Nielsen-Olesen vortices for large Ginzburg-Landau parameter

TL;DR

This paper analyzes Nielsen-Olesen vortices in the Ginzburg-Landau theory for large parameters, deriving their energy asymptotics and gauge field behavior using analytic and numerical methods.

Contribution

It provides the first detailed asymptotic analysis of vortex solutions and their energies in the large Ginzburg-Landau parameter regime.

Findings

Vortex energy scales as $( ext{pi} n^2 /2) ext{log}\lambda$ for large $\lambda$

Gauge field limit expressed via modified Bessel function $K_1$

Leading asymptotic terms of solutions are explicitly given

Abstract

Using analytic and numerical techniques Nielsen-Olesen vortices, which in the context of Ginzburg-Landau theory are known as Abrikosov vortices of type-II superconductors, are studied for large Ginzburg-Landau parameter $\lambda$. We show that their energy is equal to $(\pi n^2 /2)\log\lambda$ to leading order, where $n$ is the winding number of the vortex, and find that the limit of the gauge field can be expressed in terms of the modified Bessel function $K_1$. The leading terms of the asymptotic expansion of the solution are given, and the different contributions to the energy are analyzed.