Imbalanced superfluid state in an annular disk

TL;DR

This study numerically explores imbalanced superfluid states in an annular disk, revealing how magnetic field and pairing strength influence superfluid phases, including FFLO states, phase separation, and spin polarization.

Contribution

It provides a detailed numerical analysis of imbalanced superfluid states in an annular geometry, considering both grand canonical and canonical ensembles, and identifies various phase behaviors.

Findings

Transition from uniform superfluid to FFLO and normal states with increasing magnetic field.

Periodic and sinusoidal order parameter patterns depending on pairing strength and spin imbalance.

Preference for phase separation between superfluid and polarized normal states at strong pairing.

Abstract

The imbalanced superfluid state of spin-1/2 fermions with s-wave pairing is numerically studied by solving the Bogoliubov-de-Gennes equation at zero temperature in an annular disk geometry with narrow radial width. Two distinct types of systems are considered. The first case may be relevant to heavy fermion superconductors, where magnetic field causes spin imbalance via Zeeman interaction and the system is studied in a grand canonical ensemble. As the magnetic field increases, the system is transformed from the uniform superfluid state to the Fulde-Ferrell-Larkin-Ovchinnikov state, and finally to the spin polarized normal state. The second case may be relevant to cold fermionic systems, where the numbers of fermions of each species are fixed as in a canonical ensemble. In this case, the groundstate depends on the pairing strength. For weak pairing, the order parameter exhibits a periodic domain wall lattice pattern with a localized spin distribution at low spin imbalance, and a sinusoidally modulated pattern with extended spin distribution at high spin imbalance. For strong pairing, the phase separation between superfluid state and polarized normal state is found to be more preferable, while the increase of spin imbalance simply changes the ratio between them.