Three and Four-Body Intervortex Forces in the Ginzburg-Landau Models of Single- and Multicomponent Superconductivity

TL;DR

This study systematically investigates non-pairwise vortex interactions in Ginzburg-Landau superconductors, revealing diverse three-body force behaviors across different superconductor types through high-precision numerical methods.

Contribution

It provides the first detailed numerical analysis of three- and four-body vortex interactions in single- and multicomponent superconductors, highlighting their range and nature.

Findings

Three-body interactions are short-range repulsive and long-range attractive in type-1 superconductors.

In the critical {ppa} case, three-body interactions are negligible.

Four-body forces are less significant than three-body forces.

Abstract

A systematic numerical study of non-pairwise vortex interaction forces in the Ginzburg-Landau model for single- and multicomponent superconductivity is presented. The interactions are obtained by highly accurate numerical free energy minimization. In particular a three-body interaction is defined as the difference between the total interaction and sum of pairwise interactions in a system of three vortices and such interactions are studied for single and two-component type-1, type-2, and type-1.5 superconductors. In the investigated regimes, the three-body interaction is found to be short-range repulsive but long-range attractive in the type-1 case, zero in the critical {\kappa} (Bogomoln'y) case, attractive in the type-2 case and repulsive in the type-1.5 case. Some systems of four vortices are also studied and results indicate that four-body forces are of substantially less significance than the three-body interactions.