Hall viscosity in quantum systems with discrete symmetry: point group and lattice anisotropy

TL;DR

This paper investigates the Hall viscosity in anisotropic two-dimensional quantum systems with discrete symmetries, extending theoretical frameworks and analyzing specific models to understand their viscoelastic responses.

Contribution

It extends the Kubo formalism to systems with internal degrees of freedom and discrete translational symmetry, and develops a framework to compute Hall viscosities in lattice and continuum models.

Findings

Six Hall viscosities generally exist, but only three contribute to bulk viscous forces.

The formalism is applied to lattice Chern insulators and anisotropic superfluids.

Only a subset of Hall viscosities influence the viscous force density in the bulk.

Abstract

Inspired by recent experiments on graphene, we examine the non-dissipative viscoelastic response of anisotropic two-dimensional quantum systems. We pay particular attention to electron fluids with point group symmetries, and those with discrete translational symmetry. We start by extending the Kubo formalism for viscosity to systems with internal degrees of freedom and discrete translational symmetry, highlighting the importance of properly considering the role of internal angular momentum. We analyze the Hall components of the viscoelastic response tensor in systems with discrete point group symmetry, focusing on the hydrodynamic implications of the resulting forces. We show that though there are generally six Hall viscosities, there are only three independent contributions to the viscous force density in the bulk. To compute these coefficients, we develop a framework to consistently write down the long-wavelength stress tensor and viscosity for multi-component lattice systems. We apply our formalism to lattice and continuum models, including a lattice Chern insulator and anisotropic superfluid.