ROUGH-SURFACE EFFECTS ON D-WAVE SUPERCONDUCTORS

We present a quasi-classical Green's function theory for the rough sur face effects on d-wave BCS states. We reformulate and generalize the r andomly rippled wall model of rough surfaces so that it can describe t he surface scattering ranging from the specular limit to the diffusive limit. We give a formal solution of the quasi-classical Green's funct ion in a semi-infinite geometry with arbitrarily rough surfaces. The f ormal solution satisfies the boundary condition. We apply this method to the two-dimensional d(x2-y2) and d(xy) states and show how the self -consistent order parameter and the surface density of states change a ccording to the surface roughness. The present analysis is relevant to tunneling spectroscopy of cuprate superconductors through the surface s parallel to the c-axis.