# Multiply quantized vortices in fermionic superfluids: angular momentum, unpaired fermions, and spectral asymmetry

## TL;DR

This paper investigates how multiply quantized vortices affect the orbital angular momentum in fermionic superfluids, revealing significant reductions due to unpaired fermions and spectral flow effects, supported by analytical and numerical solutions.

## Contribution

It provides a detailed analysis of angular momentum reduction in multiply quantized vortices, highlighting the role of unpaired fermions and spectral asymmetry in the BCS regime.

## Key findings

- Angular momentum is reduced from the BEC regime value in the BCS regime.
- Unpaired fermions arise due to spectral flow along vortex states.
- Results are supported by analytical and numerical solutions of Bogoliubov-de-Gennes equations.

## Abstract

We compute the orbital angular momentum $L_z$ of an s-wave paired superfluid in the presence of an axisymmetric multiply quantized vortex. For vortices with winding number $|k| > 1$, we find that in the weak-pairing BCS regime $L_z$ is significantly reduced from its value $\hbar N k/2$ in the Bose-Einstein condensation (BEC) regime, where $N$ is the total number of fermions. This deviation results from the presence of unpaired fermions in the BCS ground state, which arise as a consequence of spectral flow along the vortex sub-gap states. We support our results analytically and numerically by solving the Bogoliubov-de-Gennes equations within the weak-pairing BCS regime.