Abstract
In nano-structured superconductors, it is important to consider a discreteness of energy levels instead of continuous energy levels due to the quantum confinement effect. This discreteness causes an appearance of many peaks in a density of state (DOS). In this paper, the effect of the discreetness of energy level or the effect of the quantum confinement on the DOS in superconducting systems with superconductor / normal metal (S/N) interfaces are focused. In particular, in nano-sized finite systems, a local density of state (LDOS) becomes strongly spatial dependent because of non-uniform spatial distributions of a gap energy and a pair amplitude. We investigate the pair amplitude and the LDOS by solving the Bogoliubov-de Gennes equations self-consistently. The proximity effect leads to a penetration of the pair amplitude into the normal metal region. Then, the pair amplitude in the normal metal decays non-monotonously because of the effect of the nano-sized finite system. On the other hand, the spatial-averaged LDOS plots as a function of the energy have many peaks in both superconductor and normal metal regions. Also, a contribution of the normal metal to the superconductor causes an appearance of peaks of the LDOS at the energy below the gap energy. In the SNS junction, when width of the normal metal increases, these peaks at the energy below the gap energy appear clearly.
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