The spectral conductance of a proximity superconductor and the re-entrance effect

In a mesoscopic metal in proximity with a superconductor, the electronic conductance is enhanced in a very energy-sensitive way. In this paper, we discuss the spectral conductance of a proximity superconductor from both the theoretical and experimental point of view. The dependence of the spectral conductance on the phase-breaking length, gap of the superconductor and interface transparency is theoretically investigated. We present experimental data on the re-entrance of the normal-state conductance at very low temperature and bias voltage. A complete description of the experimental data needs taking into account heating of the reservoirs by the bias current. In addition, we show that the energy sensitivity of the proximity effect enables one to access the energy distribution of the conduction electrons inside a mesoscopic sample.