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 (<i>L</i> > 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>I</i> _C follows an exponential trend with temperature: exp(-<i>k</i> _B <i>T</i>/<i>δE</i>). Here <i>δE</i> = ℏν _<i>F</i> /2<i>πL</i>: an expected trend for intermediate-to-long junctions. From <i>δE</i>, 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 <i>δE</i>, which is attributed to the quadratic dispersion of bilayer graphene. This is in contrast to single layer graphene Josephson junctions, where <i>δE</i> 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.