# Intrinsic Spin Hall Effect with Spin-Tensor-Momentum Coupling

## TL;DR

This paper investigates the intrinsic spin Hall effect in a 2D fermion model, revealing a new spin-tensor Hall current from spin-tensor-momentum coupling that enhances spin transport.

## Contribution

It introduces a novel spin-tensor Hall current derived from spin-tensor-momentum coupling and quantifies its impact on spin Hall conductivity.

## Key findings

- Spin-tensor Hall current originates from spin-tensor-momentum coupling.
- Total spin Hall conductivity is increased by the spin-tensor contribution.
- Spin-tensor-momentum coupling enhances spin transport in the intrinsic spin Hall effect.

## Abstract

We derive the spin continuity equation by using the Noether's theorem. A new type of spin-tensor Hall current is found in the continuity equation. The spin-tensor Hall current is originating from the coupling of the spin-tensor and the momentum. The intrinsic spin Hall effect in the two-dimensional fermion model with the spin-orbit coupling and spin-tensor-momentum coupling is studied. The total spin Hall conductivity with the presence of the spin-tensor Hall current is calculated. The numerical results indicate that the total spin Hall conductivity is enhanced by the contribution of the spin-tensor-momentum coupling. The spin-tensor-momentum coupling may increase the spin transport in the intrinsic spin Hall effect.