Long range scattering effects on spin Hall current in $p$-type bulk semiconductors

TL;DR

This paper investigates how long-range hole-impurity scattering influences the spin-Hall current in p-type bulk semiconductors, revealing a non-zero contribution that can change the current's sign depending on hole density.

Contribution

It demonstrates that long-range scattering induces a nonvanishing spin-Hall current, contrasting with short-range scattering, and clarifies the origin of the disorder-independent spin-Hall effect.

Findings

Long-range scattering produces a non-zero spin-Hall current.

The contribution is independent of impurity density in the diffusive regime.

The sign of the spin-Hall current can reverse with hole density.

Abstract

Employing a nonequilibrium Green's function approach, we examine the effects of long-range hole-impurity scattering on spin-Hall current in $p$-type bulk semiconductors within the framework of the self-consistent Born approximation. We find that, contrary to the null effect of short-range scattering on spin-Hall current, long-range collisions do produce a nonvanishing contribution to the spin-Hall current, which is independent of impurity density in the diffusive regime and relates only to hole states near the Fermi surface. The sign of this contribution is opposite to that of the previously predicted disorder-independent spin-Hall current, leading to a sign change of the total spin-Hall current as hole density varies. Furthermore, we also make clear that the disorder-independent spin-Hall effect is a result of an interband polarization directly induced by the dc electric field with contributions from all hole states in the Fermi sea.