Small-angle impurity scattering and the spin Hall conductivity in 2D systems
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.
Cite
@article{arxiv.cond-mat/0509702,
title = {Small-angle impurity scattering and the spin Hall conductivity in 2D systems},
author = {A. V. Shytov and E. G. Mishchenko and H. -A. Engel and B. I. Halperin},
journal= {arXiv preprint arXiv:cond-mat/0509702},
year = {2007}
}
Comments
Errors corrected, references added