Coherent electron transport in superconducting-normal metallic films

We study the transport properties of a quasi-two-dimensional diffusive normal metal film attached to a superconductor. We demonstrate that the properties of such films can essentially differ from those of quasi-one-dimensional systems: In the presence of the proximity-induced superconductivity in a sufficiently wide film, its conductance may not only increase but also decrease with temperature. We develop a quantitative theory and discuss the physical nature of this effect. Our theory provides a natural explanation for recent experimental findings referred to as the "anomalous proximity effect."