Equilibrium simulations of 2D weak links in p-wave superfluids

TL;DR

This paper develops a 2D Ginzburg-Landau model for weak links in p-wave superfluids, analyzing symmetry, boundary conditions, and current-phase relations in superfluid 3He, providing detailed phase diagrams and numerical methods.

Contribution

It introduces a comprehensive numerical framework for studying weak links in p-wave superfluids, including various boundary conditions and phase combinations, with detailed phase diagrams.

Findings

Calculated current-phase relations for different weak link configurations.

Mapped critical currents and phase diagrams in zero magnetic field.

Analyzed symmetry properties and boundary conditions in superfluid 3He.

Abstract

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 (CPR's) 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.