Electron hydrodynamics of anomalous Hall materials

TL;DR

This paper investigates how Berry curvature influences viscous electron flow in 2D topological materials, revealing unconventional flow patterns and potential experimental signatures in non-local resistance measurements.

Contribution

It introduces a modified hydrodynamic model incorporating Berry curvature effects, predicting novel flow behaviors in anomalous Hall materials.

Findings

Berry curvature modifies Navier-Stokes equations for electron flow

Unconventional Poiseuille flow with asymmetric profile

Current whirlpools and potential asymmetry in infinite geometry

Abstract

We study two-dimensional electron systems in the hydrodynamic regime. We show that a geometrical Berry curvature modifies the effective Navier-Stokes equation for viscous electron flow in topological materials. For small electric fields, the Hall current becomes negligible compared to the viscous longitudinal current. In this regime, we highlight an unconventional Poiseuille flow with an asymmetric profile and a deviation of the maximum of the current from the center of the system. In a two-dimensional infinite geometry, the Berry curvature leads to current whirlpools and an asymmetry of potential profile. This phenomenon can be probed by measuring the asymmetric non-local resistance profile.