Rough interface effects on normal-superconducting proximity-contact systems

Abstract

A quasiclassical theory of interface roughness effects on normal-superconducting proximity-contact system is developed within the weak-coupling theory. In the present theory, the rough interface is characterized by two parameters, interface reflection coefficient R and interface roughness parameter W that specifies the specularity of the interface. By use of this model, we can discuss any interface with roughness from good metallic contact interface to almost impenetrable one. We apply the formulation to systems including isotropic s-wave superconductor and two-dimensional ${d}_{{\mathrm{x}}^{2}\ensuremath{-}{\mathrm{y}}^{2}}$ superconductor to study the rough interface effects on the profile of the pair potential and the surface density of states. We also discuss the Andreev reflection. We show that the Andreev reflection from the ${d}_{{\mathrm{x}}^{2}\ensuremath{-}{\mathrm{y}}^{2}}$ superconductor is strongly affected by the interface roughness.