Evaluation of Some Nonlocal Theories for a Thin Superconducting Film

Abstract

The magnetic susceptibility of a thin superconducting film has been evaluated as a function of film thickness on the basis of nonlocal theories proposed by Pippard, Bardeen, and Schafroth and Blatt. Two limiting boundary conditions corresponding to specular reflection and random scattering of the electrons at the surface have been applied, and the susceptibility appears to be insensitive to the boundary condition. Deviations from the London theory occur for a thickness less than twice the penetration depth and give a susceptibility smaller than the London value. Largest deviation is found for the Pippard theory and least for the Schafroth-Blatt version. The experimental data of Lock are inconclusive with regard to the validity of the nonlocal theories.