Torsional Response and Dissipationless Viscosity in Topological Insulators

TL;DR

The viscoelastic response of the electronic degrees of freedom in 2D and 3D topological insulators (TI's) is considered and it is shown that the dissipationless viscosity is the response of a TI to torsional deformations of the underlying lattice geometry.

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.

Figures (1)

• Figure 1: (a) Chern insulator deformed by a dislocation -antidislocation pair, separated in the $y$-direction. For each dislocation, the momentum-density is in the direction of the Burgers vector. (b) Chern insulator on a cylinder with a (non-uniform) dislocation threading the cylinder. Local displacements are shown by red arrows. This gives rise to a momentum-current response along the cylinder which carries a momentum component parallel to the Burgers vector of the threaded dislocation, i.e., parallel to the red arrows.