Ballistic graphene Josephson junctions from the short to the long regime

We explore the critical current ($I_C$) temperature scaling of ballistic Josephson junctions. Using encapsulated graphene/boron-nitride heterostructure devices, we vary device length from the short to the long junction regime. We extract the carrier-density-independent energy $\delta$E by calculating the ballistic cavity level spacing through the Fabry-Perot oscillations of the normal resistance. In the long and intermediate junction regimes, we find $I_C$ scales as exp(-$k_B$T/ $\delta$E) at higher temperatures. For short junctions, we find strong agreement with theoretically predicted $I_C$ behavior. In the zero temperature limit, $I_C$ of a long (short) junction saturates at a magnitude determined only by the product of $\delta$E ($\Delta$) and the number of transversal modes in the junction.