Vortices in superconducting films

The local magnetic flux density and electrical current density generated by a vortex in a superconducting film is calculated approximately using an extension of Pearl's method. The results apply to arbitrary ratios of the film thickness to the penetration depth and reduce to Pearl's thin-film and semi-infinite results in the appropriate limits. In addition, the vanishing of the order parameter on the vortex axis is accounted for by a simple model which removes the London-model divergences of the flux density and supercurrent density and leads to a physically correct description in the vortex core. The results are then applied to a calculation of the interaction energy of vortex-vortex and vortex-antivortex pairs