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Delocalization-localization Transition of Plasmons in Random GaAs/AlGaAs
Superlattices
Y.A.Pusep
Institute of Physics of São Carlos, University of São Paulo
Collaborators:
Experiment – A.D.Rodrigues, UFSCar.Theory - S.S.Sokolov, B.Verkin Institute for Low-Temperature Physics and Engineering, National Academy of Sciences of Ukraine.Samples – H.Arakaki, C.A. de Souza, IFSC/USP.
MotivationWhy plasmons ?
Advantages of optical and electrical circuits:Fast data transfer by transmitting optical signals through minuscule nanoscale structures .
Optical fibers versus electrical circuits. Diffraction limit.
Manipulation of plasmons (localization and propagation).
Electrons and Plasmons1. Electrons: single-particle excitations
2. Plasmons: collective excitations
Outline
1. Random superlattices
2. Raman scattering by collective excitations
3. Plasmon localization: theory and experiment
4. Conclusions
Artificially disordered superlattices
DSL
Nwell
E
0
= /W
(GaAs)n(Al
0.3Ga
0.7As)
m
W
Z E(kz)
kz /D
SL
Criterion of Localization
Electrons
( = 0, w T = 0) 0, /T < 0
( = 0, w T = 0) = 0, /T > 0
metal (kFl>1):
insulator (kFl<1):
Obs: l is the electron free path length, kF = 2π/λe, λe is the electron wavelength.
Criterion of Plasmonlocalization - ?
Theory of plasmon localization
Plasmon wave function:
with0.2 0.4 0.6 0.8 1.0 1.2
0
10
20
30
Lc R
0
p,
cm-1
2R0/L
c
Lc R
0
R0= 7 nm
U0= 12 cm-1
Results of calculations
Neutral impurity scattering potential:
Localized plasmon: Lc < R0
Delocalized plasmon: Lc > R0
2. Relation between Lc and R0 determine propagation of
plasmons:
1. Plasmon damping (Гp) independent ofdisorder parameter (Lc, δ) indicates localization.
Criteria of Plasmon localization
Raman scattering of plasmons in presence of disorder
2 20
2 2
( ) ( / 2)( ) exp
2 ( ) ( / 2)
c
p p
q q L dqI
q
Non-conservation of quase-momentum [Yu.A.Pusep, et al., Phys.Rev.B 58, 10683 (1998)]:
360 380 400 420 440 460 480 500
TO
Raman shift (cm-1)
Ra
ma
n in
ten
sity
Al0.2
Ga0.8
As:Si
N=2x1018cm-3L+
2
Lc= 8.6nm
p= 6 meV
0.5 1.0 1.5 2.0 2.50
5
10
0
10
20
30
0
1
2
3
p (
cm-1)
Lc (
nm
) p
(m
eV)
Electron concentration (x1018cm-1)
(a)
R0= 0.25 nm
U0 = 0.6 eV
(b)
Doped superlattices(weak plasmon localization)
Disordered superlattices(strong plasmon localization)
0
50
100
150
200
0.0 0.2 0.4 0.6 0.8 1.0 1.2
4
6
8
10
0
10
20
30
p(m
eV) (a)
R0=20nm
U0=15meV
T = 10K
Lc(n
m)
Disorder Strength,
p(c
m-1)
(b)
Lc > R0 Lc < R0
T = 250K
0 50 100 150 200 2502
3
4
5
0 50 100 1504
6
8
10
Lc (
nm
)L
c (n
m)
Lc>R
0
(a)
Lc<R
0
Temperature (K)
Temperature (K)
(b)
Lc > R0
Lc < R0
Weak plasmon localization:(plasmonic “metal”)
Strong plasmon localization:(plasmonic “insulator”)
Temperature Effect
Conclusions
Delocalized plasmon: Lc > Ro – the increasing disorder results in increasing plasmon linewidth;
Localized Plasmon: Lc < Ro – no influence of the disorder on plasmon linewidth;
The independence of the plasmon linewidth on disorder is the manifestation of plasmon localization.
The increasing temperature enhances the localization of the weakly localized plasmons, while it causes the delocalization of the strongly localized plasmons.
Yu.A.Pusep, A.D.Rodrigues, S.S.Sokolov, Phys.Rev.B 80, 205307 (2009).
Thank you!
Raman line shapes (q=0)
Damped plasmon: Overdamped plasmon:
250 300 350 400 450 500
TO
GaAs
p=450 cm-1
p=5 cm-1
L+
R
am
an
inte
nsi
ty
Frequency
LO
200 300 400 500 600 700 800
LO
Ram
an in
tens
ity
Frequency
TO GaAs
p=450 cm-1
p=500 cm-1
L+
Raman line shapes (q≠0)
360 380 400 420 440 460 480 500
TO
Raman shift (cm-1)
Ram
an in
tens
ity Al0.2
Ga0.8
As:Si
N=2x1018cm-3L+
2
L= 8.6nm
Non-conservation of the quase-momentum:
Raman scattering in disordered GaAs/AlGaAs superlattices
350 400 450
200 300 400 500
LO2
LO1 1.2x1018 cm-3
(b)
TO2
+
2+
1
1.13
0.59
= 0.18
Raman shift (cm-1)
(GaAs)m(Al
0.3Ga
0.7As)
6:Si
Ram
an in
tens
ity (
arb.
units
)
-
TO1
+
2
TO2+IF 1.1x1018 cm-3
7.0x1017 cm-3
5.0x1017 cm-3
(a)
0.2 0.4 0.6 0.8 1.0 1.20
5
10
15
Disorder Strength,
I(- )/
I( )
0.0 0.1 0.2 0.3 0.4 0.5200
250
300
350
400
450
500
550
600
650
700
TO(AlAs)
LO(AlAs)
TO(GaAs)
LO(GaAs)
-
Fre
quen
cy
(cm
-1)
Wave number q (Units of /a)
(GaAs)17
(Al0.3
Ga0.7
As)6
n = 1.2x1018cm-3
60 70 80 90 100 110
0.4
0.6
0.8
1.0
(a)
SL = 1.13
Distance Z, nm
Ele
ctro
n c
on
cen
tra
tion
, x1
018
cm
-3
40 50 60 70 80 90
0.4
0.6
0.8
1.0
(b)
SL = 0.47
50 60 70 80 90 100
0.4
0.6
0.8
1.0
(c)
SL = 0.18
Criterion of Localization
Electrons
T.F.Rosenbaum et al., Phys.Rev.Lett. 45, 1723 (1980)
Y.Liu, et al., Phys.Rev.Lett. 67, 2068 (1991)
( = 0, w T = 0) 0, /T < 0
( = 0, w T = 0) = 0, /T > 0
metal (kFl>1):
insulator (kFl<1):