# Omnidirectional spin Hall effect in a Weyl spin-orbit coupled atomic gas

## TL;DR

This paper predicts an omnidirectional spin Hall effect in a three-dimensional Weyl spin-orbit coupled atomic gas, where a transverse spin current is generated by various forces, and quantifies its conductivity.

## Contribution

It introduces the concept of an omnidirectional spin Hall effect in Weyl spin-orbit coupled gases and calculates its conductivity, extending the understanding of spin transport phenomena.

## Key findings

- Transverse spin current is generated in response to forces in any direction.
- The effect is the non-Abelian counterpart of the 2D Rashba spin Hall effect.
- Conductivity of the effect is quantified for fermions and bosons.

## Abstract

We show that in the presence of a three-dimensional (Weyl) spin-orbit coupling, a transverse spin current is generated in response to either a constant spin-independent force or a time-dependent Zeeman field in an arbitrary direction. This effect is the non-Abelian counterpart of the universal intrinsic spin Hall effect characteristic to the two-dimensional Rashba spin-orbit coupling. We quantify the strength of such an omnidirectional spin Hall effect by calculating the corresponding conductivity for fermions and non-condensed bosons. The absence of any kind of disorder in ultracold-atom systems makes the observation of this effect viable.