Orbital momentum of chiral superfluids and spectral asymmetry of edge states

TL;DR

This paper comments on prior work regarding how spectral flow affects the orbital angular momentum in chiral superfluids, confirming reductions for higher chirality and revealing new effects when parity is violated.

Contribution

It clarifies the impact of spectral flow on orbital angular momentum in chiral superfluids, especially highlighting effects of parity violation for p-wave superfluids.

Findings

Spectral flow reduces orbital angular momentum for higher chirality superfluids.

Parity violation causes reduction in angular momentum even for p-wave superfluids with |ν|=1.

Confirms previous results for |ν|>1 and extends understanding to parity-violating cases.

Abstract

This is comment to preprint arXiv:1409.7459 by Y. Tada, Wenxing Nie and M. Oshikawa "Orbital angular momentum and spectral flow in two dimensional chiral superfluids", where the effect of spectral flow along the edge states on the magnitude of the orbital angular momentum is discussed. The general conclusion of the preprint on the essential reduction of the angular momentum for the higher values of chirality, $|\nu|>1$, is confirmed. However, we show that if parity is violated, the reduction of the angular momentum takes place also for the $p$-wave superfluids with $|\nu|=1$.