Gauge Physics of Spin Hall Effect

TL;DR

This paper introduces a gauge-theoretic framework that unifies various approaches to the Spin Hall Effect, clarifying previous ambiguities and providing precise calculations of SHE conductivity in different materials.

Contribution

It presents a comprehensive gauge-theoretic, time-momentum approach that unifies kinetic, spin orbit force, and geometric contributions to SHE within a single theoretical framework.

Findings

Unified SHE equation of motion derived

Corrected SHE conductivity values for Rashba 2DEG and heavy holes

Resolved ambiguities in previous SHE theoretical treatments

Abstract

Spin Hall effect (SHE) has been discussed in the context of Kubo formulation, geometric physics, spin orbit force, and numerous semi-classical treatments. It can be confusing if the different pictures have partial or overlapping claims of contribution to the SHE. In this article, we present a gauge-theoretic, time-momentum elucidation, which provides a general SHE equation of motion, that unifies under one theoretical framework, all contributions of SHE conductivity due to the kinetic, the spin orbit force (Yang-Mills), and the geometric (Murakami-Fujita) effects. Our work puts right an ambiguity surrounding previously partial treatments involving the Kubo, semiclassical, Berry curvatures, or the spin orbit force. The full treatment shows the Rashba 2DEG SHE conductivity to be +e/8{\pi} instead of -e/8{\pi} , and Rashba heavy hole +9e/8{\pi} instead of -9e/8{\pi} .