'University of the Philippines School of Economics'
Abstract
Intro:In clean layered structure of normal metal andsuperconductor, Andreev-bound states are formed inthe normal metallic part through multiple Andreevreflections (Andreev, 1964 & 1967) of the electron andhole waves. In the Andreev approximation (AA)(Andreev, 1964 & 1967), the incident electron towardsa normal metal-superconductor (NS) interface will bereflected as a hole. Exact analysis, however, shows asmall amplitude of a normally reflected electron (Sipr& Gyorffy, 1996). In most studies (Larkin & Yu, 1975),Andreev-bound states are described using thequasiclassical description, which can be shown to beequivalent to AA (Ashida et al., 1982). Interestingly,Andreev approximation works remarkably well(Blaauboer et al., 1996). In this paper, we want toinvestigate the reliability of AA by varying the transversedimensions (dimensions perpendicular to the flow ofcurrent) of a mesoscopic superconductor-normal metalsuperconductor (SNS) sample (Bagwell, 1999). In mostsystems considered so far (Tanaka & Tsukada, 1991),the transverse dimensions which the breakdown of theAndreev approximation can hardly show up areconsidered infinite
