Gate-tunable crossover between vortex-interaction and pinning dominated regimes in Josephson-coupled lead islands on graphene

The resistance of a Josephson junction array consisting of randomly distributed lead islands on exfoliated single-layer graphene shows a broad superconducting transition to zero with an onset temperature close to the transition temperature of bulk Pb. The transition region evolves with the back-gate voltage with two peaks in the temperature derivative of the resistance. The region above the lower-temperature peak is found to be well described by the Berezinskii-Kosterlitz-Thouless model of the thermal unbinding of vortex-antivortex pairs, while that below this peak fits well with the Ambegaokar-Halperin model of thermally activated phase slip or vortex depinning. Thus, a gate-tunable crossover between interaction and pinning dominated vortices is inferred. This is elaborated in terms of free vortices as well as strong pinning sites in this highly inhomogeneous Josephson junction array.