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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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**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 • Spin flip source: Spin-orbit interaction • Requirement: Long relaxation time**A GaAs QD defined in**a 2DEG Spin relaxation time is 50 µs at an in-plane field 7.5 T**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)**Long(4 µm), wide(950 nm), thick(130 nm)**QD (40 nm below the surface)**Wide(600 nm), thick(130 nm)**• QD (40 nm below the surface)**Model**Total Hamiltonian Electron term +spin orbit coupling Phonon term + electron-phonon coupling**Single electron in a QD**Electron Hamiltonian Fock-Darwin states**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**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**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**Phonon (1)**Acoustic phonon in a free-standing structure Confined phonon modes: Shear waves, Dilatational waves, Flexural waves do not interact with electrons**Phonon (2)**Dilatational waves Symmetric waves Dispersion relation**Phonon (3)**Flexural waves Antisymmetric waves Dispersion relation**Electron-phonon interaction**Deformation potential interaction Dilatational and flexural**Spin relaxation rate**Fermi golden rule Parameters: (1) GaAs quantum dot (2) A QD is located at z=0**A van Hove singularity occurs**This is due to zero phonon group velocity**Spin relaxation rate completely vanishes at the magnetic**field A vanishing divergence of the displacement field**phonon number**• This enhances the electron-phonon scattering**Phonon number**• Rate**Two huge rates and suppressed rates display**• Interplay between SO coupling and Zeeman levels**Two singular rates clearly occur for small width case**• They disappear as the width is large (bulk-like system)**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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