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 ($L>ξ$). We measure the device's differential resistance as a function of bias current and gate voltage for a range of different temperatures. The extracted critical current $I_{C}$ follows an exponential trend with temperature: $ \exp(-k_{B} T/ δE)$. Here $δE = \hbar ν_F /2πL $: 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. Simultaneously, we show the carrier density dependence of $δE$, which is attributed to the 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.