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)
