A Brief Introduction of Rashba Spin-Orbit Coupling in Quasi-Two-Dimensional Systems

1. A Brief Introduction ofRashba Spin-Orbit Coupling inQuasi-Two-Dimensional Systems Xiaohan Yao 11th, JUN. 2018

2. Origin of Spin-Orbit Coupling • Classical • Relativistic effect • Elementary Models & Tools • Quasi-Degenerate Perturbation Theory • K-p method & Envelope Function Approximation • Spin-Splitting at B=0 • Inversion-Asymmetry-Induced Spin-Splitting • Structure & Bulk Inversion-Asymmetric Spin-Orbit Coupling • Rashba & Dresselhaus Spin-Orbit Coupling Content

3. Origin of Spin-Orbit Coupling (SOC)

4. Origin of Spin-Orbit Coupling (SOC) The Pauli equation emerges as a nonrelativistic approximation from the Dirac equation We obtain the Pauli equation(up to order): Third term: Zeeman term Fourth term: Pauli SOC term

5. GaAs band gap Conduction band: s-like orbital Valence band: p-like Qualitative sketch of SOC

6. Degenerate & Non-degenerate Perturbation Theory . . .

7. Quasi-Degenerate Perturbation Theory

8. Quasi-Degenerate Perturbation Theory

9. Band Structure and k·p Method

10. Envelope Function Approximation (EFA)

11. SOC in EFA Model

12. Inversion-Asymmetry-Induced Spin Splitting (B=0)

13. BIA • Zinc Blende Semiconductor • Quasi-2D System: Heterostructure • SIA • Gate-tunable • Defect • …… Structure & Bulk Inversion Asymmetric (Space)

14. Dresselhaus SOC at Quasi-2D system BIA Spin-splitting: Zine Blende Structure

15. SIA Spin-splitting: Rashba Model

16. Comparison: BIA(Dresselhaus) & SIA(Rashba) Spin orientation of the spin eigenstates in the presence of BIA and SIA spin splitting：

17. Spin orientation of the spin eigenstates in the presence of BIA and SIA spin splitting： Comparison: BIA(Dresselhaus) & SIA(Rashba) The different symmetries of the Hamiltonians for BIA and SIA, which become visible in the quantity ⟨σ⟩, is also the reason for the anisotropy of the B = 0 spin splitting even in the leading order of k∥ for the case where both BIA and SIA are present.

18. Calculation

19. Need further discussion • RSOC in other systems • Topological insulators • Weyl semimetals • Quasi-1D systems • …… • RSOC related problems • Weak anti-localization • Anomalous Magneto-Oscillations (SdH Oscillations) • Majorana Fermions • …… • Spintronics • Spin-FET • Spin inject & Spin current • ……

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