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Brief introduction to Superconductivity and Mesoscopic Physics

It is well known that it took 46 years after the discovery of the phenomenon of superconductivity by Kamerlingh Onnes in Leiden, in 1911, before a convincing theory was developed. That BCS theory, named after the inventers of it, Bardeen, Cooper and Schrieffer, was a microscopic theory, and it explained how electrons could form Cooper pairs by a weak attractive interaction, mediated by the electron-phonon interaction. After 1957 a lot of activity was employed, which has led to an impressive description. While the original BCS theory dealt with homogeneous bulk superconductors only, methods were developed to describe the proximity effect, which shows up as soon as a superconductor has an interface with another metal. By now one believes, that the superconductors known up to 1987 are well understood.

Nevertheless, even in that field a huge new activity was developed in attempts to understand small samples. This latter rather recent activity has led to a complete new field of research, called Mesoscopic Physics. This field has been inspired by the miniaturization achieved in the chips industry, and it has as the object of study all types of effects in all types of small samples, including samples with an S/N interface. A phenomenon known already from the beginning of the sixties of the previous century, namely Andreev reflection, is now omnipresent in the theories developed in Mesoscopic Physics.

We study layered systems with sheets of superconducting metal (S) and of normal metal (N). Our special interest is in boundary effects. These effects can be impressive in clean SNS-type junctions, particularly if the transverse size of such a junction is critical. The transverse size determines the number of transverse modes which can propagate. At a critical width a new mode is going to contribute. The effects come from the fact, that initially such a new mode has almost all its energy in the transverse direction, so that the motion in the longuitudinal direction is very slow.