Tomasch effect and superconducting proximity

Tunneling conductance measurements (dI/dV)(V) on thick and clean super-conducting films (S₁) backed by normal metals (M₂) show geometrical resonance effects, which have been associated with the variation (x) of the pair potential near the interface. We analyze both theoretically and experimentally the three factors involved in the resonance effect on S₁/M₁ sandwiches where one of the films is superconducting. The first factor, period, has already received considerable attention and is connected with the ratioV_F^*/d₁ of the renormalized Fermi velocity and the thicknessd₁ of the film S₁. We show that generally subharmonic effects, related to multiple interference effects, are expected. This result is demonstrated experimentally on Pb/M₂ sandwiches. The phase depends on the sign of (x), the detailed shape of its variation, and on the nature of the tunneling process. Unfortunately the interplay among these parameters is difficult to analyze, although directive tunneling is found to fit better with experiments than the generally assumed diffuse tunneling. The amplitude of the resonance should be proportional to the change of (x). The ambiguity in the experimental results is pointed out and an experiment that shows clearly the role of the superconducting proximity mechanisms is described where the proximity on several simultaneously prepared Pb/Al films is controlled by deposition of various third upper layers. The theoretical discussion is an extension of the Ishii matrix formulation, itself based on an application of the Andreev scattering process.