THEORY OF ROUGH-SURFACE EFFECTS ON THE ANISOTROPIC BCS STATES

We present a Green's function theory of the rough surface effects on t he anisotropic BCS states using the formulation developed in the rando mly rippled wall model. It is shown that the randomly rippled wall for mulation is general enough to treat rough surface effects from the spe cular limit to the diffusive limit. We propose a statistical wall conf iguration such that gives the diffusive limit in the normal state. Wit hin the weak coupling theory, we give a formal solution of the quasi-c lassical Green's function in a slab geometry and in a semi-infinite ge ometry with arbitrarily rough surfaces. The formal solution already sa tisfies the boundary condition. In the diffusive limit, the present th eory correctly recovers the linearized gap equation obtained by Kjaldm an et al. for the p-wave state in a slab geometry.