Vorticity-induced anomalous Hall effect in electron fluid

TL;DR

This paper develops a hydrodynamic model showing that vorticity near boundaries induces an additional anomalous Hall effect in electron fluids, with implications for thin systems.

Contribution

It introduces a hydrodynamic theory linking vorticity to an anomalous Hall effect, including effects of Hall viscosity and boundary-induced vorticity.

Findings

Vorticity near boundaries induces an additional Hall effect.

The additional Hall force can reverse the sign of the conventional effect.

Non-uniform flow and Hall viscosity are key factors in the model.

Abstract

We develop a hydrodynamic theory for an electron system exhibiting the anomalous Hall effect, and show that an additional anomalous Hall effect is induced by a vorticity generated near boundaries. We calculate the momentum flux and force proportional to the electric field using linear response theory. The hydrodynamic equation is obtained by replacing the local electric field with the electric current, focusing on a scale that is sufficiently larger than the mean free path. It is demonstrated that there is a coupling between a vorticity of an electric current and a magnetization which generates a pressure from non-uniform vorticity. Taking into account Hall viscosity and relaxation forces, a non-uniform flow near a boundary and an additional Hall force are calculated. The additional anomalous Hall force is opposite to conventional anomalous Hall force, resulting in a sign reversal in thin systems.