Graphene overlaid by a thin film of the superconducting material InO exhibits intriguing transport behavior, tunable by gating of the graphene layer across the charge neutrality point. In particular, a double-peak feature in the resistance is detected in samples where the InO is driven into the insulating side of the superconductor-insulator transition (SIT). As the InO turns superconducting, its critical temperature Tc is enhanced by the coupling to the graphene layer. Contrary to naïve expectation, Tc is found to increase with decreasing carrier density and is largest close to charge neutrality. I will discuss a theoretical interpretation of these results, based on the key idea that superconducting puddles in the InO layer proximitise the graphene, simultaneously hole-doping the underlying regions relative to their background. As a result, SN and SNS interfaces are formed in the graphene layer, where either the S or N regions can be tuned arbitrarily close to their Dirac point. The hybrid system therefore provides access to the fabrication of superconducting devices with ultra-law carrier density.
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