Disordered Josephson junctions of d-wave superconductors

We study the Josephson effect between weakly coupled d-wave superconductors within the quasiclassical theory, in particular, the influence of interface roughness on the current-phase relation and the critical current of mirror junctions and 45degrees asymmetric junctions. For mirror junctions the temperature dependence of the critical current is nonmonotonic in the limit of low roughness, but monotonic for very rough interfaces. For 45degrees asymmetric junctions with a linear dimension much larger than the superconducting coherence length we find a sin(2Phi)-like current-phase relation, whereas for contacts on the scale of the coherence length or smaller the usual sin Phi-like behavior is observed. Our results compare well with recent experimental observations.