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We report a theoretical study on the phase transition between superconductingstates with and without spontaneous surface current. The phase transition takesplace due to the formation of surface Andreev bound states in unconventionalsuperconductors. Based on the quasiclassical theory of superconductivity, weexamine the influence of atomic-scale surface roughness on the surface phasetransition temperature $T_s$. To describe the surface effect, the boundarycondition for the quasiclassical Green's function is parameterized in terms ofspecularity (the specular reflection probability in the normal state at theFermi level). This boundary condition allows systematic study of the surfaceeffect ranging from the specular limit to the diffuse limit. We show thatdiffuse quasiparticle scattering at a rough surface causes substantialreduction of $T_s$ in the d-wave pairing state of high-$T_c$ cupratesuperconductors. We also consider a p-wave pairing state in which Andreev boundstates similar to those in the d-wave state are generated. In contrast to thed-wave case, $T_s$ in the p-wave state is insensitive to the specularity. Thisis because the Andreev bound states in the p-wave superconductor are robustagainst diffuse scattering, as implied from symmetry consideration forodd-frequency Cooper pairs induced at the surface; the p-wave state hasodd-frequency pairs with s-wave symmetry, while the d-wave state does not.

physical review. b./physical review. b

Influence of diffuse surface scattering on the stability of  superconducting phases with spontaneous surface current generated by Andreev  bound states