Quasiparticle bound states and low-temperature peaks of the conductance of NIS junctionsin d-wave superconductors

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Abstract
Contributions of quasiparticle states, bound to the boundary of anisotropically paired superconductors, to the density of states and to the conductance of normal-metal–insulator–superconduction (NIS) junctions are studied both analytically and numerically. For smooth surfaces and real order parameters, we find some general results for the bound-state energies. In particular, we show that under fairly general conditions quasiparticle states with nonzero energies exist for momentum directions within a narrow region around the surface normal. The energy dispersion of the bound states always has an extremum for the direction along the normal. Along with the zero-bias anomaly due to midgap states, we find, for quasi-two-dimensional materials, additional low-temperature peaks in the conductance of NIS junctions for voltages determined by the extrema of the bound-state energies. The influence of interface roughness on the conductance is investigated within the framework of Ovchinnikov's model. We show that nonzero-bias peaks at low temperatures may give information on the order parameter in the bulk, even though it is suppressed at the surface.