Properties of rough interfaces in superconductors with d-wave pairing

Theoretical model of a rough interface in a superconductor with d-wave symm etry of the order parameter is proposed. The surface roughness is introduce d by means of a surface layer with small electronic mean free path, The pro ximity effect between such a layer and a bulk d-wave superconductor is stud ied theoretically in the framework of the quasiclassical Eilenberger theory . It is shown that as a result of strong scattering in the interlayer the d -wave component of the order parameter near the interface is reduced while the s-wave component localized near the interface is generated. Angular and spatial structure of the pair potential and the electronic density of stat es near the interface is calculated. The interplay of the zero-energy (midg ap) and finite-energy bound states leads to peculiarities in the energy dep endence of the angle-averaged density of states. We argue that the model is relevant for the description of rough interfaces in high T-c superconducto rs. In the framework of the present approach we calculate the Josephson cri tical current for several types of junctions with rough interfaces.