Vortex structure in p-wave superconductors

TL;DR

This paper investigates vortex structures in p-wave superconductors using a coupled Ginzburg-Landau model, establishing existence of energy-minimizing solutions and analyzing their qualitative properties.

Contribution

It introduces a coupled PDE framework for p-wave vortices, proving existence of solutions and exploring their asymptotic behavior, which differs from classical Ginzburg-Landau vortices.

Findings

Existence of energy-minimizing solutions in bounded domains.

Qualitative analysis of solutions' asymptotic behavior.

Differences from classical Ginzburg-Landau vortex properties.

Abstract

We study vortices in p-wave superconductors in a Ginzburg-Landau setting. The state of the superconductor is described by a pair of complex wave functions, and the p-wave symmetric energy functional couples these in both the kinetic (gradient) and potential energy terms, giving rise to systems of partial differential equations which are nonlinear and coupled in their second derivative terms. We prove the existence of energy minimizing solutions in bounded domains $\Omega\subset\mathbb R^2$, and consider the existence and qualitative properties (such as the asymptotic behavior) of equivariant solutions defined in all of $\mathbb R^2$. The coupling of the equations at highest order changes the nature of the solutions, and many of the usual properties of classical Ginzburg-Landau vortices either do not hold for the p-wave solutions or are not immediately evident.