Torsional Response and Dissipationless Viscosity in Topological Insulators

We consider the viscoelastic response of the electronic degrees of freedom in 2D and 3D topological insulators (TI’s). 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 viscoelastic 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.

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 (nonuniform) 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.