Generalized Electron Hydrodynamics, Vorticity Coupling, and Hall Viscosity in Crystals

TL;DR

This paper develops a generalized framework for electron hydrodynamics in crystals, revealing how anisotropy, symmetry, and Hall viscosity influence electron fluid behavior in various materials.

Contribution

It introduces a comprehensive treatment of viscosity tensors in electron fluids, accounting for crystal symmetries and time-reversal breaking effects, extending beyond isotropic models like graphene.

Findings

Hexagonal 2D materials behave like isotropic fluids.

3D materials show significant anisotropic deviations.

Hall viscosity couples to vorticity without breaking time-reversal symmetry.

Abstract

Theoretical and experimental studies have revealed that electrons in condensed matter can behave hydrodynamically, exhibiting fluid phenomena such as Stokes flow and vortices. Unlike classical fluids, preferred directions inside crystals lift isotropic restrictions, necessitating a generalized treatment of electron hydrodynamics. We explore electron fluid behaviors arising from the most general viscosity tensors in two and three dimensions, constrained only by thermodynamics and crystal symmetries. Hexagonal 2D materials such as graphene support flows indistinguishable from those of an isotropic fluid. By contrast 3D materials including Weyl semimetals, exhibit significant deviations from isotropy. Breaking time-reversal symmetry, for example in magnetic topological materials, introduces a non-dissipative Hall component to the viscosity tensor. While this vanishes by isotropy in 3D, anisotropic materials can exhibit nonzero Hall viscosity components. We show that in 3D anisotropic materials the electronic fluid stress can couple to the vorticity without breaking time-reversal symmetry. Our work demonstrates the anomalous landscape for electron hydrodynamics in systems beyond graphene, and presents experimental geometries to quantify the effects of electronic viscosity.