Competition between the Yu-Shiba-Rusinov and Kondo screening in double quantum dot based Cooper pair splitters

The Andreev transport properties of double quantum dot based Cooper pair splitters with one superconducting and two normal leads are studied theoretically in the Kondo regime. The influence of the Yu-Shiba-Rusinov screening resulting from superconducting pairing correlations on the local density of states, Andreev transmission coefficient, and Cooper pair splitting efficiency is thoroughly analyzed. It is shown that finite superconducting pairing potential quickly suppresses the SU(2) Kondo effect, which can however reemerge for relatively large values of coupling to superconductor. In the SU(4) Kondo regime, a crossover from the SU(4) to the SU(2) Kondo state is found as the coupling to superconductor is enhanced.