥ s s rtrsst ② t ①♣t♦♥ t ♦ ❱ ♣s ♥ t t♠♣rtr r♥♦♠♣r t♦ ts t ♦tr t♠♣rtrs s s♥♥t ♥♥ ♦ F ♥ F+

t sts ♦♥ ♦♥t♥ r♦ss r②st♥ rrrs s ♥ r♠♥t t ♦rsts ♣r♦r♠ ♦♥ r②sts ♣rs♥t ♥ st♦♥

Irel st② ♦ ♥♥ ♥t♦♥s t t♠♣rtrs r t♥ s♦s

♦♠♥② t♦ t t♥ss ♦ t ♦♠♣① ♥ strtr ♦ r♦♥ ♠♣ t ♦♥ tr♦♥ t♥♥♥ s♦ ♥st♥s s ♦♥ s t t ♦s ♥♦t r② ♦s t♦t t♦♣ ♦ t ♥ ♥ r t ♦ r ♣r♦t② ♦ ♥ ♦ t ∆5 s②♠♠tr②s

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♦♦

r Irel rs ♦r ♥ ♥♥ ♥ t P t♦♣ ♥ P ♦tt♦♠rt ♠♥t③t♦♥ stt t♥ t r♥t t♠♣rtrs t♥ ♥ ♥ ♣♦tt ♥ rs♣t t♦ t t ♦t♥ r♦♠ t ♣r♥ ♠sr♠♥t t t♦r t♠♣rtr rs r ♣♦tt ♥ t ♦rt♠ s ♦r rt② rs♦♥s

tt t ♠①♠♠ ♦sr t ♦r P ♥ P ♦♥rt♦♥ t ❱ ♠♦st♦rs ♦r ♦ts ♦♥ t t t♠♣rtr rs ❲t♥ t r♥ t rs ❱ ♥ t P ♦♥rt♦♥ ♥ ❱ ♥ t P ♦♥rt♦♥ s st ♠② ①♣♥ s t rst ♦ t r♦♥ ♦♠♥♥ t♥rs♥ t♠♣rtr t♥ t r♥ ♥ s♣② t♥ ♦ tr♥s♣♦rt tt s ssst ② t ①t stt F+∗ t ❱ ♦ F s t♦ t tr♠♥t ♦ ts r♦♥ stt ♦♥tr♣rt F+ ♥ tr♥ ts ♦①♣♥ t ♥ ♥ t tr tt♦♥ tr♥ ♦sr t ♥ t

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P ❯ ❳

t s♠ s ♦r ♥r② ts t♠♣rtr♥ ♥ ♥ t t②♣♦ t tt ♠ts ♦♣♣♥ tr♥s♣♦rt ♠② ①♣♥ t t♦♥ rs ♥P ♥t♦♥ rsst♥ ♥ ss♦t t ♦ s ♣st t tt♠ ♦ ts rt♥ r ♥tr♣rt♥ ts rsts ♣♦t♥t② ♦♥sttt♦♥s t tr ♥tt♦♥ ♦ t stts sr ♦ ♦rr♦♦rt♥ tr♠ ♥tt♦♥ t♥ t ♦♥t①t ♦ t♠♣rtr ♣♥♥t ttt♦♥ ♣r♦sss s sss ♥ r ❬❪ ❲ ♥♦t ♦r tt t ♣♥ t P ♥♥ t ♦rs t ❱ t s r♥t r♦♠ tt ♥ t Ps ♦♥sst♥t t ♦r ♥tr♣rtt♦♥ ts ♦ ♠♣② tt t rt ts♦ t FF+ ♥ F+∗ tt♦♥s t♥ ❱ s♣ r ♥♦t t s♠ ♦r P ♥P t ♣rs♥t r ♥stt♥ ts r♥ ♥ tr♠s ♦ s②♠♠tr②♣♦r③tr♥s♣♦rt ♥♥s ♥ ♦♥rt♦♥

♥♦♥♥♥ s②st♠

❲ ♥♦ ♦♥sr r♣rs♥tt tst ♦r r♦♠ t ♥♦♥♥♥ s♠♣ Irel rs ♦t♥ ♦♥ ♥♦♥♥♥ ♦ µ♠ ♠tr r s♦♥ ♦♥ P ♥ P ♠sr♠♥ts s♦ r② s♠r rtrsts t ♦♥② s♥♥t r♥ ♥ t t ♦ t ③r♦ s ♥♦♠② ♣ s ♦♦s②♠♦r ♣r♦♥♦♥ ♥ t P ♦♥rt♦♥ s s♠r ♦r ♦r P ♥ P Itst ♦sr ♦r ♥♦♥♥♥ ♥t♦♥s s ♥ ♦♥trst t♦ tt ♦r tr ♥♥♦♥tr♣rts rtr♠♦r ♥♥ s ♦ ♥♦t ①t st♥t ♥tr♥s ♥①tr♥s tr♥s♣♦rt r♠s t♥ t ♣r♠tr s♣ ♦ t♠♣rtr ❲ tr♦r s♣♣♦s tt t♥ t rrr ♦ ♥♦♥♥♥ ♥t♦♥s tr♥s♣♦rt st♦♠♥t t t♠♣rtrs s s ♦♥sst♥t t t ♠♦♥♦t♦♥ rs t ♥rs♥ t♠♣rtr ♦sr t ♦ s s

t♦ t s♠ ♦♥② r♥ ♦ t rst ♠sr♠♥t t r ts rs♦t♦♥ s rt② ♣♦♦r t r♦ ♣ s ♦sr ss♠ t♦ rst r♦♠ ♦♥♦t♦♥ ♦ t♦ ♣s ♦♥ t ❱ ♥ ♦♥ t ❱s ♥tr♣rtt♦♥ s s♣♣♦rt ② t t♠♣rtr ♦t♦♥ ♦ t rt I t ♥t t ♣rs♥ ♦ ts t♦ trs ♠♦r r② rst ♣ t❱ ♠② ♦rrs♣♦♥ t♦ t tr♠② tt t♥♥♥ r♦ss FF+ tsts r② ♣rs♥t ♥ t s ♦ t ♥♥ s♠♣ ts ♥♥ ♦♥ t♦♥t♥ s♠s t♦ ♣rsst ♣ t♦ t r♥ r tr t ♦♠s② ♦rs♦ ② t tr t ❱ ♦♠s ♣r♦♥♦♥ ♠♦r t tt♠♣rtr ♥rs ❲ ttrt ts ♣ t♦ t ①t ♦♥③ ♦①②♥ ♥② t F+∗ ♥tr s

r s♦s t t♠♣rtrs Irel tst ♦t♥ r♦♠ ♥♦♥♥♥ ♥t♦♥s t t s♠ ♣r♦♣rts s t ♦♥ ♦r t ♦ t♠♣rtrst② s ♣rs♥t ♠sr♠♥t s s♦ ♣r♦r♠ s♥ t ♣♦♥t ♦♥tt♠♦ t s ♥t tt ♦ t ♦♥t♦♥ rs t F+∗ ♥tr ♦♠s♦♠♥♥t ♣ t♦ ♦r ♦t ♠♥t ♦♥rt♦♥s trrs t ♠①♠♠

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♦♦

r Irel rs ♦r ♥♦♥♥♥ ♥ t P t♦♣ ♥ P ♦tt♦♠rt ♠♥t③t♦♥ stt t♥ t r♥t t♠♣rtrs t♥ ♥ ♥ ♣♦tt ♥ rs♣t t♦ t t ♦t♥ r♦♠ t ♣r♥ ♠sr♠♥t t t♦r t♠♣rtr sr♠♥ts r ♣r♦r♠ s♥ t ♣♦♥t ♦♥tt ♠♦

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P ❯ ❳

r Irel rs ♦t♥ ♦♥ t s♠ ♥♦♥♥♥ s ♦♥ ♥ t P t♦♣ ♥ P ♦tt♦♠ rt ♠♥t③t♦♥ stt t♥ t r♥t t♠♣rtrs ♣ t♦ ♥ ♣♦tt ♥ rs♣t t♦ t t ♦t♥ r♦♠ t ♣r♥♠sr♠♥t t t ♦r t♠♣rtr sr♠♥ts r ♣r♦r♠ s♥ t♣♦♥t ♦♥tt ♠♦

strts t♦ st t♦rs ♦r ♦ts r♥ ❱ t s s ♥♦t② ♦rt♥ t s ♦sr rr♥ ♥♥ s ♥ ♣r♥♣ F2 stt ♠②♣r♦ s♣tr t t♦ t I t ❱ s tr② ①♣♥♥ t st

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♦♦

t ♥♦t ♥♦r r♠ sttst② r♥t ♥ ♦ ts t stt♥ ♦r ♠♥t♦tr♥s♣♦rt ①♣r♠♥ts

♦r ♥r② ♦r ♠♥t♦tr♥s♣♦rt ①♣r♠♥ts s♦ ♦ ♥♥ s♠♣s♥ ①t t ♦ t♠♣rtr ♠♥t♦tr♥s♣♦rt r♠ tt s ♥tr♥s ♥ t♠t tr♥s♣♦rt s ss♥t② r♦③♥ ♦t ♥ ♦♥trst t♦ ♥♦♥♥♥s♠♣s ❯♣♦♠♥ P ①♣r♠♥ts t ♥t ♣ ♦ ♣r♦♥ ♥♦t s♠♣②F2 t F F+ F ∗ ♥ F+∗ ♥trs ♠② s♥ ♥ t♦♥ t ♣♦♥ t ♣②ss♥r♥t

♦ ♦♥ ts st♦♥ ♦r ♠♥t♦tr♥s♣♦rt rsts ♦♥ ♦ ss ♥ tr ♦♠♣♥②♥ s♦♥sst♥t ♥②ss s♦ tt tr♦ sttr ♥♦r tr♠ tt♦♥ s♣ rs♦♥② ♥t t stts♣rs♥t t♥ t t♥♥ rrr ♠② ♣rt♣t ♥ s♣♥♣♦r③ tr♥s♣♦rts t stts ♣♣r t♦ rs♣♦♥s t ♦ s ♦r t rs t♥rs♥ t♠♣rtr tr♦ t♦ s♣rt t♠♣rtr r♠s ❲ r ♣rs♥t②♦r♥ t♦ sr ♥ t♦♥ tr♠ s♥tr t♦ t tr s♥tr ♦ tst stts

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P ❯ ❳

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Prt ❱

♦♥s♦♥s ♥ ♣rs♣ts

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♣tr

♠♠r②

s ♣tr s♠♠r③s t ♦r ♣r♦r♠ t♥ t t♠r♠ ♦ ts tss♦♥ ♠♥t t♥♥ ♥t♦♥s ♦♥sst♥ ♦ tr♥st♦♥ ♠t ♦① ♥ ♦♥ ♠♥s♠ ♦① trs s tss r♣rs♥ts ♦♠♣♥♠ ♦ ♦r ♦♠♣s♦♥ t rsr ♥ ♦♥sst♥ ♦ s♠♣ r♦t ♥ rtr③t♦♥ t♥♦♦ ♣r♦ss♥ ♥t♦ s ♥ ♠sr♠♥t ♦ ts s

t t ♦♥st ♦ ts ss s♦♠ ♣r♠♥r② ♦r t♥ ♣ t♦rs②♥ts③♥ s s ♦♥ sts ♣♦st ② P t t P ②r♠t♠r s②st♠ ♥ ♦♥② r♥t② ss♠ ♥ ♥ ♣rtr ♦♥②r♥t② t s♣ttr ♠r ♥ t♦ ♦♣rt ② s ss ♥♦①♣♦r♥ t r♦t ♣ts ♦ ♦t ts ♣♦st♦♥ s②st♠s ♥ ♣rtr t②r s♣ttr♥ s②st♠ t♦r ♠♥ ♥♦r♥ s♣♥tr♦♥ sts

t t ♦♥st ♦ ts ss t rt ♦ ♣r♦ss♥ s♠♣ sts ♥t♦ t♥♥♥t♦♥s st ♣♣r t t P ②t ♦♥sst♥t ♣r♦t♦♦ ♥t ②t ♥ ♥♦t② t♦r ♣r♦ss♥ s♠ s♠♣s s s t♦s r♦♠ t P srs ♦ trt♦♥s t♦ ♦t t ❯❱ ♥ s♦ ♠ss t♦ ♠♣r♦ strtrs

♥t♦tr♥s♣♦rt ♠sr♠♥ts ♠ r♦t♥ ♣rt ♦ t rsr ♦r♦ ♦♥str♠ ♥ ts rsr ♥ ♠② tr♦ ts ss t♥s t♦ tss♠② ♦ t ♦♣♥ss rt ♥

s s t s♠♠r② ♦ s♥t rsts ♦r ts tss tt r ♣rs♥t rtr ♥♦♠♣sss ♦t ♠trt♦♥ ♦ ♥rstrtr rsr ♣ts ♦♥s s♥t ♣r♦r♠ t♦ ♦♠♣s ♦♥ ts rsr ♥ ♦rr♥ ♦ s t♦ ♥rst♥ t ♠♣t ♦ ts ♦♥ ♠♥t♦tr♥s♣♦rt r♦ss♥♦r♥ t♥♥ rrrs

r♥st♦♥ ♠t ♦①s

s tss ♥stt ♠♥t t♥♥ ♥t♦♥s s ♦♥ tr♥st♦♥ ♠t ♦①rrrs t ♥ ♠♣ss ♦♥ ♣r♥ ts rrrs t tr♥st♦♥ ♠t tr♦s

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P ❯❨

s s ♦♥ r3 ♥ 2 rrrs r st ♦2r3♦2strtrs rt t t P s②st♠ s♦ ♦ s♣♥tr♦♥ ♦r♥ rs♦♥s ♦r tr ♠♦rt ♣r♦r♠♥ r ♥t ♥ tr♠s ♦ ♥tr♥ s②♠♠tr② tr♥ sss ♦r♦r t t♠♣rtr ♣♦st♦♥rst ♥ t ② ♦①t♦♥ ♦ ♥trs s♦ s t♦ ①♣♥ ♥ ♣♣r♥t t♥♥♥♦r ♣r t t s♥ ♦ ♥ ♥ tt♠♣t t♦ s♦ ts sss tr3 rrr s r♣ t 2 t♦ ♥sr ♦♠♦♥♦s rrr ♣r♦sttr♠♥t♦♥ ♥ t♦♥ ♦t ②rs r ♥srt t ♥trs s ♦♥ t sts r ♣r♦r♠ ♦♥sst ♦ ♦22♦2 ♥ ♦2♦sts rs♣t② ❯♥♦rt♥t② ts s②st♠s ② s③ s♥ ♦♥②t ♦ t♠♣rtr ♥ tr srt♥ ♥♥♥ ♦ t s ♥rs trrsst♥s ② ♣ t♦ ♦♥ ♦rr ♦ ♠♥t t s t ♠♥t♦rsst♥ t♦♥s ♥tr② I ♠sr♠♥ts ♣r♦r♠ ♦♥ ♦t t②♣s ♦ s s♦ r②♥♦♥♥♦r♠ ♥ ♦ ♦♥ t♦ ❱ rrr ts r t st② ② ♥rt♥ ss s♠♣s t r♣r♦ ♣ t♦ t r♦♦♠ t♠♣rtr ♥♥ ♥st♥s s tt r ≈ ± t ♦ t♠♣rtr t♥s t♦srt♥ ♦ t st ♦ ♦r ♥♦ ts rsts ♦♥sttt t stt♦trt rr♥ tr♥st♦♥ ♠t ♦① rrrs ♣r t tr♥st♦♥ ♠t tr♦s

①ss 2·10−7♠r ♣rssr r♥ ♦r tr♦ ♣♦st♦♥ s ♥ts t ♠♥ rs♦♥ ♦r t ♣♦♦r ♣r♦r♠♥ ♦ ♦2 ♥ ♦s s sss ♦ ♥♦t ♣rs♥t 0.7r0.3♥3 s s s t ♦r tr♦ t♦ t st② ♦ s s ♠s t♥ ts st② ①t rt♠♣rtr ♦ tt s rs♦♥ ♦r ts s②st♠ ♦r ♦r st② s♦♥ tt ♥♦rt♥t② t ♣rs♥t P tr s♥ ♥ ♣♠♣♥ sts ♥♦t ♦♠♣t t t ♦①②♥ ♣rt ♣rssrs rqr t♦ ♦t♥ ♠s t ♦①②♥ ♦♥t♥t tt r♠♥s st ♣♦♥ t♦r♣ ♣r♦ss♥♥ ts s♣t sr tt♠♣t ♥s ♥ t r♦t ♦♥t♦♥s

♥s♠ ♦①

❯s♥ t s♣ttr ♠r ♦ t P ②r s②st♠ ♠s r r♦♥ r②♥ t ♦①②♥ ♦♥t♥t t♥ t r♦♥ ♣s♠ ♣t sts r tt♣♦♥ ♥rs♥ t ♦①②♥t♦r♦♥ rt♦ ♦♣t s♦r♣t♦♥ t♦ s♣ tt②♣s ♠♥ss s♥♥t② ♥rs♣♣r♥ ♦ ♦♥t F ♥ F+

♥trs s ♦♥r♠ ② ♦ ♠sr♠♥ts ♥ ♥tr♦♥ ♦①②♥ t♦ r♠t ♠♣r♦♠♥t ♥ t t♥♥♥ qt② t♦t tr♥ tst♦♣♦r♣② ♥ s ttrt t♦ rt♦♥ ♦ t t sts ♦♥♥trt♦♥♥ rtr ♦♥r♠ tr♦ rr♥t♦t rtrsts s♣tr♦s♦♣s♥trs ♣rs♥t ♥ ♦t t ♦♣t ♥ ♦ t♥♥♥ sts ♥♠♦s②sr t ♠♣t ♦ ♥tr♦♥ ♦①②♥ r♥ r♦t t♦ t ♣♦♣t♦♥rt♦♥ ♦ s♣ ♥t ts s s ts s♦ ♦ ts

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❯ ❳

t♥ t rrr ♥ ♦♥tr♦rt♦♥ ♦ s s ♣ttr♥ ♥ st r♥ t r♦t t♦t

t ♥ ♦r rtr ♣r♦ss♥ ② ♦♣t t♦r♣② s tt♠♣t ♥t♦ ♥t ts rst ♠♦st② ♥ s♦rt s sr t♥ ♠♣r♦♠♥ts r t♦ t r♦t ♣r♦r ♥ s t t t♥♥♥ r♠♥ stst♦r② rrr ts r ♥② ♦t♥ t♦ t ♥t♦♥s ♥♦t② ♥② s♥ ♠♥ rs♦♥ ♦r ts str s♣♥tr♦♥ ♣r♦r♠♥s ttrt t♦ ①ss ♦①t♦♥ ♦ t ♦r tr♦ t♦ 10−7 ♠rr♥ ♣rssr r♥ t ♥♥♥

♦s s♠♣s r r♦♥ ② ♥ t t ♥sttt ♥ ♠♦r ♥ ♥② r ♦ t♠ r ♥♥ ♥ ♦rr t♦ ♦♠♣r t ♠♣t ♦ts ♦♥ tr♠♥t♦rsst ♣r♦♣rts ♥♥ s s♦ s♥♥t② r rt♦ ♦♥ t♦ t t①tr③t♦♥ ♦ ♦t t rrr ♥♥tr ♦ ②rs s rs t♦ ♠♣r♦ s②♠♠tr② tr♥ ♥ ♦r♥t tr♥s♣♦rt r♦ss t r②st♥ strtr ② ①♣♦r♥ ♦ tr ♥tr♠ tt♦♥ ts r ♥ s♣♥♣♦r③ tr♥s♣♦rt s♦ ♦ t s♣♦ss t♦ tr② rss t stts r rsts t♥tt② s♦ tt tst stts ♣② ♥ ♠♣♦rt♥t r♦ ♥ ♠t♥ ♥ t ♣r♦ss s ♠♥ t t♦r r♦♥♥ t s♣rt ♠sr♠♥ts ♦ rrr ts r♣♦rt ♥ t s ♦trs ♦♥sr t ♠♦st ♠str t♥♥♥ s♣♥tr♦♥s②st♠

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P ❯❨

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♣tr

♦♠♣

❲t♥ ts ♣tr ♣rs♣ts ♦ rtr ♦♣♠♥t ♦ sts ♣r♦r♠ r♥ts tss r ♣r♦♣♦s ② ♥♦♠♣ss ♦t ♣r♦♣♦s ①t♥s♦♥s ♥ ♠♦t♦♥s t♦ r♦t st♣s s s ♣r♦♣♦s rt♦♥s ♥ t rt rsr♠② ♣r♦

r♥st♦♥ ♠t ♦①s

Prs♣ts ♦ sts ♦♥ tr♥st♦♥ ♠t ♦①s t♥ P r♠♥ ♠♦st② ♥ss ♦ t ♠tr s♥ ①♣r♠♥ts ♣r♦r♠ t♥ t t♠r♠ ♦ tstss s♦ tt trt♦♥ ♦ rt♥ s♣ts ♦ t P r♦t r ss♥t ♥♦rr t♦ ♦t♥ s t ♣r♦♣rts sr r♦♠ t s♣♥tr♦♥ st♥♣♦♥t

2 ·10−7 ♠r ♣rssr r♥ t ♣♦st♦♥ ♦ ♦r tr♦ ♠trs ♥s t♦ r ♥ ♦rr t♦ r♦ qt② ♦2 tr♦s t♦t ♥tr ♦①t♦♥ ts ♥♥♦t ♦♥ t tr♥t ♥ ♦r♠ ♦ 0.7r0.3♥3 s ss ♥t♣t ♦r sss ♦ ♦①②♥ st♦♦♠tr② ♥ ♦①②♥ rt♥t♦♥ t♥t ♠ r♥ t♦r♣② ♥ t♦ rss ❲ ♣r♦♣♦s st ♦♦♣t♦♥s t♦ ♥stt ♦r ♥r② t♦ t ♦r ♥ ♣ ♦ tr♥st♦♥ ♠t♦①s ♥ ② rt ♦ tr ♠♦r ①♦t ♦♠♣① ♥ strtr tr♥st♦♥ ♠t♦①s ♠♥t t♥♥ ♥t♦♥s ♦♥sttt ♣r♦♠s♥ tst s②st♠ ♦r ♠t♥t♦♥ s♣♥tr♦♥s tt ♦♠♥ ♠♥t tr ♥ ♦♣t ♥t♦♥tss rtr

♥s♠ ♦①

♥ tr♠s ♦ ts st② t♥ tr r②sts sr rtr st♣s r ♣r♦♣♦sr♥ t ♠♣t ♦ s♠♣ ①♣♦sr t♥ t r♦t ♥ rtr③t♦♥tr♠♥♥ t ♦t♦♥ ♦ t ♥ ♣ r♦ss t♦♠ ♣♥s ♥ t♦♥ st②♦ t sr♥tr ♥tr ♦ ts ♥ t♥ ♠s ♦s tr♥st♦♥ ♥rs ♥

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P P

♣♦st♦♥s t♥ t ♥ ♣ r r♥t r♦♠ t♦s ♦ t ♥ r♠♥ r②♥st s sts r st ♦r t r t♠♣rtr tt ♦♥♥t t♦ t ②r s②st♠ ♥ t ♥r tr

♠r② t♦ t P r♦t t♥q t rtr ♣♦♦r s♣♥tr♦♥ ♣r♦r♠♥♦ t s♦♠ss s s t♦ ♠♣r♦ ② rs♥♣rssr ♥ t ②r ②st♠s ♠r r♥ t ♥♥♥ ♦ t ♦r tr♦♥ ♠② ♠♣r♦ t ♠ ♣♦t♥t② ② ♦ttt♥ t s♣ttr ♠rs ♠♥st t r♥t ♣♠♣♥ ♥ ♠② s♦ ♣♦t♥t② ♦♥sr r♣♥ ♥ ♦ tr♦s t ♦ ♦♠♣♦♥s s♦ s t♦ r♠♥t ♦①t♦♥ sss tt ♥t♦♥ ♥tr

①♣r♠♥ts ♣r♦r♠ ♦♥ ♦s s ♣♣r t♦ r② ♣r♦♠s♥sss rt t♦ t t ♥②ss r♠♥ s♠r t♦ ts rt t♦ ♦ r②sts t ♣tt♦♥ ♦ ♦r ♠♦ ♦ t t ♥s♣ ♥ r②st ♦r tt♥ ♠s ♥ t♥ ♥tr ♥tr ♦ ts ♥t♦ t ♦♥t ♦rrt♦♥t♥ s♣rt② ♦♥t ♦♣t ①♣r♠♥ts ♥ ♠♥t♦tr♥s♣♦rt ①♣r♠♥ts s t♦ t♥tt② ♣♦st♦♥ t r♠ ♦ t tr♦s rt t♦ t♥ ♥ ♦♥t♦♥ ♥ s ♦ Pr♦r♠♥ ts ①♣r♠♥ts ♦♥t②♦ rt② ♣ s♦ ts ♠♣♦rt♥t ♣♦♥t s rtr ♥ tr♠s ♦ t tr st② sr t♦♥ s②st♠s r ♣♥♥ t♦ tst ♥ ♦♦♣rt♦♥t ♥sttt ♥ ♠♦r ♥ ♥② s ♥ ♥t♦♥s t sr ①ss t♥sss t strt② ♥t② ♦♣ ② ♦♥ r♥ s ssrr♥ s ♥ r♥t② r♣♣ t♥ t ❯P② r♦♣ ♥ t s♦ s ♥ ♦rr t♦ st② s②st♠s ♥ t ♦♥t♥ s r③ t sts ♦♥② ♦r ♥r② ts rsts ♥ t s♥t ♠t♦♦♦② tt♥rs♦rs t♠ ♠② r♣♣ t♦ ♦tr ♦①s ♥♦t② t♦s t ♥♦♠♥②①♣t rr♦trt② ♦r ♠trr♦t② s♦ s t♦ ♥rst♥ t♦ t ①t♥t ts♥tr♥s ♠trs ♣r♦♣rts r ♦r♥ ♥ s ② ts

♣t ss

r♥ t t♠ ♦ t rt♥ ♦ ts ♠♥sr♣t r♥ ♥ st♦♠♠ st♣ t♥t♦♥ ♥ ♥ t♦♥t♦♥♥ ♥ r♥ ♦r s ss♠ ♥ s t t t♠ ♦ ts rt♥ ♦♣rt♦♥ t ♥♦♠♥ ♠♥t♦tr♥s♣♦rt♥ r♠♥tr② ♦♣t ♣ts t s s♥ t♦ ♥ ♦♠♥ ♦♣t ♥tr ♠t♣①♥ sts ♦♥ s s s ♠♥t t♥♥ ♥t♦♥s st♣ ♥ts r♦♠ rt② ♠♦r♥③ s♥ ♦♠♣r t♦ t rt st♣s♦ t t③s t s♠ ♣ s♥ ♦r t ♦s t♦ ♣s t♦ ♠♦♥t ♥♠sr s♠t♥♦s② r♦♦t ts ss t ♦s s ♥ t♦ t③ ts♥ ♦♥ ♦♣rt♦♥ t♦ ①♣♦r t ♥tr♣② ♦r ② t stts t♥t t♥♥ rrr t♥ t ♠♥t tr ♥ ♦♣t ♥t♦♥ts ♥ ♠♥t t♥♥ ♥t♦♥ ♦r ts ♥ ❯❱ t♦r♣② ♠ss r s♥

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strt♥ ♥ r② s♦ s t♦ ♥ ♦♣t ss ♥ r ♠♣r♦ s ①♣rtss tt♥ ♦♥ ♦ t♦ st ts ♦♣t ss s ②♦ r ts ♥s s♦ ♣r♦r♠♥ t rst ♦♠♥ ♦♣t♦♠♥t♦rsst ♠sr♠♥ts ♦♥t ♠♦ ♥♦r♥ ♠♥t t♥♥ ♥t♦♥ s②st♠ ♦♦ t②t♥

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♦r♣②

❬❪ ♦♦r r♠♠♥ ♠♦r ♦♠♣♦♥♥ts ♦♥t♦ ♥trt rts r♣r♥tr♦♠ tr♦♥s ♦♠ ♥♠r ♣r ♣♣ ♦ttrts sttr ♦ ♣♣ s♣t

❬❪ r♦t♦ rt ❱♥ Ptr♦ P t♥♥ r③t rr ♥ ③s ♥t ♠♥t♦rsst♥ ♦r ♠♥t s♣rtts P②s tt ♦ ♣♣ ♦

❬❪ ♥s P rü♥r r♥ ♥ ❲ ❩♥♥ ♥♥ ♠♥t♦rsst♥ ♥ ②r ♠♥t strtrs t ♥trr♦♠♥t ♥tr②r①♥ P②s ♦ ♣♣ r

❬❪ Pr♥ ❳ ♥ sr P♥ ♦ ♥ ♠♥t ♥t② ♥♥r s♣♥tr♦♥ s♥s♦rs ♥ ♠♠♦r② Pr♦♥s ♦ t ♦ ♣♣ ♠②

❬❪ P r♦ ♥ sr② ♣♥ ♣♦r③t♦♥ ♦ tr♦♥s t♥♥♥ r♦♠♠s ♦ ♦ ♥ ♥ P②s ♦ ♣♣ ♥

❬❪ P s♣r♦♥tt② ♥ t♥ ♠s ♥s ♥ P②ss♦ ♥♦ ♣♣

❬❪ ♦♦r ♥r ❲♦♥ ♥ sr② r ♠♥t♦rsst♥ t r♦♦♠ t♠♣rtr ♥ rr♦♠♥t t♥ ♠ t♥♥ ♥t♦♥sP②s tt ♦ ♣♣ ♣r

❬❪ ❲♥ ♦r♠♥ t♦♥ ❩ ♥ ♥ ♥ t♠♣rtr♦r st s♥ ♥t♦♥s t ♦ s r ♥ rr♥ ②rs ♥ts r♥st♦♥s ♦♥ ♦ ♣♣ ②

❬❪ r♥ ❲ tr ♥ ❳ ❩♥ ♣♥♣♥♥t t♥♥♥♥ ♣t① s②st♠s ♥ ♣♥♥ ♦ ♦♥t♥ ♦r♥ ♦ ♣♣P②ss ♦ ♥♦ ♣♣

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❬❪ t♦♥ ♥ ❯♠rs ♦r② ♦ t♥♥♥ ♠♥t♦rsst♥ ♦ ♥♣t① ♠♦ ♥t♦♥ P②s ♦ ♣ ②

❬❪ ♦♥ ❱ r♦s Ptr♦ rt ♦t ♦str♠r ❱ ♥t ♦ r♦♥s rs ♦r♦♥ rr Pr♦ ♥ ♦r♥t r ♠♥t♦rsst♥♥ ♠♦♦ ♣t① t♥♥ ♥t♦♥s ♦♥ s ♣♣ P②ssttrs ♦ ♥♦ ♣♣

❬❪ P♦♣♦ r❱♥♥t s♥ ♦r sr ♥ ♦♥t♥ ♥♦t ♥r ♥♦ ♥ ❱ ♦st♣t① ♠♦ ②r ♦r ♦rsst♥ ♥ ♦♣♥r ♠♥t t♥♥ ♥t♦♥s ♣♣ P②ss ttrs ♦ ♥♦ ♣♣

❬❪ ❨s s♠ ♠ ♥♦ ♥ ❨ ③ t♥♥ ♠♥t♦rsst♥ t r♦♦♠ t♠♣rtr ♥ ② ♣t① ♠♦ t♥♥♥t♦♥s t♦ ♦r♥t s♣♥♣♦r③ t♥♥♥ ♣♥s ♦r♥ ♦ ♣♣ P②ss ♦ ♥♦ ♣♣

❬❪ ❨s ♥ ②♣rr ♥t t♥♥ ♠♥t♦rsst♥ ♥ ♠♥t t♥♥ ♥t♦♥s t r②st♥ ♠♦ rrr ♦r♥ ♦ P②ss ♣♣ P②ss ♦ ♥♦ ♣

❬❪ ② ❨ s③ ❨ r s s♥♦ tsr ♥ ♥♦ ♥♥ ♠♥t♦rsst♥ ♦ ② s♣♣rss♦♥ ♦ t s♦♥ ♥ ♦♠♦♦ ♣s♦s♣♥s ♥♥ t t♠♣rtr ♣♣ P②ss ttrs ♦ ♥♦ ♣

❬❪ Pr ❱s♦♦ ♠ ♦♥ ♠s ♥ ❱♥ts♥rt ♥ ♦r ♠t rr♦♠♥t tr ♦♥♦♥ ♦ ♣

❬❪ ♦♥ s rt♠② P ♦♥t♦r ♥♥ ❨ ♠tr♥ rt r② t♦t s♣♥ ♣♦r③t♦♥ ♥ ❬s ❪sr❬s ❪♠♥♦❬s ❪r♦♠ t♥♥♥ ①♣r♠♥ts ♣♣ P②ss ttrs ♦ ♥♦ ♣♣

❬❪ t♦ s ♥ ♥♦ ♥t♦rsst♥ ♦ rr♦♠♥t t♥♥♥t♦♥s ♥ t ♦①♥ ♠♦ P②s tt ♦ ♣♣ r

❬❪ ♦r ♥ tr♦♥s ♦rt ♠♥t tr ♦ ♣♣ ②

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❬❪ ❲ tr ♥♥♥ ♠♥t♦rsst♥ r♦♠ s②♠♠tr② tr♥ t♥ ♥ ♥♦♦② ♦ ♥ trs ♦ ♥♦ ♣

❬❪ ♠♠♦♥s ♥r③ ♦r♠ ♦r t tr t♥♥ t t♥s♠r tr♦s s♣rt ② t♥ ♥st♥ ♠ ♦r♥ ♦ ♣♣P②ss ♦ ♥♦ ♣♣

❬❪ ❲ r♥♠♥ ②♥s ♥ ♦ ♥♥♥ ♦♥t♥ ♦s②♠♠tr rrrs ♦r♥ ♦ ♣♣ P②ss ♦ ♥♦ ♣♣

❬❪ ❩ ♥ Pr ♥t t♥♥ ♥t♦♥s trs ♦② ♦ ♥♦ ♣♣

❬❪ ❲ ❩♦♥ r♥② ♥ ♦♠ trtr ♣r♦♣rts ♦ r②stsP②s ♦ ♣♣ ♥

❬❪ r ♥♥♥ t♥ rr♦♠♥t ♠s P②ss ttrs ♦ ♥♦ ♣♣

❬❪ ♦♥③s ♦♥t♥ ♥ ①♥ ♦♣♥ ♦ t♦ rr♦♠♥tss♣rt ② t♥♥♥ rrr P②s ♦ ♣♣ ♣r

❬❪ ❲ tr ❳ ❩♥ tss ♥ r♥ ♣♥♣♥♥t t♥♥♥ ♦♥t♥ ♦ Fe|MgO|Fe s♥s P②s ♦ ♣ ♥

❬❪ ❳ ❩♥ ❲ tr ♥ ♥②♦♣②② ts ♦ t r♦♥♦①②r ♥ ♦♠♦ t♥♥♥ ♥t♦♥s P②s ♦ ♣ ♣

❬❪ ❨ ❲♥ ❩♥ ❳ ❩♥ P ♥ ♥ ❳ ♥ rst♣r♥♣sst② ♦ ♠♦ s ♠♥t t♥♥ ♥t♦♥s t ♠ ♥tr②rs P②s ♦ ♣

❬❪ s♥ rt ♥ ♦♥t♥ ♥r ♥ ♣♥ t♥♥♥ ♣♥♦♠♥ ♥ s♥r②st ♠♥t t♥♥ ♥t♦♥ s②st♠s ♦r♥ ♦ P②ss ♦♥♥s ttr ♦ ♥♦ ♣

❬❪ P rs P r♦♣♦♦s ❲♥♥ P♣♥♦♦ ❱ ♥ ❩r ❱ r ♥ r♥♦s ♠♣♦rt♥ ♦ ♦♠♣① ♥ strtr ♥ rs♦♥♥t stts ♦r t♥♥♥ ♦r♥ ♦ ♥ts♠ ♥ ♥ttrs ♦ ♥♦ â⑨➇ ♣♣ ttt ♥tr♥t♦♥ ②♠♣♦s♠ ♦♥ t t②rstt

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❬❪ ❱ ♥ ♦r② ♦ sr stts P②s ♦ ♣♣ ♥

❬❪ P r♦♣♦♦s P♣♥♦♦ ♥ P rs ♦♠♣① ♥ strtr ♥ t♥♥♥ tr♦ rr♦♠♥t /♥st♦r /rr♦♠♥t ♥t♦♥sP②s tt ♦ ♣♣

❬❪ r❱♥♥t s♥ ♦t ♥t ♥ ♦r P♦♣♦ ♥ ♦♥t♥ ♥ t♥♥ ♠♥t♦rsst♥ ♥ ♣t① ♠♦ t♥♥ ♥t♦♥s ♣♣ P②ss ttrs ♦ ♥♦ ♣♣

❬❪ ❩♥ P ② r② ♥ P Pr♥ ♥♥ ♦♠♥t♦rsst♥ ② ♦t tr♦♥s ♥ ♠♥t t♥♥ ♥t♦♥s P②s tt ♦ ♣♣ ♦

❬❪ s♥ r❱♥♥t ♦t ♥ ♦r ♦♥t♥ ♥r ♥ ♣♥ tr♥ ts ♥ ♠♦♥♦rst♥ ♠♦♠♥t t♥♥ ♥t♦♥s trs ♥ ♥ ♥♥r♥ ♦ ♥♦ â⑨➇ ♣♣ tt ②♠♣♦s♠ ♣♥tr♦♥stt

❬❪ P r② r Pr① ♥ ♥♦ ♥rr ♦♣t ♦♥st♥ts ♦ ♥st♦rs tr♠♥ ② rs♦t♦♥ tr♦♥♥r②♦ss s♣tr♦s♦♣② P②s ♦ ♣♣ ♣r

❬❪ ❱ r♦ ärs ♠ ♥ ü♥♥rr ♠♦rst ss ♥ ♦♠s ♥st tr♦♥ t♥♥♥ s♣tr ♦ ♠♦s ♠♥t t♥♥ ♥t♦♥s t r♥t tr♦ s♥sP②s ♦ ♣ ②

❬❪ ❩♥ ❳ ❩♥ ♥ ❳ ♥ ♣♥ ♦①s t❬s ❪ s♣♥tr rrr ♦r ss ♦ ♠♥t t♥♥ ♥t♦♥s ♣♣ P②ss ttrs♦ ♥♦ ♣

❬❪ trt t②♣ ♦ ♠♥t t♥♥ ♥t♦♥ s ♦♥ s♣♥ tr♥tr♦ r s②♠♠tr② ♦① ♦⑤♠♦⑤♦ ♥♦ ttrs ♦ ♥♦ ♣♣ P

❬❪ ♦♥ r rt♠② s ♠♦ ❱ ♥ rt♦ ❲♦rt♠♥♥ P ♥♦r qt ❱rs ♠rtP ♦♥t♦r ♦① ♥ P rs ❯s♥ ♠t♠♥♥t ♥trs t♦ r ♥sts ♥t♦ s♣♥tr♦♥s ♦r♥ ♦ P②ss♦♥♥s ttr ♦ ♥♦ ♣

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❬❪ r ♠♦ P ♦♥t♦r ♥ ♦① ♥trs ♥ ♣t① tr♦strtrs ♦ ♣r♦st ♦①s P♦s♦♣ ③♥ ♦ ♥♦ ♣♣

❬❪ ♦♥ rtéé♠② ❱ ♥ s P ♥♦r qt P♦♥t♦r ♥ P rs srt♦♥ ♦ ♦r♥♦r♠ ♦ t♥♥♥r♦ss ♥ tr♦♥ t♥♥ ♥t♦♥ t♦ t♦t s②♠♠tr② tr♥ P②s ♦ ♣ ♣r

❬❪ ❱r rú♥ P♦st♠ ♦r ♥ ♥s♥ ♥♥♥♠♥t♦rsst♥ t ♣♦st ♥ ♥t s♥ ♥ la0.67sr0.33mno3/srtio3/Co♥t♦♥s P②s ♦ ♣

❬❪ s ♦♥ rt♠② ♥♥ ♦③♦♥ rrtr♦ qt P ♦♥t♦r ♥ r♥ r♦t ♥ rtr③t♦♥ ♦t♦❬s ❪ s rrr ♦r s♣♥♣♦r③ t♥♥♥ ♣♣ P②ss ttrs♦ ♥♦ ♣♣

❬❪ s ❲ ❨ ♥ ❯♥ ❨ ♥ ♥ ❨ ♦♦♥♦♣s t♦❬s ❪ ♠s ♣♦st ♦♥ srt♦❬s ❪ ② ♣s srt♦♥ ♦r♥ ♦ ♣♣ P②ss ♦ ♥♦ ♣♣

❬❪ ♥ rt③ rt ♠♥③ ♥ tr♦♠ ♥ ♣♦t♦tr♦♠ ♥stt♦♥ ♦ s♥r②st ♥ts♦r♥ ♦ t ♠r♥ ♠ ♦t② ♦ ♥♦ ♣♣

❬❪ s ❨ ❲ ♥♥stt ♥ r♠♥ tr♦♥ ♥ ♦♣t♣r♦♣rts ♦ ♥ts tio2 P②s ♦ ♣♣ r

❬❪ ❨s s♠ ♦t ❨ ③ ♥ ♥♦ ♥t t♥♥♥♠♥t♦rsst♥ ♣ t♦ ♣r♥ts t r♦♦♠ t♠♣rtr ♥ ② ♣t①♦♠♦♦ ♠♥t t♥♥ ♥t♦♥s t ♦ tr♦s ♣♣P②ss ttrs ♦ ♥♦ ♣

❬❪ ❳ ❩♥ ♥ ❲ tr r ♠♥t♦rsst♥ ♥ Co/MgO/Co♥ FeCo/MgO/FeCo t♥♥ ♥t♦♥s P②s ♦ ♣ ♦

❬❪ Pr♥ sr P♥ P s ♠♥t ♥ ❨♥ ♥t t♥♥♥ ♠♥t♦rsst♥ t r♦♦♠ t♠♣rtr t ♠♦ t♥♥ rrrs tr trs ♦ ♥♦ ♣♣ t ② s♥

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❬❪ ♦♥ t ♥r rtr♥ P èr ♠s ♦♥t♥ ❲r♦t♦♥r♦s ♦♦ ♥ r♠ ♣♥♣♦r③ tr♦♥ t♥♥♥ ♥ FeCo/MgO/FeCo(001) ♠♥t t♥♥ ♥t♦♥s P②s tt ♦ ♣ ♣r

❬❪ ❨s t②♠ ♠ s♠ ♦t ❨ ③♥ ♥♦ ♥t t♥♥♥ ♠♥t♦rsst♥ ♥ ② ♣t① ♦②♥tr ♦♠♦ ♠♥t t♥♥ ♥t♦♥s ♣♣ P②ss ttrs♦ ♥♦ ♣

❬❪ ❲ ♦♥♥r ♦s ts ♥ rü rt s♦r♣t♦♥ ♥ ♠♥s♦♥ r♦ss♦r ♥ ♣t① ♦ ♠s P②s tt♦ ♣♣

❬❪ ❨s ❨ ③ t②♠ ♥ ♥♦ rtr③t♦♥ ♦ r♦t♥ r②st③t♦♥ ♣r♦sss ♥ ♦♠♦♦ ♠♥t t♥♥ ♥t♦♥strtr ② rt ♥r② tr♦♥ rt♦♥ ♣♣ P②ss ttrs ♦ ♥♦ ♣

❬❪ ❨ ♦ s♥ ❨ ♠♥ ♥ ②♣rr r♥s♠ss♦♥tr♦♥ ♠r♦s♦♣② st② ♦♥ t ♣♦②r②st♥ ♦♠♦♦ s ♠♥t t♥♥ ♥t♦♥ s♦♥ t♥♥♥ ♠♥t♦rsst♥ ♣rt ♥s♥ r②st ♠♥t t♥♥ ♥t♦♥ ♦r♥ ♦ ♣♣ P②ss ♦ ♥♦ ♣

❬❪ ③ ❨ ③ ♠ ♥ ❨s ♥ st s♥♥♥ t♥♥♥ ♠r♦s♦♣② ♦srt♦♥s ♦ ♣♦②r②st♥ ♠♦ t♥♥♥ rrrsr♦♥ ♦♥ ♠♦r♣♦s ♦ tr♦ ♣♣ P②ss ttrs ♦ ♥♦ ♣

❬❪ r s ♦r ♥ ♦r ❨ ♥♥ ♦♥t♥ ♦rt r ♥ s♥ ♠♦ t①tr t♥♥ ♥t♦♥s ①t♥ s♣♥ ♣♦r③t♦♥ trs ♦ s♥r②st ♥t♦♥s ♣♣ P②ss ttrs ♦ ♥♦ ♣

❬❪ rr ❨ ♦ ❨ r♠♦♥t ♠♥ ♥ Pt♦r♦♥ ♥♥ ♠♥t♦rsst♥ ♥ ♥tr② ♦①③ ♠♦s ♠♥t t♥♥ ♥t♦♥s t rr♦♠♥t ♦♦ ②rs ♣♣ P②ss ttrs ♦ ♥♦ ♣

❬❪ r♦♦t r P ♥♥ ♥ s♦ ss ♦ ♠trs ♠t rr♦♠♥ts P②s tt ♦ ♣♣ ♥

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❬❪ ♦♠s tr♦♥ strtr ①♥ ♥ ♠♥ts♠ ♥ ♦①s ♥♣♥ tr♦♥s ❩s ♥ ♦r♥t♦♥ s ♦ ♦ tr ♦ts♥ P②ss ♣♣ ♣r♥r r♥ r

❬❪ ❩♥r ♥trt♦♥ t♥ t dss ♥ t tr♥st♦♥ ♠ts rr♦♠♥t ♦♠♣♦♥s ♦ ♠♥♥s t ♣r♦st strtr P②s ♦ ♣♣ ②

❬❪ s r ♥ r♠♥ r♠qt♦♣♦r♦♥r♦ss♦r ♦ ①♥ ♥ t ♣②ss ♦ ♦♦ss ♠♥t♦rsst♥P②s ♦ ♣♣

❬❪ P ❲ ♥rs♦♥ ♥ s ♦♥srt♦♥s ♦♥ ♦ ①♥ P②s ♦ ♣♣ t

❬❪ s P tt♦♦ ♥ r♠♥ ♦ ①♥ ♦♥♦s ♥♦t ①♣♥ t rsstt② ♦ La1−x

srxmno3 P②s tt ♦ ♣♣ ♥

❬❪ ♥ ♥ r tt② ♦ ♣♦②t♦♠ ♠♦s ♥ ♥rttr♦♥ stts ♦rt ♥r② Pr♦♥s ♦ t ♦② ♦t② ♦♦♥♦♥ rs t♠t ♥ P②s ♥s ♦ ♥♦ ♣♣

❬❪ P ♥♥s ts ♦ ♦ ①♥ ♥ ♠♥t r②sts P②s ♦ ♣♣ ♣r

❬❪ ♥ ♥ r♥ ♥ ♦♠s ♦ ①♥ ♥rt ♦rtsP②s tt ♦ ♣♣

❬❪ ❱ r s rtéé♠② ♦♥ qt P ♦♥t♦r♥ rt ♠♣rtr ♣♥♥ ♦ t ♥tr s♣♥ ♣♦r③t♦♥ ♦la2/3sr1/3mno3 P②s ♦ ♣

❬❪ Pr ❱s♦♦ ♠ ♦♥ ♠s ♥ ❱♥ts♥ ♥t ♣r♦♣rts t sr ♦♥r② ♦ ♠t rr♦♠♥tla0.7sr0.3mno3 P②s tt ♦ ♣♣

❬❪ s s ❱♥ ♦♥trt ❲♦ r②♥ ♦s ♥♦s ♠t♣s s♣rt♦♥ t la2/3ca1/3mno3/srtio3♥trs P②s tt ♦ ♣

❬❪ s ❱♥ s rt♥③ ♦♥trt ❲♦ ♦s ♥ r② r tr♣♣♥ ♥ ♦♣t♠② ♦♣ ♣t①♠♥♥t t♥ ♠s P②s ♦ ♣ t

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❬❪ ró♥ r② ♥ ♥ r tr♦♥ strtr ♥♠♥t ♣r♦♣rts ♦ ♦♣ ♠♥♥ts P②s ♦ ♣♣ ♣

❬❪ ♠ ♠♦r ♥ ❨ ♦r t♥st♦r tr♥st♦♥s ♦ P②s ♦ ♣♣ t

❬❪ ❨ ❳ ♥ ♦ ①②♥♥②♥ s sttr♥ ♥Fe/MgO/Fe ♠♥t t♥♥ ♥t♦♥s P②s tt ♦ ♣ ♦

❬❪ rs♦ ♦tt② rrr ts ♥ t ♦♥t♥♠ ♦ ♣ stts P②s tt ♦ ♣♣

❬❪ ♥ ♦ ♥s♥ ♥ ♦♦r ♠♣rtr ♣♥♥ ♦ ♠♥t♦rsst♥ ♥ sr ♠♥t③t♦♥ ♥ rr♦♠♥t t♥♥♥t♦♥s P②s ♦ ♣♣

❬❪ ❨ r♥ rès P ♥♦r r♥♦t Ptr♦ ♦r é♣♥ ♦ ♥ é③éq ♣♥♣♦r③ ♥st t♥♥♥tr♦ ♥st♥ rrrs P②s tt ♦ ♣ ♣r

❬❪ ♦r②♠ ❲ ❲♥ ❳ ❩♥ ♥ ❳♦ ♥♥♥♠♥t♦rsst♥ ♥ ♦r♥t ♦♠♦♦ ♠♥t t♥♥♥ ♥t♦♥s r♦♥ ② s♣ttr♥ ♣♦st♦♥ ♣♣ P②ss ttrs ♦ ♥♦ ♣

❬❪ t♦♥ ♥ ❯♠rs ♦r② ♦ t♥♥♥ ♠♥t♦rsst♥ ♥ s♦rr Fe/MgO/Fe(001) ♥t♦♥ P②s ♦ ♣ t

❬❪ ❨ ♥ ♥ ♥ ♦② ♥ ♥r ♠♥t♦rsst♥♥ ♠♦ ♠♥t t♥♥ ♥t♦♥ s♥s♦rs s♥ t♦ ♣♥♥ ♦ tr♦s♣♣ P②ss ttrs ♦ ♥♦ ♣

❬❪ ♠r ♦s s r③rt ♦♠r Pr♥ ② ♥ ♥② r tr♣♣♥tr♣♣♥ ♠♥s♠ ♦ rrr r♦♥ ♥ ♠♦ ♠♥t t♥♥ ♥t♦♥s ♣♣ P②ss ttrs ♦ ♥♦ ♣

❬❪ ①r ❱♥tr P r♦ ♦s P r♥♥③rP ❲s♥♦s ♥ P P rts ♥ ♦ s♣♥♣♦r③ rt st t♥♥♥ ♥ ♦♥st ♦ s♣r♣r♠♥ts♠ ♥ ♠♦ ♠♥t t♥♥ ♥t♦♥sP②s ♦ ♣ ♣r

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❬❪ ❲ ❲♥ ❳ ♦ ❲♥ ❳ ♥ P Prs♦♥ ♦r♥st ❳ ♦ ❨ P ❩♥ trrtt ♦ ♣ ♦♦r ♥ ❳♦ ❯♥rst♥♥ t♥♥♥ ♠♥t♦rsst♥r♥ tr♠ ♥♥♥ ♥ ♠♦s ♥t♦♥s t ♦ tr♦s P②s ♦ ♣ ♣r

❬❪ r♥♦s ♥ ♦♥t♥ s♥ ♦r ♥♦t s ♥♥ ♥♦ ♥ ♠♣t ♦ tr♦♥tr♦♥♥trt♦♥s ♥ ② s♦rr t ♥trs ♦♥ s♣♥♣♥♥t t♥♥♥♥ ♦♠♦♦ ♠♥t t♥♥ ♥t♦♥s P②s ♦ ♣

❬❪ ② ❨ tsr ♥ ♥♦ t♦ ♥♥♥ t♠♣rtr ♦♥ ♥t t♥♥ ♠♥t♦rsst♥ rt♦ ♦♦♠♦♦ ♠♥t t♥♥ ♥t♦♥s ♣♣ P②ss ttrs ♦ ♥♦ ♣

❬❪ ② ❨ ♥ tsr ♥ ♥♦♥♥ ♠♥t♦rsst♥ ♥ ♠♦rrr ♠♥t t♥♥ ♥t♦♥s t ♦ ♥ ♦ r ②rs ♦r♥ ♦ ♣♣ P②ss ♦ ♥♦ ♣

❬❪ ②♣rr s♥ r ❨♠t ❲t♥ ❨s ❨ ③ ♥ ♥♦ ♠♥t♦rsst♥ ♥♦♠♦♦ ♠♥t t♥♥ ♥t♦♥s ♣♣ P②ss ttrs ♦ ♥♦ ♣

❬❪ r ❨♠♠♦t♦ ③♥♠ ♥ ♥♦ ♥ ② tsr ♥ ♥♦ ♣r♣♥r♥s♦tr♦♣② ♦♠♦ ♠♥t t♥♥ ♥t♦♥ t tr ♦ ♣ ♣

❬❪ rr♥③ ♦♠③r rs r ss ♥ ♦ rq♥② ♥♦s t♦ ♠♥t ♥♦♠♦♥ts ♥ s♠r♦♥♦♠♦♦ ♠♥t t♥♥ ♥t♦♥s ♣♣ P②ss ttrs ♦ ♥♦ ♣

❬❪ ❲ ❲♥ ♠③ ❨ ❲♥ ❳ ♥ ♦r②♠ ♦ ❨❲♥ ❲ ❩♥ ♥ ❳♦ t♠ ♦t♦♥ ♦ t♥♥♥ ♠♥t♦rsst♥ r♥ ♥♥♥ ♥ ♦♠♦♦ ♠♥t t♥♥ ♥t♦♥s♣♣ P②ss ttrs ♦ ♥♦ ♣

❬❪ P ❩r♠tt♥ ♦♥ ♥r s s♥ ♥ ♥ ♥♥ ♦ ♦①②♥ ♠♦♥♦②r t ♠♦ ♥tr ♦♥ tr♥s

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♣♦rt ♣r♦♣rts ♥ ♠♦ ♠♥t t♥♥ ♥t♦♥s ♣♣ P②ss①♣rss ♦ ♥♦ ♣

❬❪ ♦♥ ♥r t s♥ ♥ ♥♥ ♦♥sq♥s ♦ ♥tr ♦ ♦♥♥ ♥ s♦rr ♥ ♣t① ♠♦♠♥t t♥♥ ♥t♦♥s P②s ♦ ♣ ♥

❬❪ ❳ ♦ ❨ Pr ♦♦r t rs ♥ ü♥③♥r str♥ ♦ t♥♥♥ ♦r♥ ② ♦①②♥ ♥② ♥ ♣t①Fe/MgO/Fe ♠♥t t♥♥ ♥t♦♥s P②s tt ♦ ♣ ♥

❬❪ ❨s ♠ s♠ ❨ ③ ♥ ♥♦ ♥t r♦♦♠t♠♣rtr ♠♥t♦rsst♥ ♥ s♥r②st ♠♦ ♠♥t t♥♥♥t♦♥s t tr ♦ ♣

❬❪ t♦♠♦ r r③ ♥ ❨ ♥ rt r♠♦t♦♥♥ t♦♠s ♣r♦st tt♥t s♣rtts tr ♦ ♣ ♣

❬❪ ♦s♥tt ❲ ♦ P ❲♠s ❲♠s ♥ ❨ ♥♠♥s♥ ♦ ♥ F+ ♥trs ♥ ♠♥s♠ ♦① P②s ♦ ♣♣ ②

❬❪ ♣♣rs r♦s ♥ ♥s② F+ ♥ F′

♥trs ♥ ♠♥s♠ ♦① P②s ♦ ♣♣ ②

❬❪ ♦♠♥③r③ ♦s s ♥ P♦♥ r♦♥♥ ①tstt ♣r♦♣rts ♦ ♥tr ♦①②♥ ♥② rts ♥ t ♥ sr ♦ ♠♦ P②s ♦ ♣

❬❪ s♦♥ ②♦ ♥ P ♠♥ tt② ♦ ♥② ts ♥♠♦ r♦ ♦ r ♥trt② P②s ♦ ♣♣

❬❪ ♦♥ ♥ r♥r ♠rs♦ s♣tr♦s♦♣② ♦ t s ♠ss♦♥ ♥ ♥ str♦♥t♠ tt♥t P②s ♦ ♣♣ ♥

❬❪ s♦r♦é♥ ♥② ♥ ❩♥r t♦♠ ♦♥tr♦ ♦ ♦♥tt②rss rr♦♠♥ts♠ ♥ ♣ ♦①s st ♦♣♥ ❱ ♥ t ♥♥ts tio2 P②s tt ♦ ♣ ♥

❬❪ ❨ ❯♥ ♥ ❯♥♦ P♦t♦①tt♦♥ tr♣♣♥ ♥ r♦♠♥t♦♥ ♣r♦sss ♦ t f t②♣ ♥trs ♥ s♥ ♠♦ ♠r♦r②sts P②s ♦ ♣ ②

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❬❪ ♥s P♦ts♥ ♥ ❨ ♥ ♣t ♣r♦♣rts ♦ ttts ♥ ❰♦ r ♥str♠♥ts ♥ t♦s ♥ P②ss srt♦♥ ♠ ♥trt♦♥s t trs ♥ t♦♠s ♦ ♥♦ â⑨➇♣♣

❬❪ ♣③③ ♥ r♦ ♣t ♣ ♦ str♦♥t♠ tt♥t t♦♥ r♦♠r t ♦r P②s tt ♦ ♣♣ ♦

❬❪ ♦ ♥ ❨ ♦ ♥ ❲ ♠ ♥ ♠ ♥♥ ♦ P♦t♦♠♥s♥ ♥ ② tr♠ ♥♥♥ ♥ srt♦❬s ❪t♥ ♠ ♣♣ P②ss ttrs ♦ ♥♦ ♣

❬❪ ♦♥ ♦ ♥ ♥ ♥ ①②♥♥② str♥ ♥ tr♦♥ ♦③t♦♥ ♥ ♦①②♥♥t srtio3 LDA+ust② P②s tt ♦ ♣ r

❬❪ ♥ rs♠ ♥ s♥♦ ♥ ♥ s③♠ ❨ ♥♠ts ❨ ♠ ♥ ♥♦ t ♠ss♦♥ t r♦♦♠ t♠♣rtr r♦♠ rrrt srt♦ t tr ♦ ♣ ♦

❬❪ r♥r P♦t♦♠♥s♥ ♥ srto3 P②s ♦ ♣♣ ♥

❬❪ ❩s ♦♣t♦ r ♥t Pt♥ts ♦♥ ♥♥r♥ ♦ ♥♦ ♣♣

❬❪ ♣♣♥s rtr♥sr s♣tr ♦ tr♥st♦♥♠t ♦♥s ♥ ♦r♥♠P②s ♦ ♣♣ ♥

❬❪ ♥♠r ♠♣s② ss r♥ ♥ rr♦s s♦♥ ♦①t♦♥ ♥ rt♦♥ t t ♦♠♦ ♥tr st ② s♦t ①r② s♦r♣t♦♥ s♣tr♦s♦♣② ♥ ♠♥t rrr♦s♠ ♣♣ P②ss ttrs ♦ ♥♦ ♣

❬❪ ❲st ♥ st ♥♦♦ ♦ ♠str② ♥ P②ss t Prss ♦ t♦♥

❬❪ rt♦♥ s ❨ s②♠ r②s♦ ♥ ♥♦♥♥t♦♠ ♥ tr♦♥ strtr ♦ t ♦♠♦ ♥tr r♦♠ rst ♣r♥♣s ♣♣ P②ss ttrs ♦ ♥♦ ♣

❬❪ ❲ ♦ P ❨ ♥ ❲ s♥ ❨ r♠♥ ♥ r t♦♠s s♣tr♦s♦♣ ♠♥ ♦ ♦♠♦♦ ♠♥t t♥♥ ♥t♦♥s ♣♣ P②ss ttrs ♦ ♥♦ ♣

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❬❪ ❨ ♥ ♥ ♦ ♥ ♥ ♦♥ t ♦ s r♥♥♥♥ ♦♥ t tr♦♥ strtr ♦ t ♠♦ rrr ♥ ♦♠♦♦♠♥t t♥♥ ♥t♦♥s ♣♣ P②ss ①♣rss ♦ ♥♦ ♣

❬❪ ❱ rt ❨ s ♦ ♦♥♦ ♥ ♥♦r♥s♠ss♦♥ tr♦♥ ♠r♦s♦♣② ♥stt♦♥ ♦ ♦♠♦♦ ♣s♦s♣♥ s ♥♥ t r♥t t♠♣rtrs ♦r♥ ♦ ♣♣ P②ss♦ ♥♦ ♣

❬❪ rs♦♥ rqs P Pr♦s sr ❨♥ ♥ Pr♥♥♥s s♦♥ ♥ ♥♥ ♠♥t t♥♥ ♥t♦♥s t ♠♦ t♥♥rrrs r♣t tr ♦ ♥♦ ♣♣

❬❪ ♥ ❨ s②♠ ♥ Ptt♦r t♦♠ ♥ tr♦♥strtr ♦ Co/srtio3/Co ♠♥t t♥♥ ♥t♦♥s P②s ♦ ♣

❬❪ r③r ♥s♦r ♥ rs rr♦tr t ♦♣③rt♦❬s ❪ t♥ ♠s ♠sr ♥ t♠♦s♣rs ♦ r②♥ ♦①②♥ ♦♥♥trt♦♥ ♣♣ P②ss ttrs ♦ ♥♦ ♣♣

❬❪ tr♦ ♥r trt ♥ ❲♠s ♠ss♥♠♠rst♦r ♦♥ tr ♦ ♣ ②

❬❪ ♦♥ r rt♠② P Pr♦♦♠♠ qt P♦♥t♦r ♠♦ ♥ ♦① srt ♠♥t t♥♥ ♥t♦♥st st s♣♥♣♥♥t stts ♣♣ P②ss ttrs ♦ ♥♦ ♣

❬❪ ♥t ♥ r♠ tr♦♥ strtr ♦ tr♦♥ ♦♣ srtio3srtio3−δ ♥ sr1−xlaxtio3 P②s ♦ ♣♣ ♥

❬❪ ❨ ❲t♥ ♥♦r③ ts rr ❲♠r ♥ ❲♥ rr♥tr♥ ♥st♦r♦♥t♦r tr♥st♦♥ ♥ ♥♦♥♦t♠♠♦r② ♥ r♦♠♠♦♣ srt♦❬s ❪ s♥ r②sts ♣♣ P②ss ttrs ♦ ♥♦ ♣♣

❬❪ sst st♥ ♥ tr♥st♦♥ ♠t ♦①s trs ♦②♦ ♥♦ ♣♣

❬❪ rt♥ ② ❨ ♥r② r ♦♥ ❱ ♦st rs ♥ ♦♥ ♥♦♠ rrr ♦ ♠♦ ♦rrsst st♥ ♥ t♥♥ rrrs ♦r♥ ♦ ♣♣ P②ss ♦ ♥♦ ♣

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❬❪ ② ♦♥ r ❨ ♥r② ❯q♦t❲ ❲r rt♦♥ ❱r ♥ ❱ ♥♦♦ tr st♥♥ r♠♦ ♠♥t t♥♥ ♥t♦♥s ♣♣ P②ss ttrs ♦ ♥♦ ♣

❬❪ r ② ♦♥ ❨ ♥r② ♥ ♦♥tr st♥ ♥ ♠♦ t♥♥ ♥t♦♥s P②s ♦ ♣ ②

❬❪ rr t♥ t ♥ ♠♥t t♥♥ ♥t♦♥s s ♦♥ ♠♦P tss

❬❪ ♠r ❨ ❨♠ ♦②♦s s ♦♥♠ ♥ s ①♣♦rt♦♥ ♦ ♦①s t ♠♥t s♠♦♥t♦rst♦r tr♥s♣r♥t s♣♥tr♦♥s ♣♣ r ♥ ♦ ♥♦ â⑨➇♣♣ ttPr♦♥s ♦ t ♦♥ ♣♥❯ ❲♦rs♦♣♦♥ ♦♠♥t♦r trs ♥ ♥ ♥♦♦②tt

❬❪ t t♥②r ♣rs♣t ♦♥ t ♠♥t s♠♦♥t♦rs ♥ ♦①s t tr ♦ ♣♣

❬❪ ❨ ts♠♦t♦ r♠ ♦♥♦ s ♠r s P ♠t ②♦ ② ♦sr ♥ ♦♥♠♦♦♠t♠♣rtr rr♦♠♥ts♠ ♥ tr♥s♣r♥t tr♥st♦♥ ♠t♦♣ tt♥♠ ♦① ♥ ♦ ♥♦ ♣♣

❬❪ rt♥③♦t rt♥③ r♥♥③ P Pr♥♦ ♥t♦♥② rt♦♠ s ❩ ♦♥st♥t♥♦ ♥ rt♥③ ♠♥s♥ t r♦♦♠ t♠♣rtr ♥ t ♠♦ ♠s ♦ tt ♦♠♠♥t♦♥s ♦ ♥♦ ♣♣

❬❪ rt♥③♦t tr♥ s ❩ ♦♥st♥t♥♦ ❱♥ ♠t③ r♦ str ♦r♥ ♥ rt♥③ rr♦♠♥ts♠♥ tr♥s♣r♥t t♥ ♠s ♦ ♠♦ P②s ♦ ♣

❬❪ ♠♥ ♦♠♦ ♥ r♣r ♥♦♦② ♥ ♣♣t♦♥s ♦ r♦♠ ♦♥ s♦rs s ♥ s♣ttr♥ ♣rt ♦♥ s♦r t♥♦♦② ♦r♥ ♦ ❱♠ ♥ ♥ ♥♦♦② ♦ ♥♦ ♣♣

❬❪ ♠ rs ❱ ♦st ♠rr ♦♥ ♦r ♥ r♣r ♥♥ ♦ ♥ st ♥♥♥ ♦♥ t ♥♥♦s t♦♣♦r♣tr ♣r♦♣rts ♦ t t♥♥ rrr ♥ s♣ttr ♣t① ♠♦♠t②rs ♦r♥ ♦ P②ss ♣♣ P②ss ♦ ♥♦ ♣

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❬❪ ❲♦r ♥ ♣♥♣♦r③ t♥♥♥ ♥ ❬s❪sr❬s ❪♠♥♦❬s ❪ ♣♣ P②ss ttrs ♦ ♥♦ ♣♣

❬❪ Prs♥ ♥ ❱r♥♦♥ t ♦ ♠ rsst♥ ♦♥ ♦♠♣♥t♥♥♥ ♠sr♠♥ts ♣♣ P②ss ttrs ♦ ♥♦ ♣♣

❬❪ ♥ ♥ ♥♥s r tr♦♥ ♥rs ♦ t ♦tr s tr♦♥sr ♥ ♦ ♥♦ ♣♣

❬❪ P ♦ttä♥r ♥ ♥ tr♠♥♥ t ♥tr rrrt ♥ ts rt♦♥ t♦ t♥♥ ♠♥t♦rsst♥ P②s ♦ ♣ ♥

❬❪ P ❱ s♥♦ trt ♥ r s ♥ ❨ s②♠ t s♣♥ ♣♦r③t♦♥ ♥ r t♥♥♥♠♥t♦rsst♥ ♥ ♣t① Co|srtio3|Co ♠♥t t♥♥ ♥t♦♥s P②s tt ♦ ♣ ♦

❬❪ ttss t ♦ t ♣s tr♥st♦♥ ♦♥ t srto3 ♦♥t♦♥♥s P②s ♦ ♣♣

❬❪ ♦③ sr♦ ♥ ♥♠ P♦t♦♠♥s♥ ♥ rrs♣♦t♦♥ s♣tr ♥ ♦ srt♦ ♦r♥ ♦ P②ss ♦♥♥s ttr ♦ ♥♦ ♣

❬❪ ♦ ♦s r r ❱rs♥ rr ❯q♦t ♠rr ♦♥ ♥ ♥ t ♦ ♥tr ♦♥♥ ♦♥ t tr♥s♣♦rt ♣r♦♣rts ♥ ♦2/srt♦3/♦2/ ♠♥tt♥♥ ♥t♦♥s P②s ♦ ♣

❬❪ ♦♥ ①♣r♠♥t ♥sts ♥t♦ s♣♥♣♦r③ s♦ stt t♥♥♥P tss

❬❪ ❨ s②♠ ♥ Ptt♦r ♣♥♣♦r③ tr♦♥ t♥♥♥ r♦ss s♦rr ♥st♦r P②s ♦ ♣♣

❬❪ ❨ s②♠ ♦♦♦ r♥♦ ♥ ♦♥ s♦♥♥t ♥rs♦♥ ♦ t♥♥♥ ♠♥t♦rsst♥ P②s tt ♦ ♣ ②

❬❪ ♠ ❲ ♦ r ♥ ♦r ❱ s♥ r rs ♠rr r♣r ❲ ♦ ♥ ♦♥♦♥tr♦ ♦ t♠t t♥♥♥ rrr ts ♥ trt♥ ♠♦ ♠s♣♣ P②ss ttrs ♦ ♥♦ ♣

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P❨

❬❪ s ♥ P♦♥ ♣t ♣r♦♣rts ♦ sr ♥ ♥trs♥ ♠♦ r♦♠ ♥t♦ str ♠♦ t♦♥s ♦r♥ ♦ ♠P②ss ♦ ♥♦ ♣♣

❬❪ ❨ ♥ ❲♠s ♥ ❲ ② t str ♥trs ♥ ♠♦P②s ♦ ♣♣ ♥

❬❪ P ♦♥r ♥ rt♠♥ ♥ s♦r♣t♦♥ ♥s ♥ ♠♦ r②stsP②s ♦ ♣♣ ♣

❬❪ r♦ r ♥ts ♥ q♥t♠ t♥♥♥ P r♦♣②ss ttrs♦ ♥♦ ♣

❬❪ ①r ❱♥tr P r♦ ♦s P ❲s♥♦s r♦s♦ ♥ P P rts s♦♥♥t t♥♥♥ tr♦ tr♦♥ tr♣♣♥ stts♥ t♥ ♠♦ ♠♥t ♥t♦♥s P②s tt ♦ ♣ ②

❬❪ rt s♥ ♦♥t♥ ♥ ② ♥♦♥ ♦♥ ♥ ❲ ❲r ♥ ♦ s②♠♠tr②♣♥♥t ♠t rrr ♥ ② ♣t① ♠♦ s ♠♥t t♥♥ ♥t♦♥s P②s tt♦ ♣ ♦