Numerical simulation of vortex arrays in thin superconducting films

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Abstract
Numerical simulations of the evolution of the order parameter and the vector potential in thin type-II superconducting films are reported. The theoretical framework is provided by the well-known time-dependent Ginzburg-Landau (TDGL) equations coupled with the Maxwell equations. The external field is applied parallel to the surfaces. Several maxima appear in the magnetization curve, a phenomenon that has been observed in experiments and up to now only explained using a London approach. It is proved that these maxima are indeed predicted by the full TDGL approach, and are not necessarily linked with structural changes in the vortex lattice. A mechanism for the appearance of magnetization maxima in finite samples is identified, based on the behavior of surface supercurrents.