Critical Field of Thin Superconducting Shapes

Abstract

Considerations of the thermodynamics pertaining to the critical field of small superconducting samples of various shapes results in an explicit relation for the ratio of the critical field of small samples to that of bulk in terms of the magnetic moment. The magnetic moment has been calculated using Miller's modification of the Bardeen-Cooper-Schrieffer kernel which includes mean free path. The critical-field ratios of various shapes in decreasing order are sphere, cylinder in parallel field, cylinder in transverse field, and plate in parallel field. The findings are compatible with the fact that dislocations (cylinder like) may be the filaments responsible for hard superconductivity. Under certain conditions the filaments could be numerous and large enough for an appreciable fraction of the sample to appear superconducting in a specific heat measurement. The size of the filaments would also account for the lack of latent heat observed in hard superconductors. Because of the relative orientation of dislocations with respect to the applied field, not all dislocations will serve equally as filaments, thus explaining the current density vs critical-field curve and accounting for an anisotropic critical field when there is a preferred orientation of dislocations.