Onset of surface superconductivity

Abstract

We examine the onset of superconductivity in the surface region of a metal. Surface effects are particularly important in systems with a short bulk coherence length ξ0. We show that, to the accuracy of the calculation, the surface transition temperature TcS equals the bulk transition temperature TcB if the electron-electron interaction is of the standard BCS form, i.e., a single attractive square well, extending up to some critical energy ω0 much smaller than the Fermi energy ɛF. If one takes into account, in addition, the repulsive part of the interaction extending beyond ω0 up to energies of order ɛF, then one may have TcS>TcB in certain cases, although, due to restrictions imposed on the parameter values by various physical conditions, the relative increase of Tc is very small, typically 10−3, at least in the weak coupling limit. However, we also find a considerable gap enhancement, of order 20%, near the surface which could be of interest for critical-current measurements. Therefore we suggest an experimental reexamination of systems with short ξ0, i.e., superconducting degenerate semiconductors and the new high-Tc oxides in confined geometries where the surface-to-volume ratio is non-negligible.

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