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We realize superconductor-insulator transitions (SIT) in mechanicallyexfoliated Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (BSCCO) flakes and addresssimultaneously their transport properties as well as the evolution of densityof states. Back-gating via the solid ion conductor engenders a reversible SITin BSCCO, as lithium ions from the substrate are electrically driven into andout of BSCCO. Scaling analysis indicates that the SIT follows the theoreticaldescription of a two-dimensional quantum phase transition (2D-QPT). We furthercarry out tunneling spectroscopy in graphite(G)/BSCCO heterojunctions. Weobserve V-shaped gaps in the critical regime of the SIT. The density of statesin BSCCO gets symmetrically suppressed by further going into the insulatingregime. Our technique of combining solid state gating with tunnelingspectroscopy can be easily applied to the study of other two-dimensionalmaterials.

Electric-Field Induced Superconductor-Insulator Transitions in Exfoliated Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ Flakes