Theory of charge transport in diffusive normal metal / conventional superconductor point contacts

TL;DR

This paper develops a comprehensive theory for tunneling conductance in diffusive normal metal / superconductor junctions, accounting for various parameters and revealing complex voltage-dependent behaviors including ZBCP and ZBCD.

Contribution

It introduces a generalized boundary condition that unifies ballistic and diffusive theories, enabling detailed analysis of conductance in DN/I/S junctions with varying parameters.

Findings

Proximity effect can enhance or reduce tunneling conductance depending on barrier transparency.

Various voltage bias dependencies are demonstrated, including U-shaped gaps, ZBCP, and ZBCD.

The theory unifies previous models and explains diverse experimental observations.

Abstract

Tunneling conductance in diffusive normal metal / insulator / s-wave superconductor (DN/I/S) junctions is calculated for various situations by changing the magnitudes of the resistance and Thouless energy in DN and the transparency of the insulating barrier. The generalized boundary condition introduced by Yu. Nazarov [Superlattices and Microstructures 25 1221 (1999)] is applied, where the ballistic theory by Blonder Tinkham and Klapwijk (BTK) and the diffusive theory by Volkov Zaitsev and Klapwijk based on the boundary condition of Kupriyanov and Lukichev (KL) are naturally reproduced. It is shown that the proximity effect can enhance (reduce) the tunneling conductance for junctions with a low (high) transparency. A wide variety of dependencies of tunneling conductance on voltage bias is demonstrated including a $U$-shaped gap like structure, a zero bias conductance peak (ZBCP) and a zero bias conductance dip (ZBCD).