Semiclassical theory of viscosity in quantum Hall states

TL;DR

This paper develops a semiclassical framework to understand Hall viscosity in quantum Hall states, linking it to electric field inhomogeneities that induce strain and shear in cyclotron orbits, providing new physical insights.

Contribution

It introduces an extended semiclassical approach to compute conductivity and connect electric field inhomogeneity with Hall viscosity in quantum Hall states.

Findings

Electric field inhomogeneity can tune the metric and induce strain.

Hall viscosity arises from shearing of local cyclotron orbits.

Electric fields can be used experimentally to control Hall viscosity.

Abstract

Quantum Hall (QH) states are predicted to display an intriguing non-dissipative stress response to a shear deformation rate, a phenomenon variously known as asymmetric or Hall viscosity, or Lorentz shear response. Just as the QH effect results from the coupling of Chern-Simons fields of the effective theory to the electromagnetic field, so also Hall viscosity is found to arise from coupling of these fields to the 'metric' of the quadratic kinetic energy. In this paper I derive new physical insights for Hall viscosity by using an extended semiclassical approach to compute the conductivity of a single Landau level in a nonuniform electric field. I demonstrate that the inhomogeneity of an applied electric field is a viable experimentally tunable parameter for altering the metric, and hence creating strain in the QH state. Using these results, I argue that Hall viscosity arises from the shearing of local cyclotron orbits by the applied nonuniform electric fields.