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 κ, and have determined the maximum superheating field H sh for the existence of the metastable, superheated Meissner state as an expansion in powers of κ 1/2 . Our numerical solutions of these equations agree quite well with the asymptotic solutions for κ < 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-κ against recent asymptotic results for large-κ, 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.

Using the time-dependent Ginzburg-Landau equations we study the propagation of planar fronts in superconductors, which would appear after a quench to zero applied magnetic field. Our numerical solutions show that the fronts propagate at a unique speed which is controlled by the amount of magnetic flux trapped in the front. For small flux the speed can be determined from the linear marginal stability hypothesis, while for large flux the speed may be calculated using matched asymptotic expansions. At a special point the order parameter and vector potential are dual, leading to an exact solution which is used as the starting point for a perturbative analysis.Comment: 4 pages, 2 figures; submitted to Phys. Rev. Letter

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