Noise cross-correlation and Cooper pair splitting efficiency in multi-teminal superconductor junctions

We analyze the non-local shot noise in a multi-terminal junction formed by two Normal metal leads connected to one superconductor. Using the cross Fano factor and the shot noise, we calculate the efficiency of the Cooper pair splitting. The method is applied to d-wave and iron based superconductors. We determine that the contributions to the noise cross-correlation are due to crossed Andreev reflections (CAR), elastic cotunneling, quasiparticles transmission and local Andreev reflections. In the tunneling limit, the CAR contribute positively to the noise cross-correlation whereas the other processes contribute negatively. Depending on the pair potential symmetry, the CAR are the dominant processes, giving as a result a high efficiency for Cooper pair split. We propose the use of the Fano factor to test the efficiency of a Cooper pair splitter device.