paper

Small-angle impurity scattering and the spin Hall conductivity in 2D systems

arXiv:cond-mat/0509702 · doi:10.1103/PhysRevB.73.075316

Abstract

An arbitrarily small concentration of impurities can affect the spin Hall conductivity in a two-dimensional semiconductor system. We develop a Boltzmann-like equation that can be used for impurity scattering with arbitrary angular dependence, and for arbitrary angular dependence of the spin-orbit field b(k) around the Fermi surface. For a model applicable to a 2D hole system in GaAs, if the impurity scattering is not isotropic, we find that the spin Hall conductivity depends on the derivative of b with respect to the energy and on deviations from a parabolic band structure, as well as on the angular dependence of the scattering. In principle, the resulting spin Hall conductivity can be larger or smaller than the ``intrinsic value'', and can have opposite sign. In the limit of small angle scattering, in a model appropriate for small hole concentrations, where the band is parabolic and b ~ k^3, the spin Hall conductivity has opposite sign from the intrinsic value, and has larger magnitude. Our analysis assumes that the spin-orbit splitting and the transport scattering rate tau^{-1} are both small compared to the Fermi energy, but the method is valid for for arbitrary value of b*tau.

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