• Open Access

Hall Viscosity in Quantum Systems with Discrete Symmetry: Point Group and Lattice Anisotropy

Pranav Rao and Barry Bradlyn
Phys. Rev. X 10, 021005 – Published 7 April 2020

Abstract

Inspired by recent experiments on graphene, we examine the nondissipative 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 multicomponent lattice systems. We apply our formalism to lattice and continuum models, including a lattice Chern insulator and anisotropic superfluid.

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  • Received 27 October 2019
  • Accepted 28 February 2020

DOI:https://doi.org/10.1103/PhysRevX.10.021005

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Pranav Rao and Barry Bradlyn*

  • Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA

  • *Corresponding author. bbradlyn@illinois.edu

Popular Summary

From the stagnant flow of honey to the drag forces on a ball in air, nature provides many examples of viscosity, which dissipates power and slows things down. In some exotic classical and quantum fluids, there are also “Hall” viscosities, components of viscosity that do not dissipate power, instead providing forces transverse to fluid motion. Until now, the Hall viscosity was truly understood only in the simplest of cases. Upon considering anisotropy and internal rotational degrees of freedom (for example, spin), we find that several new chapters to the story of viscosity appear and that more realistic domains can be described. Our work has key applications to electronic materials in the “hydrodynamic regime,” wherein strong interactions cause electrons to flow like a fluid.

We first show that there are generally six Hall viscosities, but surprisingly only three independent viscous forces that result. We show that only three pairs of Hall viscosities are observable, even in incompressible fluids. We show how to compute all these coefficients for both lattice and continuum quantum fluids and highlight the importance of spin angular momentum to Hall viscosity through several examples.

Our framework was developed to study the Hall viscosity, but most broadly, it provides researchers across disciplines with a way of approaching the effects of strain (viscous and elastic) in a large set of classical and quantum systems, including graphene.

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Vol. 10, Iss. 2 — April - June 2020

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