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The magnetic penetration depth influenced by the proximity to the surface

The effect of smooth inhomogeneities near a superconductor boundary on the magnetic penetration depth $λ$ is studied with emphasis on the proximity-induced spatial dependence of the Cooper pair amplitude. The influence of surface pair breaking or pair formation on $λ$ is described within the Ginzburg-Landau theory, with no model assumptions, for both strongly type-II and strongly type-I homogeneous superconductors. Generic values of $λ$, which can differ greatly from the London penetration depth, are identified and demonstrated to be induced by large-scale inhomogeneities, when superconductivity is strongly suppressed on the surface.