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Anticrossing and Spin Relaxation of Electrons and Holes in Quantum Dots

Anticrossing and Spin Relaxation of Electrons and Holes in Quantum Dots. Denis Bulaev and Daniel Loss Department of Physics University of Basel, Switzerland. Outline. Dresselhaus and Rashba SO Coupling Electrons in Quantum Dots Heavy holes in Quantum Dots.

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Anticrossing and Spin Relaxation of Electrons and Holes in Quantum Dots

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  1. Anticrossing and Spin Relaxation of Electrons and Holes in Quantum Dots Denis Bulaev and Daniel Loss Department of Physics University of Basel, Switzerland

  2. Outline • Dresselhaus and Rashba SO Coupling • Electrons in Quantum Dots • Heavy holes in Quantum Dots

  3. Dresselhaus spin-orbit coupling conduction band Kane model bulk valence band 2D Quantum Well

  4. Dresselhaus spin-orbit coupling 2D Quantum Well 0D Quantum Dot

  5. Rashba spin-orbit coupling From the Group Theory: due to the coupling between the conduction band ( ) and the valence band ( ). due to the coupling between more remote bands ( and ). [1] E. A. de Andrada e Silva, G. C. La Rocca, and F. Bassani, PRB 50, 8523 (1994). [2] R. Winkler, H. Noh, E. Tutuc, and M. Shayegan, Phys. Rev. B 65, 155303 (2002).

  6. Effective Hamiltonian of electrons

  7. Three lowest electron energy levels DresselhausSO couplingRashba SO coupling Anti-crossing (crossing) of the levels E2 and E3 at

  8. Anticrossing due to Rashba coupling E3 – E1 0.25 0.20 orbital Energy [meV] 0.15 0.10 Zeeman E2 – E1 0.05 E1 – E1 8 0 2 4 6 10 B [T] [1] C. F. Destefani, S. E. Ulloa, and G. E. Marques. Phys. Rev. B 69, 125302 (2004).

  9. Anticrossing due to Rashba coupling E3 – E1 0.25 0.20 Energy [meV] 0.15 G31 G32 0.10 E2 – E1 0.05 G21 E1 – E1 8 0 2 4 6 10 B [T] [1] C. F. Destefani, S. E. Ulloa, and G. E. Marques. Phys. Rev. B 69, 125302 (2004).

  10. Relaxation, Decoherence, and Dephasing Spin dephasing rate Orbital dephasing rate

  11. Electron relaxation rates Dresselhauscoupling Rashba coupling

  12. Zeeman energy for holes bulk 2D case [1] J. M. Luttinger, Phys. Rev. 102, 1030 (1956). [2] H.W. van Kestern, et al., PRB 41, 5283 (1990). [3] M. Bayer,et al., PRL 82, 1748 (1999).

  13. Heavy holes and SO interactions

  14. Effective Hamiltonian of heavy holes

  15. Heavy-hole relaxation rates (GaAs) Dresselhauscoupling Rashba coupling the maximum in the rate

  16. Heavy-hole relaxation rates (InAs) Dresselhauscoupling Rashba coupling

  17. Magnetic-field dependence of rates Electrons phonons Hso Heavy holes Dresselhaus SO coupling Rashba SO coupling

  18. Electrons vs. heavy holes GaAs QD with l0=30 nm, d=5 nm InAs QD with l0=30 nm, d=5 nm

  19. Summary Electrons • Anticrossing and spin mixing • Cusp-like behavior of the spin relaxation Heavy holes • Anticrossing and spin mixing (GaAs QD) • Cusp-like behavior of the spin relaxation (GaAs QD) • No cusp in spin relaxation (InAs QD) • RashbaDresselhaus • Spin relaxation time for heavy holes CAN BE longer than for electrons

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