Transport signatures of Hall viscosity

TL;DR

This paper proposes a method to measure Hall viscosity in two-dimensional quantum systems through non-local resistance experiments, linking transport signatures to topological properties.

Contribution

It introduces a novel experimental approach to detect Hall viscosity via charge transport measurements, which was previously lacking an accessible signature.

Findings

Hall viscosity influences charge transport at finite wavelengths.

Electrochemical potential profiles near contacts reveal Hall viscosity values.

Method enables experimental distinction of quantum Hall states with different topological orders.

Abstract

Hall viscosity is a non-dissipative response function describing momentum transport in two-dimensional systems with broken parity. It is quantized in the quantum Hall regime, and contains information about the topological order of the quantum Hall state. Hall viscosity can distinguish different quantum Hall states with identical Hall conductances, but different topological order. To date, an experimentally accessible signature of Hall viscosity is lacking. We exploit the fact that Hall viscosity contributes to charge transport at finite wavelengths, and can therefore be extracted from non-local resistance measurements in inhomogeneous charge flows. We explain how to determine the Hall viscosity from such a transport experiment. In particular, we show that the profile of the electrochemical potential close to contacts where current is injected is sensitive to the value of the Hall viscosity.