Equilibrium Simulations of 2D Weak Links in p-wave Superfluids

A two-dimensional Ginzburg-Landau theory of weak links in a p-wave superfluid is presented. First we consider the symmetry properties of the energy functionals, and their relation to the conserved supercurrents which play an essential role in the weak link problem. In numerical studies, we use the A and B phases of superfluid 3He. The phases on the two sides of the weak link can be chosen separately, and very general soft degrees of freedom may be imposed as boundary conditions. We study all four inequivalent combinations of A and B which are possible for a hole in a planar wall, including weak links with a pinned A-B interface. In all cases, some illustrative current-phase relations (CPRʹs) are calculated and the critical currents are mapped. Phase diagrams covering the relevant phase space in zero magnetic field are constructed. The numerical methods are also described in some detail.