Transverse size effects in the local density of states and supercurrent in clean mesoscopic SNS junctions

Abstract

A Green's function formalism is used to study the local density of states (LDOS) and supercurrent in a clean mesoscopic superconductor – normal metal – superconductor (SNS) junction. In the Andreev approximation, it is found that the number of Andreev bound states in the normal – metallic part becomes infinite if the transverse width is tuned such that the quasiparticles have zero longitudinal velocity. The LDOS in the superconducting part exhibits peaks whose energy locations are the same as in the Andreev peaks in the normal – metallic part. A steep rise of the supercurrent is also observed for transverse width tuned such that the longitudinal kinetic energy of the quasiparticles is 0.5Δ. Comparison of the current with and without Andreev approximation confirms the effect of the 0.001 probability of normal reflection.