Effective theory of chiral two-dimensional superfluids

TL;DR

The paper develops a leading-order and next-to-leading-order effective theory for a two-dimensional chiral $p_x+ip_y$ fermionic superfluid at zero temperature that is invariant under nonrelativistic diffeomorphisms. By coupling the Goldstone mode to a spin connection through a covariant derivative with chirality $s=\pm n/2$, it derives a parity-violating edge current and a Hall viscosity, and it computes the $U(1)_N$ current and the stress tensor along with their linear responses to electromagnetic and gravitational sources. A key result is the explicit relation between the Hall conductivity and Hall viscosity at leading order, and a vortex solution showing chirality first appears in a $1/r^4$ tail of the density depletion, with distinct behavior near weak- and strong-coupling regimes. These findings offer concrete, testable predictions for ultracold, spin-polarized fermions in two dimensions and illuminate how topological edge modes and parity-violating transport emerge in a systematically improvable hydrodynamic framework.

Abstract

We construct, to leading orders in the momentum expansion, an effective theory of a chiral $p_x + ip_y$ two-dimensional fermionic superfluid at zero temperature that is consistent with nonrelativistic general coordinate invariance. This theory naturally incorporates the parity and time reversal violating effects such as the Hall viscosity and the edge current. The particle number current and stress tensor are computed and their linear response to electromagnetic and gravitational sources is calculated. We also consider an isolated vortex in a chiral superfluid and identify the leading chirality effect in the density depletion profile.