Modification of the Blonder, Tinkham and Klapwijk theory of normal metal-superconductor point contact due to contact heterogeneity

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Abstract
A modification is proposed of the Blonder, Tinkham and Klapwijk (BTK) theory for heterogeneous normal metal-superconductor (N-S) point contact. Contact is heterogeneous when the normal state electronic dispersion relations in the left-hand and right-hand electrodes are different (in the original BTK theory dispersion relations in both electrodes are equal). For characterization of the dispersion relation difference the author uses the amplitude of reflection r(E) at the clear interface for electrons incoming from the normal metal electrode with energy EF+E when the 'superconductive' electrode is in the normal state. He calculates the amplitudes of ordinary and Andreev reflection at the N-S interface for electrons incoming from the normal metal electrode as functions of r(E). This enables him to obtain an expression for differential conductance of the point contact as a function of applied voltage and r(eV). For a suitable function r(eV) the calculated differential conductance decreases with increasing voltage in the low-voltage region (as is observed experimentally for some point contacts between normal metal-high-Tc superconductor) in contrast to the BTK theory which provides only non-decreasing dependences of differential conductance against voltage.