Phase Transition to a Time-Reversal Symmetry-Breaking State in d-Wave Superconducting Films with Rough Surfaces

The normal-superconducting phase transition in d-wave superconducting films is discussed with a focus on the effect of diffuse surface scattering. A specularity parameter S characterizing the boundary condition is introduced for systematic analysis of the surface effect. When S = 1 (the specular limit), the film can exhibit a novel superconductivity that spontaneously breaks time-reversal symmetry, as was shown by Vorontsov [Phys. Rev. Lett. 102, 177001 (2009)]. We find that this superconducting phase is suppressed as the degree of surface roughness increases, i.e., as the specularity S decreases. In particular, it is completely suppressed when S = 0 (the diffusive limit). Those results are explained from the viewpoint of surface odd-frequency pairing.