Josephson Current through a Quantum Dot Connected with Superconducting Leads

In this study, we consider the Josephson current in a system composed of a superconductor/quantum dot/superconductor junction. In the model, the Coulomb interaction in the quantum dot is taken into consideration, and the Lacroix approximation is applied to study the electron correlation. We derive Green's function of the quantum dot by applying the Lacroix truncation. Although the Andreev bound state does not occur in our formulations, the pi-junction occurs for a restricted parameter range. On comparing the Kondo temperature with that estimated by another method, it is found that our Lacroix approximation does not capture well the Kondo physics in the superconductor/quantum dot/superconductor junction.