MAGNETIC SUSCEPTIBILITY OF A THIN SUPERCONDUCTING FILM

The weak-field magnetic susceptibility of a thin superconducting film is calculated with a microscopic theory based on the work of Bardeen, Cooper, and Schrieffer. The finite sample size is taken into account by forming "Cooper pairs" from one-electron states whose wave functions vanish at the film boundary. Although the excitation spectrum of the superconductor remains essentially unchanged by this discrete quantization, the weak-field magnetic susceptibility is found to have a considerably lower value than previous theoretical estimates.