dc Josephson current through a quantum dot coupled with superconducting leads

The transport in a superconductor--quantum-dot--superconductor tunnel junction with a Coulomb repulsion in the dot was studied numerically. We calculated the dc Josephson current by noncrossing approximations varying the strength of the Coulomb repulsion. The critical current has a peak structure that is a function of the energy-level position in the dot, but the number of the peaks changes depending on the temperature, the strength of electron tunneling, and the Coulomb repulsion. It has been predicted previously that the junction behaves as a {π} junction for an infinitely strong Coulomb repulsion. We obtained the conditions for the strength of the Coulomb repulsion necessary for the {π} junction.