Hall Viscosity Revealed via Density Response

TL;DR

This paper establishes a universal relation between Hall viscosity and density response in Galilean-invariant quantum Hall systems, enabling experimental measurement of Hall viscosity through susceptibility analysis.

Contribution

It derives a general relation linking Hall viscosity to density response, verified in quantum Hall systems and applicable broadly due to minimal assumptions.

Findings

Derived a relation between Hall viscosity and susceptibility.

Verified the relation in integer quantum Hall systems.

Proposed a method to measure Hall viscosity via density response.

Abstract

Quantum Hall systems are recently shown to possess a quantity sensitive to the spatial geometry and topology of the system, dubbed the Hall viscosity $\eta_H$. Despite the extensive theoretical discussions on its properties, the question of how to measure $\eta_H$ still poses a challenge. In this paper, we present a general relation between Hall viscosity and susceptibility for systems with Galilean invariance. Thus, it allows for determination of $\eta_H$ through density response signatures. The relations are verified in the integer quantum Hall example, and is further illustrated in an effective hydrodynamic analysis. Since the derivation is based on Kubo formulae and assumes no more than conservation laws and translational symmetry, the results are applicable to a wide range of systems.