Influence of surface roughness on subdominant pairing in d-wave superconductors

We study a d-wave superconductor with dominant $d_{x^2-y^2}$-wave order parameter and subdominant pairing in either the $s$- or the $d_{xy}$-wave channel near a surface. In particular we analyze the influence of surface roughness on the mixed order parameter which may break the time-reversal symmetry. We find that the subdominant component is suppressed by the roughness independent of its pairing symmetry; for very rough surfaces the subdominant component may even vanish completely. Additionally we discuss a possible real-valued admixture which counteracts the suppression of the $d_{x^2-y^2}$-wave order parameter at the surface.