Ballistic graphene Josephson junctions from the short to the long regime

We investigate the critical current, $I_C$, of ballistic Josephson junctions made of encapsulated graphene/boron-nitride heterostructures. We observe a crossover from the short to the long junction regimes as the length of the device increases. In long ballistic junctions, $I_S$ is found to scale as $\propto \exp(-k_bT/\delta E)$. The extracted energies $\delta E$ are independent of the carrier density and proportional to the level spacing of the ballistic cavity, as determined from Fabry-Perot oscillations of the junction normal resistance. As $T\rightarrow 0$ the critical current of a long (or short) junction saturates at a level determined by the product of $\delta E$ (or $\Delta$) and the number of the junction's transversal modes.