Critical Magnetic Field of a Thin Film of Superconductor

Abstract

A theory of the critical field of a thin superconductive film is given based on the assumption that this is the field in which the normal state becomes unstable to the formation of Cooper pairs. Only the case where $l$, the mean free path for the electrons is much less than $d$, the thickness of the film, and where the coherence length is less than $\frac{d^2}{l}$ is discussed. The resulting field for temperatures near $T_c$ agrees with that predicted by the Ginzburg-Landau theory. At lower temperatures, the field is greater than that predicted by an earlier theory of Maki and appears to be in better agreement with the experimental results.