Existence of Bulk Vortices in Superconductors with Strong Magnetic Fields

TL;DR

This paper rigorously proves the existence of isolated bulk vortices in extreme type-II superconductors under strong magnetic fields using Ginzburg-Landau theory, advancing understanding of vortex behavior in high-field regimes.

Contribution

It provides the first rigorous mathematical proof of isolated vortices in the bulk of superconductors at fields near the second critical magnetic field.

Findings

Existence of isolated vortices in high magnetic fields.

Precise vortex distribution estimates.

Vortices with non-trivial winding numbers.

Abstract

We study the vortex formation in extreme type-II superconductors immersed in strong magnetic fields in the framework of the the Ginzburg-Landau theory. We focus on the regime where superconductivity survives in the bulk of the material but the magnetic field penetrates the sample, i.e., for applied field much larger than the first critical one, but below the transition to surface superconductivity. Through a two-scale vortex construction, we obtain precise estimates for the vortex distribution and prove the existence of isolated defects with non-trivial winding numbers. In this respect, our work provides the first rigorous mathematical proof of the existence of isolated vortices for fields comparable to the second critical one.