Rough surface effects on d-wave superconductors

We present a quasi-classical Green's function theory for the rough surface effects on d-wave BCS states. We reformulate and generalize the randomly rippled wall model of rough surfaces so that it can describe the surface scattering ranging from the specular limit to the diffusive limit. We give a formal solution of the quasi-classical Green's function in a semi-infinite geometry with arbitrarily rough surfaces. The formal 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 according to the surface roughness. The present analysis is relevant to tunneling spectroscopy of cuprate superconductors through the surfaces parallel to the c-axis.