Effect of interdot Coulomb interaction on the Josephson phase transition in a double-quantum-dot junction

We pay attention to the supercurrent in one Josephson junction embedded by coupled double quantum dots, by taking the interdot Coulomb interaction into account. It is found that this interaction can change the Josephson phase transition initiated by the intradot Coulomb repulsion, and its effect is strongly dependent on the structural symmetry of the Josephson junction. In comparison with the parallel-coupled and T-shaped double-dot cases, the influence of interdot Coulomb interaction is relatively weak in the serially-coupled double-dot geometry. All the supercurrent properties are discussed by analyzing the interplay between the Cooper-pair correlation and the Kondo effect in different geometries. We believe that this work can be helpful in understanding the co-influence of intradot and interdot Coulomb interactions on the Josephson phase transition.