Quasi-Classical Boundary Conditions at Rough Surfaces on the Basis of the Thin Dirty Layer Model

Boundary conditions for the quasi-classical Green's function at rough surfaces are studied on the basis of the thin dirty layer model. We construct a formal solution of the quasi-classical Green's function in semi-infinite superconductors with rough surface which is simulated by a specular wall coated by a thin layer containing random impurities. Using the current conservation in the thin dirty layer, we propose a new boundary condition for the quasi-classical Green's function at rough surfaces, which is available to treat rough surface effects from the diffusive limit to the specular limit. It is shown that our boundary condition is equivalent to the Ovchinnikov boundary condition and the random S-matrix model in the diffusive limit.