Orbital Angular Momentum and Spectral Flow in Two Dimensional Chiral Superfluids

Abstract

The orbital angular momentum in a chiral superfluid has posed a paradox for several decades. For example, for the $p+ip$-wave superfluid of $N$ fermions, the total orbital angular momentum should be $N/2$ if all the fermions form Cooper pairs. On the other hand, it appears to be substantially suppressed from $N/2$, considering that only the fermions near the Fermi surface would be affected by the pairing interaction. To resolve the long-standing question, we studied chiral superfluids in a two-dimensional circular well, in terms of a conserved charge and spectral flows. We find that the total orbital angular momentum takes the full value $N/2$ in the chiral $p+ip$-wave superfluid, while it is strongly suppressed in higher-order ($d+id$ etc.) chiral superfluids. This surprising difference is elucidated in terms of edge states.