Superheating fields of superconductors: Asymptotic analysis and numerical results

TL;DR

This paper combines analytical and numerical methods to study the superheating fields in type-I superconductors using Ginzburg-Landau theory, providing new asymptotic expansions and validating them with numerical results.

Contribution

It introduces a systematic asymptotic expansion for the superheating field in the small $ppa$ limit and compares it with numerical solutions, extending analysis to nonlocal electrodynamics.

Findings

Asymptotic solutions agree with numerical results for ppa<0.5

The method effectively handles boundary layers in inhomogeneous superconductivity

Numerical results for large ppa match recent asymptotic predictions

Abstract

The superheated Meissner state in type-I superconductors is studied both analytically and numerically within the framework of Ginzburg-Landau theory. Using the method of matched asymptotic expansions we have developed a systematic expansion for the solutions of the Ginzburg-Landau equations in the limit of small $\kappa$, and have determined the maximum superheating field $H_{\rm sh}$ for the existence of the metastable, superheated Meissner state as an expansion in powers of $\kappa^{1/2}$. Our numerical solutions of these equations agree quite well with the asymptotic solutions for $\kappa<0.5$. The same asymptotic methods are also used to study the stability of the solutions, as well as a modified version of the Ginzburg-Landau equations which incorporates nonlocal electrodynamics. Finally, we compare our numerical results for the superheating field for large-$\kappa$ against recent asymptotic results for large-$\kappa$, and again find a close agreement. Our results demonstrate the efficacy of the method of matched asymptotic expansions for dealing with problems in inhomogeneous superconductivity involving boundary layers.