On Abrikosov Lattice Solutions of the Ginzburg-Landau Equations

TL;DR

This paper refines previous proofs demonstrating the existence of Abrikosov vortex lattices in the Ginzburg-Landau model, confirming the triangular lattice as the lowest energy configuration, with streamlined proofs and stronger results.

Contribution

It provides a stronger version of earlier results on Abrikosov lattices, confirming the triangular lattice as the energy-minimizing configuration with streamlined proofs.

Findings

Triangular lattice minimizes energy per cell

Existence of Abrikosov vortex lattices is established

Proofs are streamlined and strengthened

Abstract

Building on earlier work, we have given in our paper in Contemporary Mathematics 535, 195-213, 2011 (referred here as [TS]) a proof of existence of Abrikosov vortex lattices in the Ginzburg-Landau model of superconductivity and have shown that the triangular lattice gives the lowest energy per lattice cell. After [TS] was published, we realized that it proves a stronger result than was stated there. This result is recorded in the present paper. The proofs remain the same as in [TS], apart from some streamlining.