Spin Relaxation and Anticrossing in Quantum Dots: Rashba versus Dresselhaus Spin-Orbit Coupling
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Transcript of Spin Relaxation and Anticrossing in Quantum Dots: Rashba versus Dresselhaus Spin-Orbit Coupling
Spin Relaxation and Anticrossing in Quantum Dots:
Rashba versus Dresselhaus Spin-Orbit Coupling
Denis V. Bulaev and Daniel LossDepartment of Physics
University of Basel, Switzerland
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Hamiltonian of electrons in a quantum dot
./4
,2
,2
,2
21
221
13
12
1
RZ
Z
lw
wE
wE
E
Three lowest electron energy levels
Rashba term as perturbation Dresselhaus term as perturbation
./ ,/ ,2
,4/ 2,122
0 RRc
c mml
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13
2
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Z
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E
E
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Anti-crossing (crossing) of the levels E2 and E3 at ./||1 Bg BZ
Anti-crossing of levels due to Rashba coupling [1]
0
0.05
0.10
0.15
0.20
0.25
2 4 6 8 10
Energy [meV]
B [T]
|↑
|↓
|↑ |↓
|↑E2 – E1
E3 – E1
E1 – E1
T 2.50 B
.m 8 s 103.1T 02.0mK 6eV 5.0)/(2 9 RRZ l
[1] C. F. Destefani, S. E. Ulloa, and G. E. Marques. Phys. Rev. B 69, 125302 (2004).
.222
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Z
R
ZZ
slw
Z
R
c
w
slw
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c
w
slw
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Spin relaxation rates (Rashba coupling)
.
,22
2/1
,28
2/1
,28
2/1
132
2232
7
2/2
2
2
1
125
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5
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2/2
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1
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Z
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s
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s
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s
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s
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Spin relaxation rates (Dresselhaus coupling)
B(T)B(T)
1.1 T
(a) (b)
1/T
1 (1/
s)
1/T
1 (1/
s)
B(T)5.1 5.2 5.3
B(T)5.1 5.2 5.3
Ene
rgy
(meV
)
Ene
rgy
(meV
)
0.13
0.135
0.13
0.135
0 3 6 9 12 15 0 3 6 9 12 15
109
108
107
106
105
104
103
102
10
109
108
107
106
105
104
103
102
10
E2 – E1
E2 – E1
E3 – E1
E3 – E1
21
31
32
Spin relaxation rates
Dresselhaus coupling Rashba coupling
21
21
3
3
15
0
0
/
,At . ,At
m.8 ,44.0 nm, 5 meV, 1.1
ZZ
Z
ZZcB
DR
Tk
gd
(for the Dresselhaus SO coupling),
(for the Rashba SO coupling).