Abrikosov Vortex Lattices at Weak Magnetic Fields

TL;DR

This paper proves the existence of Abrikosov vortex lattice solutions in two-dimensional Ginzburg-Landau equations near the first critical magnetic field, advancing understanding of vortex patterns in superconductors.

Contribution

It establishes the existence of vortex lattice solutions for magnetic fields slightly above the first critical field, a new result in the mathematical theory of superconductivity.

Findings

Existence of vortex lattice solutions near the first critical magnetic field.

Mathematical proof of vortex patterns in 2D Ginzburg-Landau equations.

Contribution to the theoretical understanding of superconducting vortices.

Abstract

We prove existence of Abrikosov vortex lattice solutions of the Ginzburg-Landau equations in two dimensions, for magnetic fields larger than but close to the first critical magnetic field.