Theory of the Andreev reflection and the density of states in proximity contact normal-superconducting infinite double-layer

Proximity contact N-S double-layer with infinite layer widths is studied in the clean limit. The finite reflection at the interface is taken into account. Starting from a recent theory of finite width double-layer by Ashida et al., the authors obtain explicit expressions for the quasi-classical Green's function which already satisfy the boundary condition and include no exploding terms at infinities. The self-consistent pair potentials are obtained numerically with sufficient accuracy. The Andreev reflection at the N-S interface is discussed on the basis of the self-consistent pair potential. It is shown that there exists a resonance state in a potential valley formed between the depressed pair potential and the partially reflecting interface, which leads to a peak of the Andreev reflection coefficient with the height unity slightly below the bulk superconductor energy gap. They also find general relationship between the Andreev reflection coefficient and the local density of states of the superconductor just at the interface.