Vortex-vortex interaction in thin superconducting films

The properties of vortices in superconducting thin films are revisited. The interaction between two Pearl vortices in an infinite film is approximated at all distances by a simple expression. The interaction of a vortex with a regular lattice of real or image vortices is given. The two spring constants are calculated that one vortex in the vortex lattice feels when the surrounding vortices are rigidly pinned or are free. The modification of these London results by the finite size of real films is obtained. In finite films, the interaction force between two vortices is not a central force but depends on both vortex positions, not only on their distance. At the film edges the interaction energy is zero and the interaction force is peaked. Even far from the edges the vortex interaction considerably deviates from the Pearl result and is always smaller than it.