Transcript Обучение
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
CONTENS
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.
The level-anticrossing effect
11
11 1
a 1
(H0 + Hmag) = E
{E} = E1, E2
aa
Energy
Energy
Energy
22 22 2
b2
2|V12|
a 2
bb
22
2
11
1
b 1
Magnetic
field
Magnetic
Magnetic
field
field
H = H0 + Hmag+ V
a = C11 + C22
b = C21 - C12
Emission
Anticrossing signal
E
a
h
b
Bc
B
Bc
Magnetic field, B
Crystalline structure
Experimental set up
Spectrometer
Pump pulse
Sample
Cu-laser
Emission spectrum of GaSe crystal
GaSe
T = 4.2 K
с
Excitation
Emission intensity, a.u.
Pulse excitation
hexc=2.14 eV
t0
FE
2,06
2,08
2,10
h, eV
2,12
FE
BE ()
BE ()
Eg
Energy level diagram of the triplet
exciton in GaSe
Sz1
B || c
E1,2 E0 0.5g zz 0 B
+
1
E0
2
2|V23|
a
E0- 3
Sz0
-
Energy
E3 E0 -
b
I (B,t)
Magnetic field
Sz-1
Experimental anticrossing signal
4000
4000
ttt000
80
80
80
Emission intensity (photon/s)
2000
2000
00
t =2 s
40
40
40
000
40
40
tt =0.5
=0.5 ss 40
-exciton emission, I(B,t),
measured at different times t
during the excited state
lifetime. The time t is specified
in the figure.
t =5 s
600
600
400
400
20
20
20
200
200
00
300
300
tt =0.8
=0.8 ss
000
333
200
200
222
100
100
111
t =15 s
000
00
0,0
0,3
0,6
0,9
0,0
0,3
0,6
0,9
0,0 0,3
0,3 0,6
0,6 0,9
0,9
0,0 0,3 0,6
0,6 0,9
0,9 0,0
B
B [T]
[T]
B
B
[T]
B [T]
[T]
Thus, the experimental data
demonstrate that the shape
of the level-anticrossing
signal measured at different
moments within the bound exciton
lifetime varies essentially from a
practically complete absence of
the signal to a complex structure
with two maxima.
Zeeman effect diagram
To interpret the observed
evolution of the level-anticrossing
signal, consider the energy level
structure of bound exciton in
GaSe.
Sublevel splitting diagram
a C2 2 C3 3
b C3 2 - C2 3
E0 - 0.5g zz 0 B V11 - E
V21
V12
0
E0 - V22 - E
'-0.5g zz 0 B
1
C 2 , 3 B
1
2
2
2
'
0
.
5
g
B
4
V
zz 0
23
Vik i V k
0.5
(i, k 2,3) ' V22 - V33
ar B C22 B r-1
br B C32 B r-1
-1
-1
a B ar-1 B 0-1
-1
b B br-1 B 0-1
-1
0.5
Level-anticrossing signal
4000
t0
80
Emission intensity (photon/s)
2000
0
t =2 s
40
t =0.5 s
0
40
t =5 s
The points are
experimental
data, and the
solid lines are plots
of theoretical relation
600
400
I i B, t P0 ir-1 B exp - t i B
20
200
0
300
t =0.8 s
0
3
200
2
100
1
(i a , b )
t =15 s
0
0
0,0 0,3 0,6 0,9 0,0 0,3 0,6 0,9
B [T]
B [T]
I - B, t I a B, t I b B, t
r = 1.2510-7 s,
0 = 710-6 s,
' = 0.0357 meV,
2V23 = 0.0045 meV
Theoretical diagram of emission
components
80
4000
b
t =0.5 s
400
0
2|V23|
a
E0-
3
2
t =5 s
b
20
Magnetic field
200
10
0
300
0
t =0.8 s
2
t =15 s
200
1
100
0
0
0,0 0,3 0,6 0,9 0,0 0,3 0,6 0,9
B [T]
B [T]
Total population n a(B, t) + n b(B, t)
Emission intensity (arb.units)
E0
40
2000
0
t =2 s
t0
Energy
a
1
B || c
t = 0.2 s
t = 2 s
0,0
Bc
0,5
Magnetic field, T
Electronic band model of GaSe
at 4.2K near Г and M points
≈
CONCLUSIONS
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 time
Excitons (bound electron-hole pair)