Mass flows and angular momentum density for $p_x+ip_y$ paired fermions in a harmonic trap

TL;DR

This paper models a 2D $p_x+ip_y$ superfluid, calculating mass flow and angular momentum density via numerical methods, confirming the Ishikawa-Mermin-Muzikar formula at zero temperature.

Contribution

It introduces a simple 2D model for $p_x+ip_y$ superfluids that allows direct numerical calculation of mass flow and angular momentum density.

Findings

Mass flow closely follows the Ishikawa-Mermin-Muzikar formula at zero temperature.

Numerical diagonalization effectively computes mass flow in the model.

The model simplifies understanding of angular momentum in $p_x+ip_y$ superfluids.

Abstract

We present a simple two-dimensional model of a $p_x+ip_y$ superfluid in which the mass flow that gives rise to the intrinsic angular momentum is easily calculated by numerical diagonalization of the Bogoliubov-de Gennes operator. We find that, at zero temperature and for constant director $\bf l$, the mass flow closely follows the Ishikawa-Mermin-Muzikar formula ${\bf j}_{\rm mass}= \frac 12 {\rm curl} (\rho \hbar {\bf l}/2)$.