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 sin(2ϕ)-like current-phase
relation, whereas for contacts on the scale of the coherence length or smaller
the usual sinϕ-like behavior is observed. Our results compare well with
recent experimental observations.Comment: 10 pages, 12 figures; accepted for publication in Phys. Rev.