The Influence of the Transverse Width on the Andreev Bound States and Self-Consistent Gap Function in Clean SNS System

R. E. S. Otadoy, A. Lodder


In clean layered structure of normal metal and superconductor, Andreev-bound states are formed in the normal metallic part through multiple Andreev reflections (Andreev, 1964 & 1967) of the electron and hole waves. In the Andreev approximation (AA) (Andreev, 1964 & 1967), the incident electron towards a normal metal-superconductor (NS) interface will be reflected as a hole. Exact analysis, however, shows a small amplitude of a normally reflected electron (Sipr & Gyorffy, 1996). In most studies (Larkin & Yu, 1975), Andreev-bound states are described using the quasiclassical description, which can be shown to be equivalent to AA (Ashida et al., 1982). Interestingly, Andreev approximation works remarkably well (Blaauboer et al., 1996). In this paper, we want to investigate the reliability of AA by varying the transverse dimensions (dimensions perpendicular to the flow of current) of a mesoscopic superconductor-normal metalsuperconductor (SNS) sample (Bagwell, 1999). In most systems considered so far (Tanaka & Tsukada, 1991), the transverse dimensions which the breakdown of the Andreev approximation can hardly show up are considered infinite.

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