Multiply Quantized Vortices in Fermionic Superfluids: Angular Momentum, Unpaired Fermions, and Spectral Asymmetry

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 a winding number vertical bar k vertical bar > 1, we find that in the weak-pairing BCS regime, L-z is significantly reduced from its value (h) over bar Nk/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 subgap states. We support our results analytically and numerically by solving the Bogoliubov-de Gennes equations within the weak-pairing BCS regime.