Disorder Effects on Superconductor-Graphene-Superconductor Arrays

Graphene coupled to a superconducting array of islands undergoes a continuous Quantum Phase Transition (QPT) from a superconducting state to an insulating or metallic state as a function of gate voltage or applied magnetic field. To study the effects of disorder on this phase transition and the related ground states, we performed transport measurements on graphene proximity-coupled to an array of Sn superconducting islands, where we added point disorder (random displacements) to each island site. We studied the Superconductor-to-Insulator Transition (SIT) as a function of applied magnetic field for devices having varying amounts of point disorder. For low disorder, a clear critical crossing point is observed from magnetoresistance measurements, and the extracted critical exponents were consistent with a continuous 2D SIT. In contrast, high disorder devices showed a disrupted crossing point and disrupted scaling. These signatures suggest unusual behavior as a function of disorder near the Quantum Critical Point (QCP) for devices having resistances less than the quantum of resistance (R_Q).