Resonant spin Hall conductance in ptype quantum well structure

1
Resonant spin Hall conductance in p-type quantum
well structure
Xi Dai
Department of Physics, University of Hong Kong
Institute of physics, Chinese Academy of Science
Zhong Fang,Yu Gui Yao
Institute of physics, Chinese Academy of Science
Fu-chun Zhang
Department of Physics, University of Hong Kong
2
Outline

• Introduction of Spin Hall effect
• Spin-orbital coupling, Rashba, Luttinger
• Extrinsic or intrinsic?
• The experimental observations.
• Effective Hamiltonian for 2DHG
• Numerical solution
• Interplay between Rashba and Luttinger
• type spin-orbital couplings resonant
  spin-Hall effect

3
Spin current do big things!

• Spin current transport of spin
  polarization----Quantum computing
• Manipulation of the spin state of the small
  devices------Memory device
• Traditional way to generate spin current
• spatial non uniform magnetic field
• Spin Hall effect A new way to generate and
  manipulate spin current

4
Spin Hall effect
5
Two experimental observations of Spin Hall effect

• 2DEG Y. K. Kato, R. C. Myers, A. C. Gossard, and
  D. D.Awschalom, Science 306, 1910 (2004). 2D
  electron gas system
• 2DHG J. Wunderlich, B. Kaestner, J. Sinova, and
  T. Jungwirth, PRL 94, 047204 (2005).
• 2D hole gas system

6
Intrinsic or extrinsic?

• Intrinsic effect intrinsic spin-orbital coupling
  
• Extrinsic effect spin-dependent impurity
  scattering
• How to distinguish them?

7
Two typical systems which has the spin Hall effect

• Two dimensional electron gas Rashba Hamiltonian
• Structural Inversion symmetry breaking

8
(No Transcript)
9

• Effective Hamiltonian for the hole doped GaAs
  Luttinger model.
• The spin-orbital coupling induce the splitting of
  light hole and heavy hole band.

10
How to model the 2D hole gas?

• Luttinger model confinement potential along the
  c-direction structural inversion symmetry
  breaking
• The effect of confinement potential sub-band
  splitting

11
Effective Hamiltonian for 2DHG
With infinite energy well V(Z)
12
Eigen-States at the G point
13
For small k (kltltq1)

• Treat k as perturbation project the Hamiltonian
  to the lowest sub-bands.
• The effective Hamiltonian for the lowest sub-band
  (HH1) cubic Rashba model (John Schliemann and
  Daniel Loss cond-mat/0405436, Bernevig and S. C.
  Zhang, cond-mat/0411457
• The effective Hamiltonian for the lowest light
  hole sub-band (LH1) linear Rashba model

14
For intermediate kq1

• Interplay between the Rashba type and Luttinger
  type spin-orbital coupling gives very interesting
  phenomena
• Numerical diagonization the above Hamiltonian for
  2DHG
• Basis functions, the eigen states at k0
• Truncated method with up limit n20

15

• Sub-band structure band crossing

16
Band crossing points magnetic monopoles in the
momentum space

• Kubo formula for the spin Hall conductance

• Band crossing resonance point

17
(No Transcript)
18
(No Transcript)
19
(No Transcript)
20
Conclusion

• Need both the Rashba and Luttinger type
  spin-orbital interaction to model the 2DHG
• Interplay between Rashba and Luttinger type
  spin-orbital interaction gives the resonance
  spin-Hall effect
• resonance spin-Hall effect can be used to
  distinguish intrinsic and extrinsic spin-Hall
  effect.

21

• Thank you for your attention!