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Using a numerical tight-binding approach based on the Chebyshev-Bogoliubov-deGennes method we describe Josephson junctions made of multilayer graphenecontacted by top superconducting gates. Both Bernal (ABA) and rhombohedral(ABC) stacking are considered and we find that the type of stacking has astrong effect on the proximity effect and the supercurrent flow. For both casesthe pair amplitude shows a polarization between dimer and non-dimer atoms,being more pronounced for rhombohedral stacking. Even though the proximityeffect in non-dimer sites is enhanced when compared to single layer graphene,we find that the supercurrent is suppressed. The spatial distribution of thesupercurrent shows that for Bernal stacking the current flows only in thetop-most layers while for rhombohedral stacking the current flows throughoutthe whole structure.

Superconducting current and proximity effect in ABA and ABC multilayer graphene Josephson junctions