Modification of the Blonder, Tinkham and Klapwijk expressions for Andreev and normal reflection coefficients due to a finite-thickness barrier at the normal metal-superconductor interface

Abstract

Amplitudes of normal and Andreev reflections for a normal metal-arbitrary potential barrier-superconductor system are derived with explicitly expressed contributions due to the superconductivity and due to the barrier at the interface. General results are illustrated by the example of a rectangular potential barrier. For somevalues of barrier parameters the results are expressively different from the ones predicted by the standard Blonder, Tinkham and Klapwijk model with a delta-functional barrier at the interface.