Crossed Andreev reflection in a zigzag graphene nanoribbon-superconductor junction

We investigate the crossed Andreev reflection (CAR) in a zigzag graphene nanoribbon/superconductor/nanoribbon junction. It is shown that when the zigzag chain number of the ribbon is even and only the zero-energy mode is involved in transport either the elastic cotunneling or the local Andreev reflection could be entirely suppressed by using a gate voltage whereas a sizable CAR is achieved. When one of the ribbon leads is magnetized not only is the CAR exclusive, but also the spin state of the CAR transmission is nonlocally controllable. The physical origin is the peculiar valley selection rule in the even zigzag graphene nanoribbon. The ideal Cooper-pair splitting in the proposed device holds for all applied bias in the superconducting energy gap.