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Correlated electron transport through double quantum dots coupled to normal and superconducting leads

We study Andreev transport through double quantum dots connected in series normal and superconducting (SC) leads, using the numerical renormalization group. The ground state of this system shows a crossover between a local Cooper-pairing singlet state and a Kondo singlet state, which is caused by the competition between the Coulomb interaction and the SC proximity. We show that the ground-state properties reflect this crossover especially for small values of the inter-dot coupling $t$, while in the opposite case, for large $t$, another singlet with an inter-dot character becomes dominant. We find that the conductance for the local SC singlet state has a peak with the unitary-limit value $4e^2/h$. In contrast, the Andreev reflection is suppressed in the Kondo regime by the Coulomb interaction. Furthermore, the conductance has two successive peaks in the transient region of the crossover. It is further elucidated that the gate voltage gives a different variation into the crossover. Specifically, as the energy level of the dot that is coupled to the normal lead varies, the Kondo screening cloud is deformed to a long-range singlet bond.