Imbalanced superfluid state in an annular disk

Abstract

The imbalanced superfluid state of spin-1/2 fermions with s-wave pairing is numerically studied by solving the Bogoliubov–de Gennesequation at zero temperature in an annular disk geometry with narrow radial width. Twodistinct types of systems are considered. The first case may be relevant to heavy fermionsuperconductors, where magnetic field causes spin imbalance via Zeeman interactionand the system is studied in a grand canonical ensemble. As the magnetic fieldincreases, the system is transformed from the uniform superfluid state to theFulde–Ferrell–Larkin–Ovchinnikov state, and finally to the spin polarized normal state.The second case may be relevant to cold fermionic systems, where the number offermions of each species is fixed as in a canonical ensemble. In this case, the groundstate depends on the pairing strength. For weak pairing, the order parameterexhibits a periodic domain wall lattice pattern with a localized spin distribution atlow spin imbalance, and a sinusoidally modulated pattern with extended spindistribution at high spin imbalance. For strong pairing, the phase separationbetween the superfluid state and polarized normal state is found to be preferable,while the increase of spin imbalance simply changes the ratio between them.