Zero-bias conductance peak in tunneling spectroscopy of hybrid superconductor junctions

A generalized method of image, incorporated with the nonequilibrium Keldysh-Green’s function formalism, is employed to investigate the tunneling spectroscopy of hybrid systems in the configuration of planar junction. In particular, tunneling spectroscopies of several hybrid systems that exhibit zero-bias conductance peaks (ZBCP’s) are examined. The well-known metal–$d$-wave superconductor (ND) junction is examined in detail. Both the evolution of the ZBCP versus doping and the splitting of the ZBCP in magnetic fields are computed in the framework of the slave-boson mean field theory. Further extension of our method to analyze other states shows that states with particle-hole pairing, such as d-density wave and graphene sheet, are all equivalent to a simple one-dimensional model, which at the same time also describes the polyacetylene. We provide the criteria for the emergence of ZBCP. In particular, broken reflection symmetry at the microscopic level is shown to be a necessary condition for ZBCP to occur.