The superconducting transition temperature ($T_c$) of single-layer graphene coupled to an indium oxide (InO) film, a low carrier-density superconductor, is found to increase with decreasing carrier density and is largest close to the average charge neutrality point in graphene. Such an effect is very surprising in conventional BCS superconductors. We study this phenomenon both experimentally and theoretically. Our analysis suggests that the InO film induces random electron and hole doped puddles in the graphene. The Josephson effect across these regions of opposite polarity enhances the Josephson coupling between the superconducting clusters in InO, along with the overall $T_c$ of the bilayer heterostructure. This enhancement is most effective when the chemical potential of the system is tuned between the charge neutrality points of the electron and hole doped regions.

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• Andreev reflection
• Josephson effect
• Proximity effect
• Graphene