On Abrikosov Lattice Solutions of the Ginzburg-Landau Equations

TL;DR

This paper proves the existence of Abrikosov vortex lattice solutions in the Ginzburg-Landau equations, including cases with multiple flux quanta, and refines previous proofs for single flux quantum lattices.

Contribution

It establishes the existence of vortex lattice solutions with multiple flux quanta and improves the proof techniques for single flux quantum cases.

Findings

Existence of vortex lattice solutions with multiple flux quanta.

Streamlined proof for Abrikosov vortex lattices with a single flux quantum.

Clarified key details missing in earlier proofs.

Abstract

We prove existence of Abrikosov vortex lattice solutions of the Ginzburg-Landau equations of superconductivity, with multiple magnetic flux quanta per a fundamental cell. We also revisit the existence proof for the Abrikosov vortex lattices, streamlining some arguments and providing some essential details missing in earlier proofs for a single magnetic flux quantum per a fundamental cell.