Superheating fields of superconductors: Asymptotic analysis and numerical results

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 \ensuremath{\kappa}, and have determined the maximum superheating field ${\mathit{H}}_{\mathrm{sh}}$ for the existence of the metastable, superheated Meissner state as an expansion in powers of ${\mathrm{\ensuremath{\kappa}}}^{1/2}$. Our numerical solutions of these equations agree quite well with the asymptotic solutions for \ensuremath{\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 \ensuremath{\kappa} against recent asymptotic results for large \ensuremath{\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. \textcopyright{} 1996 The American Physical Society.