Edge current and orbital angular momentum of chiral superfluids revisited

Cooper pairs in chiral superfluids carry quantized units of orbital angular momentum (OAM). Various predictions of the total OAM of a chiral superfluid differ by several orders of magnitude. These constitute the so-called angular momentum paradox. Following several previous studies, we substantiate the semiclassical Bogoliubov-de Gennes theory of the 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 in a non-p-wave chiral superfluid (such as d+id) confined by a rigid potential. When generalized to anisotropic chiral superconductors and three-dimensional (3D) chiral superfluids, the theory similarly returns an accurate description. We will also present a numerical study of the chiral phases in the BEC limit, where the OAM density is found to vanish in the bulk and arise purely from the boundary effects.