Study of the Josephson supercurrent through nanoscopic superconducting-quantum dot tunnel junction

The present work deals with the theoretical analysis of the Josephson supercurrent through a quantum dot sandwiched between superconducting leads having s-wave symmetry of the superconducting order parameter. Such a junction is called superconducting-quantum dot (S–QD–S) junction. For this purpose, we have considered a renormalized Anderson model that includes the single-particle coupling of the superconducting leads with the quantum dots level and an attractive BCS-type effective interaction in superconducting leads responsible for s-wave pairing. We employed the Greenʹs function technique to obtain superconducting order parameter within the BCS framework and Ambegaoker Baratoff formalism to analyze the Josephson current through such S–QD–S junction. It has been pointed out that Josephson supercurrent through such a junction is dominated by the attractive pairing interaction in the leads, energy of the level on the dot with respect to Fermi energy and also on the coupling parameter of the two in an essential way. On the basis of numerical analysis we have compared the theoretical results of Josephson supercurrent with the recent transport experiment performed on such superconducting-quantum dot junctions and existing theoretical analysis.