Transport through a single Anderson impurity coupled to one normal and two superconducting leads

We study the interplay between the Kondo and Andreev-Josephson effects in a quantum dot coupled to one normal and two superconducting (SC) leads. In the large gap limit, the low-energy states of this system can be described exactly by a local Fermi liquid for the interacting Bogoliubov particles. The phase shift and the renormalized parameters for the Bogoliubov particles vary depending on the Josephson phase ϕ between the two SC leads. We explore the precise features of a crossover that occurs between the Kondo singlet and local Cooper-pairing states as f varies, using the numerical renormalization group approach.