Cooper pair splitting controlled by a temperature gradient

Electrons in two different normal metallic electrodes attached to a sufficiently thin superconducting island may become entangled due to the effect of Cooper pair splitting. This phenomenon is of fundamental importance and may also have serious implications for developing quantum communication technologies. One way to identify Cooper pair splitting is to analyze long-range cross correlations of fluctuating currents in three-terminal hybrid normal-superconducting-normal nanostructures. Here, we theoretically investigate non-trivial behavior of cross-correlated non-local shot noise in the presence of a temperature gradient. We suggest that applying a temperature gradient may serve as an extra tool to control the phenomenon of Cooper pair splitting.