The Motion of Superconducting Vortices in Thin Films of Varying Thickness

The interaction of superconducting vortices with superconductor/vacuum interfaces is considered. A vortex is first shown to intersect such an interface normally. Various thin-film models are then formulated, corresponding to different parameter regimes. A local analysis of a vortex is performed, and a law of motion for each vortex deduced. This law of motion implies that the vortex will move to the locally thinnest part of the film, and is consistent with the vortex moving under the curvature induced by being forced to intersect the boundaries of the film normally.