Torsional Response and Dissipationless Viscosity in Topological Insulators

TL;DR

This paper explores the visco-elastic response of topological insulators, revealing a dissipationless viscosity linked to torsional deformations and implications for dislocations and surface phenomena.

Contribution

It demonstrates the existence of a dissipationless viscosity in 2D Chern insulators and extends the concept to 3D topological insulators, connecting geometry and electronic response.

Findings

Dissipationless viscosity in 2D Chern insulators.

Dislocations carry momentum density.

Surface quantum Hall viscosity in 3D topological insulators.

Abstract

We consider the visco-elastic response of the electronic degrees of freedom in 2D and 3D topological insulators (TI). Our primary focus is on the 2D Chern insulator which exhibits a bulk dissipationless viscosity analogous to the quantum Hall viscosity predicted in integer and fractional quantum Hall states. We show that the dissipationless viscosity is the response of a TI to torsional deformations of the underlying lattice geometry. The visco-elastic response also indicates that crystal dislocations in Chern insulators will carry momentum density. We briefly discuss generalizations to 3D which imply that time-reversal invariant TI's will exhibit a quantum Hall viscosity on their surfaces.