Odd viscosity and anomalous Hall effect in two dimensional electron systems with smooth disorder

TL;DR

This paper develops a microscopic theory linking odd viscosity and the anomalous Hall effect in 2D electron systems with smooth disorder and spin-orbit interaction, highlighting the role of spin polarization.

Contribution

It introduces a novel microscopic framework connecting odd viscosity with the anomalous Hall effect in systems with smooth disorder and spin-orbit coupling.

Findings

Spin-orbit scattering induces off-diagonal viscosity components.

Odd viscosity contributes to the anomalous Hall effect.

Hydrodynamic equations for spin and electric currents are derived.

Abstract

A microscopic theory of odd viscosity in two-dimensional electron systems with smooth disorder and spin-orbit interaction is developed. It is shown that spin-orbit scattering in presence of spin polarization induced by magnetic field gives rise to an off-diagonal component of the viscosity tensor. Hydrodynamic equations for spin and electric currents are derived for electrons interacting with smooth disorder. The contribution of odd viscosity to the anomalous Hall effect is calculated.