Absence of vertex correction for the spin Hall effect in p-type semiconductors

TL;DR

This paper demonstrates that in p-type semiconductors modeled by the Luttinger model, the vertex correction to the spin Hall effect vanishes, confirming the intrinsic spin Hall conductivity in the clean limit.

Contribution

It shows the absence of vertex correction in the Luttinger model for p-type semiconductors, contrasting with the Rashba model, and confirms the intrinsic spin Hall conductivity.

Findings

Vertex correction vanishes in the Luttinger model.

Self-energy becomes diagonal and independent of wavenumber.

Intrinsic spin Hall conductivity is recovered in the clean limit.

Abstract

We calculate an effect of spinless impurities on the spin Hall effect of the Luttinger model representing p-type semiconductors. The self-energy in the Born approximation becomes diagonal in the helicity basis and its value is independent of the wavenumber or helicity. The vertex correction in the ladder approximation vanishes identically, in sharp contrast with the Rashba model. This implies that in the clean limit the spin Hall conductivity reproduces the value of the intrinsic spin Hall conductivity calculated in earlier papers.