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We investigate the Josephson effect in a bilayer graphene flake contacted bytwo monolayer sheet deposited by superconducting electrodes. It is found thatwhen the electrodes are attached to the different layers of the bilayer, theJosephson current is in a $\pi$ state when the bilayer region is undoped and inthe absence of vertical bias. Applying doping or bias to the junction reveals$\pi-0$ transitions which can be controlled by varying the temperature and thejunction length. The supercurrent reversal here is very different from theferromagnetic Josephson junctions where the spin degree of freedom plays thekey role. We argue that the scattering processes accompanied by layer andsublattice index change give rise to the scattering phases which their effectvaries with doping and the bias. Such scattering phases are responsible for the$\pi-0$ transitions. On the other hand if both of the electrodes are coupled tothe same layer of the flake or the flake has AA stacking instead of common AB,the junction will be always in $0$ state since layer or sublattice index is notchanged.

Supercurrent reversal in Josephson junctions based on bilayer graphene flakes