Rough Surface Effect on a Broken Time-reversal Pairing State in d-wave Superconducting Films

We investigate the effect of a rough surface on the normal-superconducting phase transition in d-wave superconducting films on the basis of the quasiclassical theory of superconductivity with a boundary condition that allows us to treat the surface scattering from the specular limit to the diffusive limit. When the surfaces are specular, the film can exhibit a novel superconductivity that breaks continuous translational symmetry along the surface as well as time reversal symmetry. When the surfaces are rough, this superconducting phase is suppressed by diffusive surface scattering.