Density of states in layered short-coherence-length superconducting structures

We have performed a theoretical study of superconductor–normal-metal layered structures using a microscopic method. Results are given for the single-particle density of states, the order parameter, and the energy gap as a function of the coherence length, temperature, pair-breaking impurity mean-free path, and depth or probe range. The results are found to be in good agreement with those obtained from tunneling experiments on a Au-${\mathrm{NbSe}}_2$ bilayer and on the high-temperature superconductor ${\mathrm{Nd}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Ce}}_{\mathit{x}}$ ${\mathrm{CuO}}_{4\mathrm{-}\mathit{y}}$. The spatial variation of all quantities has been taken into account self-consistently. The roles of all relevant lengths and their experimental implications are discussed and emphasis is put on the case of short-coherence-length materials.