Disordered Josephson Junctions of d-Wave Superconductors

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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 non-monotonic 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 (2ϕ)-like current-phase relation, whereas for contacts on the scale of the coherence length or smaller the usual ϕ-like behavior is observed. Our results compare well with recent experimental observations.