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

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).