Transport Signatures of the Hall Viscosity

Hall viscosity is a nondissipative 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 nonlocal 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.