Hall viscosity from elastic gauge fields in Dirac crystals

TL;DR

This paper predicts a large Hall viscosity in elastic topological materials due to elastic gauge fields, suggesting it is a widespread and experimentally observable phenomenon in Dirac and Weyl systems.

Contribution

It introduces the concept that elastic gauge fields induce a significant Hall viscosity in topological materials, expanding the understanding of elastic responses in quantum materials.

Findings

Elastic gauge fields are common in topologically non-trivial materials.

A Hall viscosity with a large coefficient is predicted in these systems.

The effect is potentially observable experimentally due to its magnitude.

Abstract

The combination of Dirac physics and elasticity has been explored at length in graphene where the so--called "elastic gauge fields" have given rise to an entire new field of research and applications: Straintronics. The fact that these elastic fields couple to fermions as the electromagnetic field, implies that many electromagnetic responses will have elastic counterparts not explored before. In this work we will first show that the presence of elastic gauge fields will be the rule rather than the exception in most of the topologically non--trivial materials in two and three dimensions. In particular we will extract the elastic gauge fields associated to the recently observed Weyl semimetals, the "three dimensional graphene". As it is known, quantum electrodynamics suffers from the chiral anomaly whose consequences have been recently explored in matter systems. We will show that, associated to the physics of the anomalies, and as a counterpart of the Hall conductivity, elastic materials will have a Hall viscosity in two and three dimensions with a coefficient orders of magnitude bigger than the previously studied response. The magnitude and generality of the new effect will greatly improve the chances for the experimental observation of this topological, non dissipative response.