Vortices in Two-Dimensional Chiral Superfluids

Abstract

We study the orbital angular momentum (OAM) $L_z$ of two-dimensional chiral $(p_x+ip_y)^{\nu}$-wave superfluids (SFs) in the presence of an axisymmetric multiply quantized vortex (MQV) with vorticity $k$ on a disk at zero temperature, in the framework of Bogoliubov-de Gennes (BdG) theory. Focusing on spectral asymmetry (or spectral flow), we find that $L_z=(k+\nu)N/2$ for any integer $\nu$ and $k$ in the Bose-Einstein Condensation (BEC) regime, where $N$ is the total number of fermions. While in the weak-pairing Bardeen-Cooper-Schrieffer (BCS) regime, only for chiral $p+ip$-wave SF with $k=\pm 1$, $L_z=(k+\nu)N/2$ still holds. For chiral SFs with $\nu\ge2$ or $|k|\ge2$ in the BCS regime, the OAM $L_z$ is remarkably reduced from its ``full" value in the BEC regime. However, the deviations differ in these two cases. For chiral SFs with $\nu\ge2$, $L_z$ is sharply suppressed in this ideal setting with a specular wall, while the suppression caused by the $|k| \ge 2$ vortex is moderate, which is core-size dependent. Furthermore, for $p+ip$-wave SF with $k=-1$, the total OAM $L_z$ is zero, but the distribution $L_z(r)$ is nontrivial compared with that of vortex-free $s$-wave SF, in which the total OAM is zero as well. For chiral SFs with $\nu\ge2$ and $|k|\ge2$, the effects of circulation due to vortex and chiral pairing can coexist, and hence depress the OAM simultaneously. These observations can be explained by spectral asymmetry and unpaired fermions in the ground state of the BdG Hamiltonian. We also investigate the spatial distribution of particle density, OAM, by solving the BdG equation.