Enhanced nonlocal Andreev reflection in F|S|F graphene spin-valve

• The crossed Andreev reflection (CAR) is studied in graphene ferromagnetic (F)- superconducting (S)- ferromagnetic spin-valve.
• In anti parallel configuration of two half metallic Fs, direct Andreev reflection and electron cotunneling are suppressed.
• It reaches the maximum probability in thickness of S that is comparable to the superconducting coherence length.
• The probability for p-doped graphene allows appreciable CAR probability in parallel configuration too.

In this paper crossed Andreev reflection (CAR) conductance is calculated in graphene-based Ferromagnetic-Superconductor-Ferromagnetic heterostructure. In this spin-valve system, the ferromagnetic semi-infinite layers act as leads. The leads are assumed to be half-metallic, i.e. the respective shift of the two spin sub-bands at each lead is such that the electronic states of just one spin sub-band are present near the Fermi level. In this graphene-based system, as in the corresponding metallic structures, if the leads are in anti-parallel configuration, direct Andreev reflection (AR) and electron cotunneling(CT) are weak while crossed Andreev reflection is considerable. The CAR reaches the maximum probability amplitude for thickness of the superconducting layer that is comparable to the superconducting coherence length. The behavior of the system at parallel configuration of the leads, contradicts with metallic FSF structures, so that an appreciable amount of CAR probability is obtained. This is provided in graphene by the combination of CAR and spin-dependent Klein tunneling through p-n barrier between different spin sub-bands of the two leads. In the case that the Fermi energy of the first lead is in Dirac point the result is the enhanced CAR due to blocking CT channels in both parallel and anti parallel configurations. The resulting nonlocal conductance oscillates with L exhibiting a π-phase shift between the two configurations.