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

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 ${\bf j}_{\rm mass}= \frac 12 {\rm curl} (\rho \hbar {\bf l}/2)$.