Spin Hall effect associated with SU(2) gauge field

TL;DR

This paper explores the intrinsic quantum mechanical origin of the spin Hall effect via the AC phase, linking it to the Anandan force and improving theoretical predictions of spin Hall conductivity in two-dimensional systems.

Contribution

It introduces an AC phase-based method to derive spin force, connecting the spin Hall effect to quantum phases and refining theoretical conductivity values to better match experiments.

Findings

Spin force is part of the classical Anandan force.

The spin Hall effect originates from the AC phase, an intrinsic quantum property.

Improved theoretical spin Hall conductivity aligns better with experimental data.

Abstract

In this paper, we focus on the connection between spin Hall effect and spin force. Here we investigate that the spin force due to spin-orbit coupling, which in two-dimensional system is equivalent to forces of Hirsch and Chudnovsky besides constant factors 3 and 3/2 respectively, is a part of classic Anandan force, and that the spin Hall effect is an anomalous Hall effect. Furthermore, we develop the method of AC phase to derive the formula for the spin force, and find that the most basic spin Hall effect originates from the AC phase and is therefore an intrinsic quantum mechanical property of spin. This method differs from approach of Berry phase in the study of anomalous Hall effect, which is the intrinsic property of the perfect crystal. On the other hand, we use an elegant skill to show that the Chudnovsky-Drude model is reasonable, and further have improved the theoretical values of spin Hall conductivity of Chudnovsky. Compared to the theoretical values of spin Hall conductivity in the Chudnovsky-Drude model, ours are in better agreement with experimentation. Finally, we discuss the relation between spin Hall effect and fractional statistics.