Interaction Between Two Single Superconducting Vortices Inside A Superconducting Hollow Cylindrical domain

TL;DR

This paper develops a new approximation for the interaction between two superconducting vortices within a finite-sized hollow cylindrical domain, accounting for their internal magnetic profiles and boundary effects, using Ginzburg-Landau theory.

Contribution

It introduces a novel method considering vortex size and boundary effects for vortex interaction analysis in superconductors, extending Abrikosov's classical approach.

Findings

Vortices repel each other at large separations.

Equilibrium vortex positions are stable due to free energy convexity.

Boundary effects significantly influence vortex interactions.

Abstract

Inspired by the seminal, ground-breaking work of Abrikosov in 1957, we developed a new approximation to the interaction between two widely separated superconducting vortices. In contrast with Abrikosov's, we take into account the finite size of the vortices and their internal magnetic profile. We consider the vortices to be embedded within a superconducting, infinitely long hollow cylinder, in order to simplify the symmetry and boundary conditions for the mathematical analysis. We study this system in the context of a magnetic Ginzburg-Landau functional theory, by solving for the magnetic field profile inside each vortex, as well as in the superconducting region, subject to physical boundary conditions inspired by the classical analogue of two mutually inducting coils. Under isothermal conditions, the effective force between these vortices is given by the gradient of the Helmholtz free energy constructed from the Ginzburg-Landau functional. From our results, we explicitly show that, in agreement with well established theoretical arguments and experiments, the interaction between widely separated vortices is repulsive in this context, and their equilibrium positions are constrained by the fluxoid's conservation. Moreover, we find that the equilibrium positions of the vortices centers are stable due to the convexity of the Helmholtz free energy profile. Remarkably, the effect of the boundaries of the region over the effective interaction between the vortices is important in the chosen geometric configuration.