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Motivated by the observation of polarization superlattices in twistedmultilayers of hexagonal boron nitride ($h$-BN), we address the possibility ofusing these heterostructures for tailoring the properties of multilayergraphene by means of the electrostatic proximity effect. By using thecombination of first-principles and large-scale tight-binding modelcalculations coupled via the Wannier function approach, we demonstrate thepossibility of creating a sequence of well-separated flat-band manifolds inAB-stacked bilayer graphene at experimentally relevant superlatticeperiodicities above $\sim$30 nm. Our calculations show that the details of bandstructures depend on the local inversion symmetry breaking and the verticalelectrical polarization, which are directly related to the atomic arrangement.The results advance the atomistic characterization of graphene-based systems ina superlattice potential beyond the continuum model.

Flat bands in bilayer graphene induced by proximity with polar $h$-BN superlattices