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Insights into Rashba and Dresselha Spin-Orbit Coupling

This paper explores the origin, models, and effects of spin-orbit coupling in quasi-two-dimensional systems, detailing structure, perturbation theories, and comparison of spin-splitting mechanisms. Discover the key contributions and understand the theoretical framework behind spin orientation in the presence of inversion asymmetry. Gain insight into the anisotropy and relevance of Rashba and Dresselhaus spin-orbit coupling in semiconductor physics. Discuss further implications and related problems in spintronics, quantum mechanics, and topological insulators.

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Insights into Rashba and Dresselha Spin-Orbit Coupling

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  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 • ……

  20. J.J. Sakurai: Advanced Quantum Mechanics Winkler, Spin–orbit effects in two dimensional electron and hole systems (Springer-Verlag Berlin, 2003). G. Dresselhaus: Phys. Rev. 100(2), 580–586 (1955) E. I. Rashba, Phys. E. 34, 31 (2006). E. I. Rashba, Phys. Rev. B 68, 241315 (2003). Y.A. Bychkov, E.I. Rashba: J. Phys. C: Solid State Phys. 17, 6039–6045 (1984) S. Datta, B. Das: Appl. Phys. Lett. 56(7), 665–667 (1990) E.O. Kane: “The k · p method”, in Semiconductors and Semimetals, ed. by R.K. Willardson, A.C. Beer, Vol. 1 (Academic Press, New York, 1966), p. 75 R. Winkler: Phys. Rev. B 62, 4245 (2000) J. B. Miller, D. M. Zumbühl, C. M. Marcus, Y. B. Lyanda- Geller, D. Goldhaber-Gordon, K. Campman, and A. C. Gossard, Phys. Rev. Lett. 90, 076807 (2003). M. D’yakonovand V. Perel’, Phys. Lett. A 35, 459 (1971). Reference

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