Josephson effect in unconventional superconducting contacts

We calculate the dc Josephson current through an unconventional superconducting point contact with various pairing symmetries including s-wave, d-wave, and s+id states. We find that the phase dependence of the dc Josephson current through the contact at low temperatures exhibits a dramatical difference between the conventional s-wave and unconventional d-wave or s+id state. In particular, for the s-wave, the Josephson current is always finite for any value of the phase, while for the d-wave and s+id states, it shows singularity in certain phase values.