Josephson Effect in Unconventional Superconductors

In this letter we present a simple relation, that allows one to predict the Josephson current between two unconventional superconductors with arbitrary band-structure and pairing symmetry. We illustrate this relation with examples of s-wave and d-wave junctions and show a detailed numerical comparison with the phenomenological Sigrist and Rice relation commonly used to interpret tunneling experiments between d-wave superconductors. Our relation automatically accounts for `mid-gap states' that occur in d-wave superconductors and clearly shows how these states lead to a temperature-sensitive contribution to the Josephson current for certain orientations of the junction. This relation should be useful in exploring the effects of disordered junctions, multiple atomic orbitals and complicated order parameters.