Vortices in Ginzburg-Landau billiards

TL;DR

This paper analyzes vortex solutions in the Ginzburg-Landau equations for 2D superconductors, deriving energy expressions, exploring boundary effects, and applying findings to experimental magnetization data.

Contribution

It provides a closed-form energy expression for vortices in Ginzburg-Landau superconductors and interprets boundary effects on vortex number selection.

Findings

Derived a closed expression for superconductor energy.

Identified boundary influence on vortex number.

Applied theory to experimental magnetization data.

Abstract

We present an analysis of the Ginzburg-Landau equations for the description of a two-dimensional superconductor in a bounded domain. Using the properties of a special integrability point of these equations which allows vortex solutions, we obtain a closed expression for the energy of the superconductor. The role of the boundary of the system is to provide a selection mechanism for the number of vortices. A geometrical interpretation of these results is presented and they are applied to the analysis of the magnetization recently measured on small superconducting disks. Problems related to the interaction and nucleation of vortices are discussed.