Paramagnetic excited vortex states in superconductors

TL;DR

This paper introduces a method to analyze paramagnetic vortex states in superconductors, which are residual vortex configurations with lower energy than the normal state, using conformal mapping techniques.

Contribution

It develops a general approach to calculate the Gibbs free energy of excited vortex states in superconductors for arbitrary geometries and vortex configurations.

Findings

Paramagnetic vortex states can exist in superconductors after external fields are removed.

A conformal mapping method is formulated to analyze these states.

The approach applies to any number of vortices and geometries.

Abstract

We consider excited vortex states, which are vortex states left inside a superconductor once the external applied magnetic field is switched off and whose energy is lower than of the normal state. We show that this state is paramagnetic and develop here a general method to obtain its Gibbs free energy through conformal mapping. The solution for any number of vortices in any cross section geometry can be read off from the Schwarz - Christoffel mapping. The method is based on the first order equations used by A. Abrikosov to discover vortices.