Angular Momentum of Multiply Quantised Vortices in Fermionic Superfluids

We study vortex textures in weakly coupled $s$-wave fermionic superfuids at zero temperature. In the BCS limit, we find that for an axisymmetric multiply quantised vortex with vorticity $k>1$ the angular momentum is significantly reduced from the value $L_z = \hbar kN/2$, which naturally arises in the strongly-coupled BEC regime. This phenomenon is rooted in the presence of unpaired fermions in the BCS ground state of a superfluid with an axisymmetric multiply quantised vortex. The predicted deviation of the angular momentum can be understood from the spectral flow along the vortex sub-gap states.