(Giant) Vortex - (anti) vortex interaction in bulk superconductors: The Ginzburg-Landau theory

TL;DR

This paper numerically investigates vortex interactions in bulk superconductors using Ginzburg-Landau theory, providing new empirical formulas for interaction potentials across various regimes and vortex configurations.

Contribution

It introduces new empirical expressions for vortex interaction potentials in bulk superconductors, valid over the entire interaction range, based on numerical solutions of Ginzburg-Landau equations.

Findings

Numerical interaction potentials agree with analytical large-distance expressions.

New empirical formulas fit the full interaction range.

Interaction potentials differ between type-I and type-II superconductors.

Abstract

The vortex-vortex interaction potential in bulk superconductors is calculated within the Ginzburg-Landau (GL) theory and is obtained from a numerical solution of a set of two coupled non-linear GL differential equations for the vector potential and the superconducting order parameter, where the merger of vortices into a giant vortex is allowed. Further, the interaction potentials between a vortex and a giant vortex and between a vortex and an antivortex are obtained for both type-I and type-II superconductors. Our numerical results agree asymptotically with the analytical expressions for large inter-vortex separations which are available in the literature. We propose new empirical expressions valid over the full interaction range, which are fitted to our numerical data for different values of the GL parameter.