Double quantum criticality in superconducting tin arrays-graphene hybrid

Two magnetic-field-induced quantum critical behaviors were recently discovered in two dimensional electron gas (2DEG) at LaTiO₃/SrTiO₃ interface and interpreted by disordered superconducting puddles coupled through 2DEG. In this scenario, the 2DEG is proposed to undergo a spontaneous phase separation and breaks up into locally superconducting puddles in a metallic matrix. However, as the inhomogeneous superconducting 2DEG is only illative, this proposal still lacks the direct experimental demonstration. Here, we artificially construct superconducting puddles-2DEG hybrid system by depositing tin nanoislands array on single crystalline monolayer graphene, where the two quantum critical behaviors are reproduced. Through the finite-size scaling analysis on magnetoresistivity, we show that the two quantum critical behaviors result from the intra-island and inter-island phase coherence, respectively, which are further illustrated by the phase diagram. This work provides a platform to study superconducting quantum phase transitions in a 2D system and helps to integrate superconducting devices into semiconductor technology.