Hall and spin Hall viscosity ratio in 2d topological insulators

TL;DR

This paper introduces a new ratio of Hall viscosity to particle density in 2D topological insulators, linking topological responses to quantum Hall states and exploring dissipationless viscosity in quantum spin Hall systems.

Contribution

It proposes the Hall viscosity to particle density ratio as a novel topological quantity and extends the concept to time reversal invariant quantum spin Hall systems.

Findings

The ratio corresponds to the filling fraction in quantum Hall states.

It establishes a connection between viscosity and topological invariants.

Dissipationless viscosity is related to spin currents in quantum spin Hall systems.

Abstract

We study responses to metric perturbation in topological insulator models. In this paper we introduce a novel quantity, Hall viscosity to particle density ratio, which is analogous to the viscosity to entropy ratio suggested by AdS/CFT correspondence. This quantity corresponds to the filling fraction which characterizes the quantum Hall states, and hence it could be discussed in Haldane's zero-field quantum Hall system. We also consider dissipationless viscosity in the time reversal invariant quantum spin Hall system, which is related to a spin current.