Spin-Hall Effect in a  GaAs Quantum Well
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A self-consistent treatment of the spin-Hall effect requires consideration of the spin- orbit coupling and electron-impurity scattering on equal footing. This is done here for the experimentally relevant case of a  GaAs quantum well [Sih et al., Nature Phys. 1, 31 (2005)]. Working within the framework of the exact linear response formalism we calculate the spin-Hall conductivity including the Dresselhaus linear and cubic terms in the band structure, as well as the electron-impurity scattering and electron-electron interaction to all orders. We show that the spin-Hall conductivity naturally separates into two contributions, skew-scattering and side- jump, and we propose an experiment to distinguish between them.
Phys. Rev. Lett. 97, 266601 (2006) [4 pages]