Nonminimal solutions to the Ginzburg-Landau equations on surfaces

TL;DR

This paper demonstrates the existence of new, nonminimal solutions to the Ginzburg-Landau equations on closed surfaces with nonzero magnetic flux, using topological methods in a nonconstructive approach.

Contribution

It provides the first examples of such solutions on nontrivial line bundles, expanding understanding of the solution space in Ginzburg-Landau theory.

Findings

Existence of nonminimal, irreducible solutions on closed surfaces.

Solutions are unstable.

Method applies to all coupling constants.

Abstract

We prove the existence of novel, nonminimal and irreducible solutions to the (self-dual) Ginzburg-Landau equations on closed surfaces. To our knowledge these are the first such examples on nontrivial line bundles, that is, with nonzero total magnetic flux. Our method works with the 2-dimensional, critically coupled Ginzburg-Landau theory and uses the topology of the moduli space. The method is nonconstructive, but works for all values of the remaining coupling constant. We also prove the instability of these solutions.