Edge current and orbital angular momentum of chiral superfluids revisited

TL;DR

This paper revisits the edge current and orbital angular momentum in two-dimensional chiral superfluids, clarifying the Angular Momentum Paradox through semiclassical theory and numerical analysis across BCS and BEC regimes.

Contribution

It provides a unified semiclassical framework for understanding edge currents and OAM in chiral superfluids, resolving discrepancies in previous predictions.

Findings

OAM vanishes for non-p-wave chiral superfluids like d+id.

OAM density is localized at the boundary in both BCS and BEC phases.

The relative OAM of Cooper pairs adds to the total OAM in both phases.

Abstract

Cooper pairs in chiral superfluids carry quantized units of relative orbital angular momentum (OAM). Various predictions of the intrinsic OAM density or the macroscopic OAM of a two-dimensional chiral superfluid differ by several orders of magnitude, which constitute the so-called Angular Momentum Paradox. Following several previous studies, we substantiate the semiclassical Bogoliubov-de Gennes theory of the single-particle edge current and OAM in two-dimensional chiral superfluids in the BCS limit. The analysis provides a simple intuitive understanding for the vanishing of OAM for a non-p-wave chiral superfluid (such as $d+id$) confined in a rigid potential. When generalized to anisotropic chiral superconductors and three-dimensional chiral superfluids, the theory similarly returns an accurate description. We also present a detailed numerical study of the chiral phases in the BEC limit. Our study suggests that, in both BCS and BEC phases the relative OAM of the individual Cooper pairs contribute to the total OAM additively, and that in both phases the corresponding macroscopic OAM density distribution is localized at the boundary.