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 45° 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 45° asymmetric junctions with a linear dimension much larger than the superconducting coherence length we find a sin(2φ)-like current-phase relation, whereas for contacts on the scale of the coherence length or smaller the usual sin φ-like behavior is observed. Our results compare well with recent experimental observations.