Critical Fields of Thin Superconducting Films. I. Thickness Effects

A theoretical model is presented with which the critical magnetic fields of thin superconducting films can be calculated from any theory of superconductivity for which the kernel of the current-vector potential relationship is known. The model is worked out in detail for the nonlocal theory of Pippard with specular boundary conditions, and the critical field is shown to be a function of film thickness and the nonlocal parameters $\ensuremath{\xi}$ and ${\ensuremath{\xi}}_{0}{{\ensuremath{\lambda}}_{L}}^{2}$. The results are compared to critical-field data for pure indium films and are found to predict very well the observed thickness dependence of critical field. On the basis of reasonable assumptions, ${\ensuremath{\xi}}_{0}$ and ${\ensuremath{\lambda}}_{L}(0)$ are calculated from the indium critical field data to be 2600\ifmmode\pm\else\textpm\fi{}400 \AA{} and 350\ifmmode\pm\else\textpm\fi{}30 \AA{}, respectively.

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