Hall viscosity in the A-phase of superfluid $^3$He

TL;DR

This paper develops an effective field theory for the A-phase of superfluid helium-3, revealing a universal Hall viscosity expression that is significantly larger than in the B-phase, suggesting feasible experimental detection.

Contribution

The authors construct a detailed effective field theory incorporating nonrelativistic diffeomorphism symmetry, leading to a universal and measurable Hall viscosity in the A-phase.

Findings

Hall viscosity in the A-phase is five orders of magnitude larger than in the B-phase.

Universal expression for Hall viscosity derived from the effective field theory.

Potential for experimental observation via elliptic polarization of sound waves.

Abstract

We construct the effective field theory for the A-phase of superfluid $^3$He up to the next-to-leading order in the derivative expansion. To this end, we gauge the internal global symmetries of the theory on the curved space by introducing the background gauge fields and spatial metric so as to expose a hidden local symmetry known as the nonrelativistic diffeomorphism. The nonrelativistic diffeomorphism is particularly useful to yield an additional constraint on the effective field theory and reveal a universal expression for the Hall viscosity in the A-phase. We find it five orders of magnitude larger than that in the B-phase under a magnetic field so that its experimental observation is more feasible by measuring the induced elliptic polarization of sound waves.