Fluxoid Quantization and Critical Fields in Small Superconducting Samples

Abstract

This paper presents a theoretical treatment of the critical fields of thin superconducting films and related microgeometries. This treatment is based on the Ginzburg-Landau theory and the quantization of the fluxoid. A symmetric superconducting surface state is found which contains fluxoid vortices. This surface state may exist in type-II films in parallel fields or in small samples of thin films in normal fields. For a sample which is infinite in one transverse dimension a critical-field dependence is found which is similar to that previously found theoretically by Saint-James and de Gennes. The model is extended to treat samples which are limited in both transverse dimensions. Excellent qualitative and semiquantitative agreement is found with the experiments of Parks, Mochel, and Surgent which determine the critical field in a microscopic superconducting bridge.