A. F. Ioffe Physicotechnical Institute , St. Peterburg, Russia

A. F. Ioffe Physicotechnical Institute, St. Peterburg, Russia

Time-resolved study of the level-anticrossing effect in exciton emission

A. S. Yakunenkov, A. N. Starukhin, D. K. Nelson, B. S. Razbirin

CONTENSCONTENS The level-anticrossing effect. The anticrossing signal in optical emission

spectra under the conditition of cw excitation. Problem definition. The modelling object for study – triplet bound

excitons in GaSe. Experimental results. Interpretation of the results. Conclusion.

2

1

1

2

2

1

Magnetic field

Ener

gy

2

1

1

2

2

1

Magnetic field

Ener

gy

2

1

1

2

2

1

b

a

Magnetic field

Ener

gy

2|V12|2

1

1

2

b2

b1

a2

a1

2

1

b

a

Magnetic field

Ener

gy

(H0 + Hmag) = E

{E} = E1, E2

H = H0 + Hmag+ V

a = C11 + C22

b = C21 C12

The level-anticrossing effectThe level-anticrossing effect

Bc

Magnetic field, B

Em

issi

on

Bc

h

b

a

B

E

Anticrossing signal Anticrossing signal

Crystalline structureCrystalline structure

Experimental set upExperimental set up

Sample

Spectrometer

Pump pulse

Cu-laser

Emission spectrum of GaSe crystalEmission spectrum of GaSe crystal

2,06 2,08 2,10 2,12

Pulse excitationhexc=2.14 eVt 0

GaSeT = 4.2 K

FE

Emis

sion

inte

nsity

, a.u

.

h, eV

с

BE ()BE ()

FE

Eg

Exci

tatio

n

03

002,1 5.0

EE

BgEE zz

Sz0

Sz1

Sz1

E0

E0-

2|V23|

-

+

b

a3

2

1

Magnetic field

Ener

gy

B || c

I (B,t)

Sz0

Sz1

Sz1

E0

E0-

2|V23|

-

+

b

a3

2

1

Magnetic field

Ener

gyEnergy level diagram of the triplet Energy level diagram of the triplet

exciton in GaSeexciton in GaSe

0

2000

4000

t 0

0

200

400

600

Emis

sion

inte

nsity

(pho

ton/

s)

0,0 0,3 0,6 0,90

100

200

300

B [T]

0

40

80

0

20

40

0,0 0,3 0,6 0,90

1

2

3

B [T]

0

2000

4000

t 0

0

200

400

600

Emis

sion

inte

nsity

(pho

ton/

s)

t =0.5 s

0,0 0,3 0,6 0,90

100

200

300

B [T]

0

40

80

0

20

40

0,0 0,3 0,6 0,90

1

2

3

B [T]

0

2000

4000

t 0

0

200

400

600

Emis

sion

inte

nsity

(pho

ton/

s)

t =0.5 s

0,0 0,3 0,6 0,90

100

200

300

B [T]

t =0.8 s

0

40

80

0

20

40

0,0 0,3 0,6 0,90

1

2

3

B [T]

0

2000

4000

t 0

0

200

400

600

Emis

sion

inte

nsity

(pho

ton/

s)

t =0.5 s

0,0 0,3 0,6 0,90

100

200

300

B [T]

t =0.8 s

0

40

80t =2 s

0

20

40

0,0 0,3 0,6 0,90

1

2

3

B [T]

0

2000

4000

t 0

0

200

400

600

Emis

sion

inte

nsity

(pho

ton/

s)

t =0.5 s

0,0 0,3 0,6 0,90

100

200

300

B [T]

t =0.8 s

0

40

80t =2 s

0

20

40 t =5 s

0,0 0,3 0,6 0,90

1

2

3

B [T]

0

2000

4000

t 0

0

200

400

600

Emis

sion

inte

nsity

(pho

ton/

s)

t =0.5 s

0,0 0,3 0,6 0,90

100

200

300

B [T]

t =0.8 s

0

40

80t =2 s

0

20

40 t =5 s

0,0 0,3 0,6 0,90

1

2

3

B [T]

t =15 s

-exciton emission, I(B,t), measured at different times t

during the excited state lifetime. The time t is specified

in the figure.

Experimental anticrossing signal

Thus, the experimental data demonstrate that the shape

of the level-anticrossing signal measured at different

moments within the bound excitonlifetime varies essentially from a practically complete absence of the signal to a complex structure

with two maxima.

Zeeman effect diagramZeeman effect diagram

To interpret the observed evolution of the level-anticrossing signal, consider the energy level structure of bound exciton in GaSe.

Sublevel splitting diagramSublevel splitting diagram

110

1110

1

1123

1122

3322

5.0

5.0223

20

03,2

22021

121100

32233322

')3,2,(

45.0'

5.0'12

1

05.0

BBBB

BCBBCB

VVkiVV

VBg

BgBC

EVEVVEVBgE

CCCC

brbara

rbrrar

kiik

zz

zz

zz

ba

Level-anticrossing signal

0

2000

4000

t 0

0

200

400

600

Emis

sion

inte

nsity

(pho

ton/

s)

t =0.5 s

0,0 0,3 0,6 0,90

100

200

300

B [T]

t =0.8 s

0

40

80t =2 s

0

20

40 t =5 s

0,0 0,3 0,6 0,90

1

2

3

B [T]

t =15 s

The points are experimentaldata, and thesolid lines are plots of theoretical relation

r = 1.25107 s, 0 = 7106 s,

' = 0.0357 meV,

2V23 = 0.0045 meV

tBItBItBIbai

BtBPtBI

ba

iiri

,,,),(

exp, 10

Theoretical diagram of emission Theoretical diagram of emission components components

0

2000

4000

b

a

t 0

0

200

400

Emis

sion

inte

nsity

(arb

.uni

ts)

t =0.5 s

0,0 0,3 0,6 0,90

100

200

300

B [T]

t =0.8 s

0

40

80t =2 s

0

10

20t =5 s

0,0 0,3 0,6 0,90

1

2

B [T]

t =15 s

B || c

E0

E0-

2|V23|

b

a32

1

Magnetic field

Ener

gy

0,0 0,5Bc

t = 2 s

t = 0.2 s

Tota

l pop

ulat

ion

n a(B

, t) +

n b(B

, t)

Magnetic field, T

Electronic band model of GaSe Electronic band model of GaSe at 4.2K near at 4.2K near ГГ and M points and M points

≈

CONCLUSIONSCONCLUSIONS The investigation of the level anticrossing effect in

afterglow spectra reveals that the well-known shape of the anticrossing signal in the form of a simple maximum is only a particular case corresponding to the emission of a system at a certain time after the excitation.

The signal profile may vary substantially with time, and it is possible to isolate the contributions to this signal due to different interacting states which cannot be discriminated spectrally in emission.

An investigation of the level-anticrossing effect in afterglow spectra offers also, in principle, a possibility of obtaining information on the lifetimes of any one of the interacting states.

The phenomenon observed should have a fairly general character and be observable in various atomic systems.

Thank you for your timeThank you for your time

Excitons (bound electron-hole pair)Excitons (bound electron-hole pair)