Out-of-phase Andreev transports in a double-quantum-dot Cooper-pair splitter

We investigate the Andreev transports through a double-quantum-dot Cooper-pair splitter with an additional direct coupling between the dots. It is found that when finite magnetic flux is applied through this structure, its induced phase adjusts the local and crossed Andreev reflections in different manners. Moreover, in the presence of appropriate magnetic flux, the crossed Andreev reflection can be efficiently enhanced, accompanied by the suppression of the local Andreev reflection. Such a result exists in both the linear and nonlinear transport regions, even in the case of strong intradot Coulomb interaction. Therefore, such a work provides a promising scheme to enhance the splitting of the Cooper pair.