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The effective interaction between electrons in two-dimensional materials canbe modified by their environment, enabling control of electronic correlationsand phases. Here, we study the dependence of electronic correlations in twistedbilayer graphene (tBLG) on the separation to the metallic gate(s) in two deviceconfigurations. Using an atomistic tight-binding model, we determine theHubbard parameters of the flat bands as a function of gate separation, takinginto account the screening from the metallic gate(s), the dielectric spacerlayers and the tBLG itself. We determine the critical gate separation at whichthe Hubbard parameters become smaller than the critical value required for atransition from a correlated insulator state to a (semi-)metallic phase. Weshow how this critical gate separation depends on twist angle, doping and thedevice configuration. These calculations may help rationalise the reporteddifferences between recent measurements of tBLG's phase diagram and suggeststhat correlated insulator states can be screened out in devices with thindielectric layers.

Critical role of device geometry for the phase diagram of twisted bilayer graphene