1. ВСЕ О ТРИОНАХ
Trions at low electron density limit
• 1. Charged exciton-electron complexes (trions)
• 2. Singlet and triplet trion states
• 3. Modulation doped QWs
• 4. Trions in optical spectra
• 5. Action of magnetic fields on the trions
Trions at high electron density limit
• 6. Combined exciton cyclotron resonance
• 7. Combined trion cyclotron resonance
• 8. Combined exciton electron processes in PL spectra
• 9. Trion Zeeman splitting

2. LOW 2DEG DENSITY
Two electrons+one hole states
•Trions at weak magnetic fields
•Trions at high magnetic fields
•Excited states of trion

3. Charged exciton – electron complex (trion)
Negatively charged Trion X- Positively charged Trion X+
similar to ion H- Similar to ionized molecule H+
−
−
X + + +
-
−
X
electrons
holes
electron
hole

4. Singlet and Triplet trion states
Wavefunction for two electrons in the trion
Sz = +1
ϕ (1,2) = U (1,2) χ (1,2) Sz = 0 triplet
Sz = -1
Spatial part of the wavefunction
U nlm =
0 1
2
[ ( ) ( ) ( ) ( )]
u1 r1 unlm r2 ± u1 r2 unlm r1 Sz = 0 singlet
 
−α ( r1 + r2 )
Singlet state + Sz = 0 ∝e
Triplet state - Sz = ±1,0
Unlm ≠ 0 , if l ≠ 0 one electron is in 1S and the second is in 2P state – dark triplet
Or if n ≠ 1 one electron is in 1S, and the second is in а 2S state bright triplet

5. Experimental studies of trions

6. Modulation doped structures
100Å 100Å
QW 2DEG
I
e1
1.8eV
3.0eV
1.6eV
2.8eV
hh1
lh1
CdMgTe CdTe CdMgTe
ZnMgSSe ZnSe ZnMgSSe
2DEG density varied from ne=5*109 см-2 to 9*1011 см-2

7. Optical processes with the trion participation
B=0, T=1.6K
Trion formation time in undoped doped, ne=5 10 cm
10 -2
ZnSe structures is of the
4.8 meV
order of 2 –4 psec
Signal intensity (a. u.)
Ref. Ref.
Excited by UV-lines
ε electron trion −
Pexc=60 mW
X
−
X X
photon exciton X
PL PL
0 0
2,81 2,82 2,81 2,82
Energy (eV) Energy (eV)

8. Изменение концентрации при подсветке

9. Зависимость энергии связи триона от ширины ямы
ZnSe-based QWs
10
PL ZnSe/ZnBeMgSe
Refl. ZnSe/ZnBeMgSe
ZnSe/ZnMgSSe
X binding energy (meV) 8
ZnSe/ZnMgSSe
6
4
-
+
2 X
0
0 50 100 150 200
QW width (Å)

10. Сила осциллятора экситона
приходящаяся на элементарную
ячейку равна силе осциллятора
триона на один электрон, также
Как для связанных экситонов
Γ T
= Cne
0
Γ 0
X

11. Singlet and Triplet
Trion states in magnetic fields

12. Singlet trion in magnetic fields
+
σ
0 1 2 3 4 5 6 7 − B=7.5T, T=1.6K
σ
1.0
ZnSe
10 -2
ne=6x10 cm
ge=+1.15
0.5
ν=1
Degree of polarization
0.0 −
X lh
Reflectivity (a. u.)
1.0 10 -2
ne=9x10 cm
0.5
ν=1 Xlh
0.0
4.4 meV
1.0 n =1.5x1011 cm-2 −
e
X hh
0.5 ν=1
ν=2 Xhh
ν=3
0.0 5.5 meV 10 -2
0 1 2 3 4 5 6 7 doped, ne=5 10 cm
Magnetic field (T) 0
2,81 2,82 2,83 2,84
Energy (eV)
The circular polarization of the trion − −
absorption (reflectivity line ) in magnetic fields X hh and X lh resonances appear
can be used to determine electron in opposite circular polarizations
concentration by pure optical method

13. Triplet trion in high magnetic fields
30T Tt
d X-1
σ- Tt
d X
Ts
Photoluminescence
45T
d
29.5T Tt X-1
Ts
d
Tt X-1
25T
Ts
Ts
0T
1610 1620 1630 1640 1600 1620 1640
Energy energy, meV

15. Singlet and Triplet in high fields
1635 T=1.6K
10 -2
ne=3*10 cm Ts
+
σ-
1630
σ+
Etripbind = 3 meV
Energy, meV
1625 d-
TT
X+1 X-1
b-
TT
1620
-
Ts
1615
1610
0 10 20 30 40
Magnetic field, Т

16. EXCITON-ELECTRON
SCATTERING
(excited states of a trion in magnetic
fields)

17. Exciton – electron scattering
Exciton – electron scattering
-
T=1.6K
ε electron detected at σ
ExCR1
X (1s,hh)
Lg I
ExCR2
0T
photon exciton
PL intensity
5T
B=5T
1,64 1,66
ExCR1
X (1s,lh)
In magnetic fields in QWs the
exciton electron scattering leads
ExCR2
to the electron transitions PLE
between Landau levels - ExCR ne=8x10 cm
10 -2
1,63 1,64 1,65 1,66 1,67
Energy (eV)
The scattering leads to high energy tail of the exciton absorption line. In magnetic
fields it splits into separate lines because the electron spectrum becomes discrete =
excited states of trions in magnetic fields.

18. We can neglect the trion binding energy because Eex >> ωc >> ETr
b b
e + ph ⇒ Ex + e*
1 3 c
ω e + ω = Eexc + ω e
c
2 2
The intensity of the ExCR
absorption line is comparable
with the intensity of the exciton
line

19. Combined exciton –cyclotron resonance ExCR
The ExCR line shifts LINEARLY from the
exciton resonance to high energies with
increase of magnetic fields
me
ω ExCR = Nω ec (1 + )
M

20. Combined processes in
Dense 2DEG
Three electrons+one
hole states

21. In the dense 2DEG two-electron processes emerge in the spectra
TrCR
There are two electrons in the initial
state; an incident photon creates an
exciton which binds with one of the
electrons forming a trion; and the second
electron excites on the second Landau
level
e + e + ph ⇒ Tr + e*
1 1 3
ω ec + ω ec + ω = Etr + ω ec
2 2 2
1
ω = Etr + ω ec
2

22. Trion Cyclotron Resonance
1,618 10 -2
open symbol - σ
− ne=8x10 cm
+
solid symbol - σ
1,616
Line position (eV)
1,614 ExCR2 ExCR1
1.00 meV/T
1,612
X
1,610
TrCR1
0.64 meV/T
1,608 −
X
1,606 3 2 1
0 1 2 3 4 5 6 7 8
Magnetic field (T)

23. Line of the TrCR is observable at filling factors > 1.
The intensity of the TrCR line is proportional to the second
power of the 2DEG density
TrCR (a)
11 -2
1×10 cm ExCR
Reflectivity
10 -2
8×10 cm
Intensity of TrCR-line
10 -2
6×10 cm
−
+
σ X X 0 20 40 60 80 100 120
−
T=1.6K 2 20 -4
σ B=2.5T ne (10 cm )
0
1,605 1,610
Energy (eV)
(b)
11 -2
1×10 cm
T=1.6K
Intensity of TrCR-line
0
10
8×10 cm
-2
0 2 4 6 8 10
10 -2
Electron concenctration, ne (10 cm )
10
6×10 cm
-2 ν =1 ν =1
ν =1
0
0 1 2 3 4 5
Magnetic field (T)

24. Surprising Trion stability against free
electron screening

25. Экситон исчезает из спектра при относительно малых
концентрациях электронов, а трион остается
ZnSe/ZnMgSSe 80A
CdTe/CdMgTe 80A
− 11 -2 ZnSe/ZnMgSSe
X 1.2x10 cm
−
−
X X
11
1.2x10 cm
-2
X X 8x10 cm
10 -2
− 10 -2
X 6x10 cm
Reflectivity
Reflectivity
− 10 -2
X 4x10 cm X
0
X
0 − 10
3x10 cm
-2
10
<10 cm
-2 X
X
0 9
4x10 cm
-2
0
0
T=1.6K 0
X B=0T T=1.6K
X B=0T
0
1.620 1.625 1.630 0
2.810 2.815 2.820 2.825
Energy (eV)
Energy (eV)

26. Сила осциллятора экситона не зависит от плотности 2DEG
Затухание экситона
растет с ростом
плотности

27. Спектры поглощения (PLE) как функция концентрации

28. 2.0
Absorption (arbit.un.)
1.5 a
1.0
0.5
0
1605 1610 1615 1620
Energy (meV)
1.5
Absorption (arbit.un.)
b
1.0
0.5
0
1605 1610 1615 1620
Energy (meV)

29. Trion Zeeman splitting as a function
of the electron density

30. The value of the exciton and trion Zeeman splitting?
einit + ph → Tr = ( Ex + e fin )
Because the initial and the final state of the electron are
the same (the same spin and the same Landau level)
we should see only the exciton Zeeman splitting on exciton
and on trion line
ε electron trion
photon exciton

31. Photoluminescence
In PL the exciton and trion
Zeeman splitting are equal 1,626
1,625
H=0T
Energy, eV
10 -2
1,624 ne=4x10 cm
PL Intensity, a.u.
1,623
1,622
1,615 1,620 1,625 1,630
Energy, eV 0 1 2 3 4 5 6 7 8
Magnetic Field (T)

32. Exciton and trion Zeeman splitting at high electron concentrations
1,630
1,629
1,628 Exc
1,627
Energy (eV)
1,626
1,625
1,624
1,623
T
1,622
1,621
0 1 2 3 4 5 6 7 8
0,8
0,6 Exc
0,4
Splitting (meV)
0,2
0,0
-0,2
-0,4
-0,6
10
ne=8x10 cm
-2 T
-0,8
0 1 2 3 4 5 6 7 8
Magnetic field (T)

33. This is possible only in the case if the initial and
final spin state of the electron are not the same –
we need spin-flip
For spin-flip we need spin-orbital interaction.
This can be the triplet-singlet splitting of the trion
In the initial state the photon creates virtual state of the triplet
trion. Because of very fast spin-flip of one of the electrons in the
final state we have the singlet trion (already real).
This is the process reversal to the ExCR

34. An incident photon creates a virtual trion in the triplet state. This trion
produces a spin-flip with one of the electrons on the first Landau level.
As a result, in the final state, we get a trion in the singlet state plus an
electron on the second Landau level with opposite spin.
This reaction looks
↑ ↑ ↑ ↓
e + e + ph → Tr + e → Tr + e
1 2
t
1
s
2

35. Фотолюминесценция трионов

36. Спектры ФЛ в зависимости от концентрации электронов
Ebex >>EF
Ebtr ~EF

37. In heavily doped QW in zero magnetic fields the PL line
is shifted to the low energies from its position in low
doped structure. The value of this shift is of the order of
Fermi energy
1635
PL
1630
Tt
1625 Tt
energy, meV
X
1620
Ts
1615 Ts −
σ 3.7x1 0 cm
11 -2
+
σ
1610 −
σ 3x1 0 cm
10 -2
SU σ
+
1605
0 10 20 30 40
Magnetic field, T

38. В магнитном поле линии триона и экситона «возрождаются»
X
Τ
1600 1610 1620 1630 1640
энергия, мэВ

39. Combined processes in PL
1650 1635 T=1,6K 11
ne=3.7x10 cm
-2
T=1.6K
11 -2
ne=3.7x10 cm
1630 CCR 2ω c
1640 ω c
ССR
X 1625 (1/2)ω c Tt
FL
energy, meV
energy, meV
1630
1620
Ts
1620 Ts 1615 −
σ
ν =2 σ
+
1610 ν =3
1610 SU
ν =4
0 10 20 30 40 50 0 10 20 30 40
magnetic field, T
Magnetic field, T
Comparison of PL and reflectivity PL and SU

40. Shake-up
Shake up процессы SU 11
ne=2x10 cm
-2
1/2hωc
T=1.6 K
B=7.5T
3/2hωc
Tr ⇒ ph + e
PL Intensity, arb. u.
*
5/2hωc
1
Etr = ω + ( N + )ω ec
2
1
ω = Etr − ( N + )ω ec
2 B=0
EF
ETr
1,596 1,598 1,600 1,602 1,604 1,606 1,608 1,610
Energy, eV

41. In Emission the initial state is: trion in a ground or excited
states; ∗
Τr → ph + e
the final state is: an electron above Fermi level
The energy of the transition is ω = ETr − E ∗ ≤ ETr − EF

42. Linear shift of the trion line in magnetic fields
In the final state after the trion
recombination a free electron
remains. It can appears in the ν =3
ν =4
unoccupied states above Fermi
Fermi energy
level
Etr = ω + E F ⇒ ω = Etr − E F
ν =1
In magnetic fields the Fermi energy LL2 LL1
decreases as ne=const
T=1.6K
ν =2
1 T=0 K
ω ec
2 Magnetic field

43. Theory
±
ω ph = Ω c (n ) − E tr ± ∆( B ) − E F ( B ) + αB + βB 2 + E G
Figure gives the energy positions of
maxima of emitted bands which are
described by equation
The shape of the states in presented by 1625
the Gaussian form
[ ] [ ]
eB /( 4π) 1615
exp − E − ω ± ( n ) / 2Γn ( B ) 
± 2 2
ρ n (E) =  ph 
2
2πΓn ( B )  
1605
10 30

44. Conclusions
In 2D structures containing electron gas the
scattering effects are enhanced.
In the presence of magnetic fields the electron
energy spectrum becomes discreet and the
scattering processes revel as combined exciton-
electron processes.
In such processes we can see directly only the
exciton transition but the state of the additional
electron, which we can not see, reveals only in the
final result.