Size effects and characteristic lengths in superconducting films and interfaces

We examine geometric and finite-size effects in supeconductors, using a purely microscopic method. The case where the coherence length ξ0 is short and phenomenological methods cannot be used is emphasized. We focus on the single-particle density of states, the energy gap, and the order parameter, and obtain results as a function of temperature, coherence length, system size, distance to the boundary, and pair-breaking impurity mean free path. We discuss the roles of all of the relevant lengths and the experimental implications of our results, in particular, how data from surface probes can yield information on bulk properties.