Low-temperature transport through a quantum dot between two superconductor leads

We consider a quantum dot coupled to two BCS superconductors with same gap energies $\Delta$. The transport properties are investigated by means of infinite-$U$ noncrossing approximation. In equilibrium density of states, Kondo effect shows up as two sharp peaks around the gap bounds. Application of a finite voltage bias leads these peaks to split, leaving suppressed peaks near the edges of energy gap of each lead. The clearest signatures of the Kondo effect in transport are three peaks in the nonlinear differential conductance: one around zero bias, another two at biases $\pm 2\Delta$. This result is consistent with recent experiment. We also predict that with decreasing temperature, the differential conductances at biases $\pm 2\Delta$ anomalously increase, while the linear conductance descends.