Spin Relaxation and Anticrossing in Quantum Dots: Rashba versus Dresselhaus Spin-Orbit Coupling

1
Spin Relaxation and Anticrossing in Quantum
Dots Rashba versus Dresselhaus Spin-Orbit
Coupling

• Denis V. Bulaev and Daniel Loss
• Department of Physics
• University of Basel, Switzerland

2
Abstract

• The spin-orbit splitting of the electron levels
  in a two-dimensional quantum dot in a
  perpendicular magnetic field is studied. It is
  shown that at the point of an accidental
  degeneracy of the two lowest levels above the
  ground state the Rashba spin-orbit coupling leads
  to a level anticrossing and to mixing of spin-up
  and spin-down states, whereas there is no mixing
  of these levels due to the Dresselhaus term. We
  calculate the relaxation and decoherence times of
  the three lowest levels due to phonons. We find
  that the spin relaxation rate as a function of a
  magnetic field exhibits a cusp-like structure for
  Rashba but not for Dresselhaus spin-orbit
  interaction.

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Hamiltonian of electrons in a quantum dot
4
Three lowest electron energy levels
Rashba term as perturbation
Dresselhaus term as perturbation
Anti-crossing (crossing) of the levels E2 and E3
at .
5
Anti-crossing of levels due to Rashba coupling 1
E3 E1
0.25
??
??
0.20
orbital
B perp.
Energy meV
0.15
0.10
Zeeman
E2 E1
??
0.05
??
??
E1 E1
0
8
2
4
6
10
B T
1 C. F. Destefani, S. E. Ulloa, and G. E.
Marques. Phys. Rev. B 69, 125302 (2004).
6
Anti-crossing of levels due to Rashba coupling 1
E3 E1
0.25
??
??
0.20
Energy meV
0.15
G31
G32
0.10
E2 E1
??
0.05
G21
??
??
E1 E1
0
8
2
4
6
10
B T
1 C. F. Destefani, S. E. Ulloa, and G. E.
Marques. Phys. Rev. B 69, 125302 (2004).
7
Spin relaxation rates (Rashba coupling)
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Spin relaxation rates (Dresselhaus coupling)
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Spin relaxation rates
Dresselhaus coupling
Rashba coupling
(for the Dresselhaus SO coupling),
(for the Rashba SO coupling).