One-Dimensional Solutions of the Ginzburg-Landau Equations for Thin Superconducting Films

Solutions to the Ginzburg-Landau equations have been obtained for plane films in a longitudinal magnetic field. Only symmetrical one-dimensional solutions were generated, but without restrictive assumptions on the Ginzburg-Landau parameter $\kappa$ or the effective wave function $\psi$. The critical field has been calculated from these solutions as a function of $\kappa$ and the ratio of film thickness $d$ to penetration depth. Curves are given to show how the behavior of films at the critical field depends on the various parameters involved. The computer solutions join smoothly onto those derived in the limit $\psi \to 0$. The limit of validity of these computer solutions in the light of the vortex solutions of Abrikosov and the asymmetrical solutions of Saint-James and de Gennes is determined, and a "phase diagram" in the ($\kappa , d$) plane for all types of solutions is suggested.