Theory of charge transport in diffusive normal metal / unconventional singlet superconductor contacts

Abstract

We analyze the transport properties of contacts between unconventional superconductor and normal diffusive metal in the framework of the extended circuit theory. We obtain a general boundary condition for the Keldysh-Nambu Green's functions at the interface that is valid for arbitrary transparencies of the interface. This allows us to investigate the voltage-dependent conductance (conductance spectrum) of a diffusive normal metal (DN)/ unconventional singlet superconductor junction in both ballistic and diffusive cases. For d-wave superconductor, we calculate conductance spectra numerically for different orientations of the junctions, resistances, Thouless energies in DN, and transparencies of the interface. We demonstrate that conductance spectra exhibit a variety of features including a $V$-shaped gap-like structure, zero bias conductance peak (ZBCP) and zero bias conductance dip (ZBCD). We show that two distinct mechanisms: (i) coherent Andreev reflection (CAR) in DN and (ii) formation of midgap Andreev bound state (MABS) at the interface of d-wave superconductors, are responsible for ZBCP, their relative importance being dependent on the angle $α$ between the interface normal and the crystal axis of d-wave superconductors. For $α=0$, the ZBCP is due to CAR in the junctions of low transparency with small Thouless energies, this is similar to the case of diffusive normal metal / insulator /s-wave superconductor junctions. With increase of $α$ from zero to $π/4$, the MABS contribution to ZBCP becomes more prominent and the effect of CAR is gradually suppressed. Such complex spectral features shall be observable in conductance spectra of realistic high-$T_c$ junctions at very low temperature.