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Spin relaxation rates in quantum dots

Spin relaxation rates in quantum dots. 學生 : 廖英彥 指導教授 : 褚德三 交通大學電子物理所. Outline. Introduction Experiment Model Results Conclusion. Qubit vs Spin relaxation. Proposal: A qubit based on the electron spin of quantum dot Relaxation: Phonon induced spin flip

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Spin relaxation rates in quantum dots

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  1. Spin relaxation rates in quantum dots 學生: 廖英彥 指導教授: 褚德三 交通大學電子物理所

  2. Outline • Introduction • Experiment • Model • Results • Conclusion

  3. Qubit vs Spin relaxation • Proposal: A qubit based on the electron spin of quantum dot • Relaxation: Phonon induced spin flip • Spin flip source: Spin-orbit interaction • Requirement: Long relaxation time

  4. A GaAs QD defined in a 2DEG Spin relaxation time is 50 µs at an in-plane field 7.5 T

  5. Studies on spin relaxation Theory A. V. Khaetskii and Y. V. Nazarov, PRB 61,12639 (2000) A. V. Khaetskii and Y. V. Nazarov, PRB 64,125316 (2001) Structure: A QD in bulk material (all) Phonon: Bulk phonon (3D phonon wavevector) Our goal: (a) Different type of phonon vs spin relaxation (b) Free-standing structure (2D phonon wavevector)

  6. Long(4 µm), wide(950 nm), thick(130 nm) QD (40 nm below the surface)

  7. Wide(600 nm), thick(130 nm) • QD (40 nm below the surface)

  8. Single QD is defined in a free-standing structure (slab).

  9. Model Total Hamiltonian Electron term +spin orbit coupling Phonon term + electron-phonon coupling

  10. Single electron in a QD Electron Hamiltonian Fock-Darwin states

  11. Spin orbit coupling (1) Zinc-blende crystal : GaAs Dresselhauls vs Rashba term Origin: bulk inversion asymmetry Dependence: (a) parameter of material (b) z-direction confinement width

  12. Spin orbit coupling (2) Rashba term Origin: Structure inversion asymmetry Dependence: (a) parameter of material (b) perpendicular confinement field Comparison: Electric field : V/cm Ratio : 0.1 ~ 0.7

  13. Perturbative approach vs Exact diagonalization Perturbative approach Spin-orbit coupling is viewed as a small perturbation Exact diagonalization Large spin-orbit coupling Small electron levels

  14. Phonon (1) Acoustic phonon in a free-standing structure Confined phonon modes: Shear waves, Dilatational waves, Flexural waves do not interact with electrons

  15. Phonon (2) Dilatational waves Symmetric waves Dispersion relation

  16. Phonon (3) Flexural waves Antisymmetric waves Dispersion relation

  17. Electron-phonon interaction Deformation potential interaction Dilatational and flexural

  18. Spin relaxation rate Fermi golden rule Parameters: (1) GaAs quantum dot (2) A QD is located at z=0

  19. A van Hove singularity occurs This is due to zero phonon group velocity

  20. Spin relaxation rate completely vanishes at the magnetic field A vanishing divergence of the displacement field

  21. phonon number • This enhances the electron-phonon scattering

  22. Phonon number • Rate

  23. Two huge rates and suppressed rates display • Interplay between SO coupling and Zeeman levels

  24. Two singular rates clearly occur for small width case • They disappear as the width is large (bulk-like system)

  25. Conclusion A huge rate is due to a van Hove singularity A suppressed rate is due to a vanishing divergence of the displacement field We hope that these results are useful in understanding spin relaxation in a suspended quantum dot nanostructure

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