Nonlocal thermoelectricity in a Cooper-pair splitter

We investigate the nonlocal thermoelectric transport in a Cooper-pair splitter based on a double-quantum-dot-superconductor three-terminal hybrid structure. We find that the nonlocal coupling between the superconductor and the quantum dots gives rise to nonlocal thermoelectric effects which originate from the nonlocal particle-hole breaking of the system. We show that Cooper-pair splitting induces the generation of a thermocurrent in the superconducting lead without any transfer of charge between the two normal-metal leads. Conversely, we show that a nonlocal heat exchange between the normal leads is mediated by nonlocal Andreev reflection. We discuss the influence of finite Coulomb interaction and study under which conditions nonlocal power generation becomes possible, and when the Cooper-pair splitter can be employed as a cooling device.