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 studi ed in the clean limit. The finite reflection at the interface is taken into account. Starting from a recent theory of finite width double-la yer by Ashida et al., we obtain explicit expressions for the quasi-cla ssical Green's function which already satisfy the boundary condition a nd include no exploding terms at infinities. The self-consistent pair potentials are obtained numerically with sufficient accuracy. The Andr eev reflection at the N-S interface is discussed on the basis of the s elf-consistent pair potential. It is shown that there exists a resonan ce state in a potential valley formed between the depressed pair poten tial and the partially reflecting interface, which leads to a peak of the Andreev reflection coefficient with the height unity slightly belo w the bulk superconductor energy gap. We also find general relationshi p between the Andreev reflection coefficient and the local density of states of the superconductor just at the interface.