Fermi velocity dependent critical current in ballistic bilayer graphene Josephson junctions

We perform transport measurements on proximitized, ballistic, bilayer graphene Josephson junctions (BGJJs) in the intermediate to long junction regime. We measure the device's differential resistance as a function of bias current for different temperatures. Additionally, we take differential resistance maps at various gate voltages at the base temperature of 1.3 K. We extract the critical current I_C, which follows exp(-k_B T/δE), where δE = ℏν_F / 2πL (an energy scale related to the Andreev Bound State level spacing): an expected trend for intermediate-to-long junctions. From δE, we determine the Fermi velocity of the bilayer graphene, which is found to increase with gate voltage and saturates at high gate voltages. Simultaneously we show carrier density dependence of δE, which is attributed to quadratic dispersion of bilayer graphene. This is in contrast to single layer graphene Josephson junctions, where δE and the Fermi velocity are independent of the carrier density. The carrier density dependence in BGJJs allows for additional tuning parameters in graphene-based Josephson Junction devices.