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

TL;DR

This paper develops a Boltzmann-like equation to analyze how small-angle impurity scattering influences the spin Hall conductivity in 2D semiconductor systems, revealing conditions where the conductivity can vary significantly in magnitude and sign.

Contribution

It introduces a generalized theoretical framework for impurity scattering with arbitrary angular dependence affecting spin Hall conductivity in 2D systems.

Findings

Impurity scattering can significantly alter the spin Hall conductivity.

The conductivity can be larger, smaller, or opposite in sign to the intrinsic value.

Small-angle scattering in parabolic bands can reverse the sign of the spin Hall conductivity.

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 $b$ 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.