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Singlet and triplet trion states Singlet and triplet trion states in the

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Charged exciton complexes (trions) in low
dimensional structures
by Dmitri Andronikov
at JASS 2005
Outline
?Introduction
?Experiment
?Results and discussion
?Conclusions
Outline
?Introduction
?Experiment
?Results and discussion
?Conclusions
What are Trions?
X- Trion
X+ Trion
?
?
X +
+
+
-
?
X
electrons
hole
Similar to hydrogen ion H- if me<<mh
holes
electron
Similar to ionized hydrogen molecule H2+
if me<<mh
Short history of trions
?1958 Theoretical prediction of trion existence by
Lampert
?1977-78 Discovery of charged excitons in bulk Ge, Si
and CuCl
?1993 First report on X- trion in a CdTe/CdZnTe
semiconductor QW structure
?1995 First report on X+ trion in a GaAs QW
Singlet and triplet trion states
Wavefunction of an ion with two electrons
Sz = +1
Sz = 0
Sz = -1
? (1, 2 ) ? U (1, 2 ) ? (1, 2 )
triplet
Spatial part of the wavefunction
1
U nlm ?
0
2
?u ?r ?u ?r ? ? u ?r ?u ?r ??
1
1
nlm
2
1
2
nlm
Sz = 0
1
singlet
+ singlet state
Unlm ? 0 , only if L ? 0 (1S state and 2P state)
- triplet state
e
or if one electron is in 1S state, and the other is in
2S state
Spin part of the wavefunction
singlet state
triplet state
Sz = 0
Sz = ?1,0
? trip ? ? ? 1 / 2 , ? 1 / 2 ?
?1
?
0
sin gl
?
1
2
([ ? 1 / 2 , ? 1 / 2 ] ? [ ? 1 / 2 , ? 1 / 2 ])
?
? trip ? 1 /
0
?
2 ? ??? 1 / 2 , ? 1 / 2 ? ? ?? 1 / 2 , ? 1 / 2 ??
? trip ? ? ? 1 / 2 , ? 1 / 2 ?
?1
Singlet and triplet trion states in the magnetic field
e
Sz =-1
-5/2
+1/2
e
Triplet
Sz =0
+3/2
-3/2
-1/2
e
Sz =+1
In the magnetic field each trion level
splits into two due to Zeeman effect
thus giving 6 triplet and 2 singlet levels
+5/2
e
Singlet
+3/2
Sz =0
-3/2
electron
-1/2
ge=-1.56
+1/2
?
? transitions
?
? transitions
The allowed optical transitions must
satisfy the optical selection rule
Sfinal+Sinit = ?1. This gives 6 possible
transitions to/from trion singlet and
triplet states
Exciton and trion binding energies in 3D and 2D
structures
4
EH ?
3D
e m0
2?
2
? 13.6 eV
?
?
2
3D
EH
2D
EX
?
EX
?1 ? 1 / 2 ?2
GaAs
CdTe
ZnSe
4.2 meV
10 meV
20 meV
EXQW
9 meV
20 meV
30 meV
ETQW
1 meV
2.5 meV
5 meV
EXbulk
2D
100A QW
3D
EX
?? / m 0 ?
? 4E X
3D
Structures with modulation doping
100A 100A
2DEG
QW
I
e1
1.6eV
2.8eV
1.8eV
3.0eV
hh1
lh1
CdMgTe
CdTe CdMgTe
ZnMgSSe
ZnSe
ZnMgSSe
2DEG concentration varies from ne=5*109 cm-2 to 9*1011 cm-2
Trion PL and reflectivity spectra
B=0, T=1.6K
The formation time
of a trion in ZnSe
based structures is of
the order of 2 ?4 ps
compared to
radiative lifetime of
the exciton 40-50ps
photon
electron
-2
4.8 meV
trion
Signal intensity (a. u.)
?
10
doped, ne=5 10 cm
undoped
Ref.
Ref.
Excited by UV-lines
Pexc=60 mW
X
?
X
X
X
exciton
PL
PL
0
?
2,81
2,82
Energy (eV)
2,81
2,82
Energy (eV)
0
Singlet trion in the magnetic field
0
1 .0
1
2
n e = 6x10
10
3
cm
6
7
?
?
?
B=7.5T, T=1.6K
?
g e = + 1 .1 5
ZnSe
?=1
0 .0
1 .0
n e = 9x10
10
cm
Reflectivity (a. u.)
D egree of polarization
5
-2
0 .5
-2
0 .5
?=1
0 .0
1 .0
n e = 1.5x10
11
cm
-2
0 .5
0
1
2
3
4
X
M agnetic field (T )
6
7
lh
4.4 meV
X
?
hh
Xhh
10
5.5 meV
5
?
Xlh
?=1
?=2
?=3
0 .0
4
0
2,81
doped, ne=5 10 cm
2,82
Energy (eV)
2,83
2,84
-2
Landau levels
The polarization of the trion
reflectivity line can be used to
determine the electron
concentration by a pure optical
method
энергия Ферми
ne=const
T=1.6K
T=0 K
?=3
?=1
?=4
LL2
LL1
For the filling factors
less than 1 only the
lowest electron
Landau level will be
populated leading to
full spin polarization
of the 2D electron gas
?=2
EF=const(B)
Магнитное поле
LL4
LL4
LL4
LL3
LL3
LL3
LL2
LL2
LL2
LL1
LL1
LL1
?<1
e (-1/2)
?>1
? ?
X(+1/2, -3/2)
??
n e hc
eB
T(-1/2, +1/2, -3/2)
Outline
?Introduction
?Experiment
?Results and discussion
?Conclusions
Experimental structures
100A 100A
2DEG
QW
I
e1
1.6eV
1.8eV
hh1
CdMgTe CdTe CdMgTe
Two samples with different 2DEG concentration were analyzed ne=3*1010 cm-2
and 3.7*1011 cm-2
50
Magnetic field pulse
40
30
100 200 300 400 500
time, ms
probe with a sample
He cryostat
pulse
electromagnet
luminescence
circular polarizer
0
0
excitation signal
10
linear polarizer
20
the inside of the probe
Magnetic field, T
Experimental setup
sample
optical
fiber
H || z
z
light filter
laser with ? = 532 nm
monochromator
L1
PC
SM
CCD
camera
Pulse magnet power source
Supplying power to the world's strongest long-pulse magnet at Los Alamos'
National High Magnetic Field Laboratory is a 1.4 billion-watt generator, itself
the largest among magnetic power sources. It can produce enough energy to
power the entire state of New Mexico.
Outline
?Introduction
?Experiment
?Results and discussion
?Conclusions
Polarized magnetoluminescence of the sample with ne=3*1010 cm-2
triplet trion line has been found
?-
X
d
Tt
Tt
d
X-1
30T
Ts
45T
Tt
d
X-1
27.5T
Ts
Tt
d
X-1
25T
Ts
Ts
1610
0T
1620
1630
1640
1600
1620
energy, meV
1640
Luminescence spectra analysis I
PL maxima
T=1.6K
10
-2
ne=3*10 cm
??+
1635
energy, meV
1630
3 meV
TT
1625
TT
X
1620
b
1615
Ts
1610
0
10
20
30
Magnetic field, T
40
d
The dark triplet trion
line appears at 20T
magnetic field and
splits from the
exciton line with the
maximum splitting of
3meV at 45T
Luminescence spectra analysis II
PL intensity
4500
4000
PL intensity, arb. units
10
ne=3*10 cm
T=1.6K
3500
-2
?
?
?
?
TS
The Gauss fit of the
exciton-dark triplet
trion band allowed us
to distinguish the
triplet trion line from
the exciton line down
to magnetic field lower
than 15T
3000
2500
X
2000
d
Tt
1500
1000
X
500
0
0
5
10
15
20
25
30
Magnetic field, T
35
40
45
Luminescence spectra analysis III
Field dependence of the PL lines for the sample with ne= 3.7*1011 cm-2
T=1,6K
1635
11
ne=3.7x10 cm
energy, meV
1630
-2
ExCR
1625
d
Tt
1620
Ts
Ts
1615
?
?
?=2
?
?
?=3
1610
?=4
0
SU
10
20
30
magnetic field, T
40
For the sample with
higher electron
concentration the triplet
line can be followed
down to the fields as low
as about 13T
Reflectivity
10
0,3
At 6T magnetic field the
reflectivity line of the
singlet trion is fully
polarized
-2
ne=3x10 cm
T=1.6K
X
??
6T
Ts
?
X
0
?
?
3000
2000
1000
X
0
In reflectivity no line is
found that would
energetically coincide
with the position of the
dark triplet trion line
found in the PL
X
0,3
27T
3000
0
X
d
Ts
Tt
2000
Ts
1000
X
0
Ts
0.3
X
45T
b
0
d
Tt
Tt
2000
Ts
1610
1620
3000
X
Ts
1630
energy, meV
1000
0
1640
PL, a.u.
Reflectivity
Ts
Magnetic field
Ts
Singlet and triplet trion states formation mechanism
(-1/2,+3/2)
2DEG
Exciton
(-1/2,-3/2)
(-1/2)
(+1/2,+3/2)
(+1/2)
(+1/2,-3/2)
?
?
triplet trion
(-1/2,+1/2,+3/2)
(-1/2,+1/2,-3/2)
singlet trion
(+1/2,+1/2,-3/2)
The triplet trion
level is formed
from the lowest
Zeeman sublevels
of both electrons
and excitons and
thus will be the
most populated
Calculation of the exciton-electron energetic system
?
te
tX
+
th
+2
-
Hot X
?X
te
-2
tK
tX
?
tX
th
+
te +2
tform
+
? +3/2
?
-
-2
trec
trec
?
tX
Cold X
te
trec
tform
th
-3/2 ?
te
d
trec
tm
-1/2 ?
-1/2
-
-
Ts
b
Tt
trec
b
trec
d
Tt
tform = 10 ps, tX = tX- = 30 ps, tK = 12 ps, trecX = 40 ps, trecTs = 60 ps trecTt = 50 trecTs.
The results of the PL calculation
T=1.6K
4000
PL intensity, arb. units
calculation
experiment
4500
3500
10
ne=3*10 cm
-2
?
?
?
?
10
Ts
TS
3000
Ts
2500
-2
ne=3*10 cm
T=1.6K
-
+
X
2000
d
Tt
1500
Tt
1000
-
X
X
500
+
X
0
0
10
20
30
Magnetic field, T
40
0
10
20
30
Magnetic field, T
The intensity of the triplet PL is already noticeable at
sufficiently low magnetic field
40
d
Outline
?Introduction
?Experiment
?Results and discussion
?Conclusions
Conclusions
?Optically active and forbidden singlet and triplet trion states have been
observed in reflectivity and PL spectra.
?A model explaining the appearance of the dark triplet trion state in the PL
spectra from the studied structures state has been suggested. It is based on the
fact that the singlet trion state formation mechanism is suppressed by the
magnetic field, meanwhile the formation of the optically inactive triplet trion
state, observed in the experiment, is stimulated in the magnetic field at low
temperatures.
?A model calculation based on the system of kinetic equations of the PL of the
trion exciton energetic system has been carried out. The model took into account
the singlet and triplet trion formation mechanisms in the magnetic field. The
results of the calculation are in good agreement with the experiment.
THANK YOU!!!!
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