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 superconductors, 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 gaplike structure, zero bias conductance peak (ZBCP) and zero bias conductance dip. We show that two distinct mechanisms: (i) coherent Andreev reflection (CAR) in DN and (ii) formation of midgap Andreev bound state at the interface of d-wave superconductors, are responsible for ZBCP, their relative importance being dependent on the angle $\ensuremath{\alpha}$ between the interface normal and the crystal axis of d-wave superconductors. For $\ensuremath{\alpha}=0,$ 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 $\ensuremath{\alpha}$ from zero to $\ensuremath{\pi}/4,$ 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.