Electrostatic moir\'e potential from twisted-hBN layers

Moir\'e superlattices formed by vertically stacking van der Waals layers host a rich variety of correlated electronic phases and function as novel photonic materials. The moir\'e potential of the superlattice, however, is fixed by the interlayer coupling of the stacked functional layers (e.g. graphene) and dependent on carrier types (e.g. electrons or holes) and valleys (e.g. {\Gamma} vs. K). In contrast, twisted hexagonal boron nitride (hBN) layers are predicted to impose a periodic electrostatic potential that may be used to engineer the properties of an adjacent functional thin layer. Here, we show that this potential is described by a simple theory of electric polarization originating from the interfacial charge redistribution, validated by its dependence on supercell sizes and distance from the twisted interfaces. We demonstrate that the potential depth and profile can be further controlled by assembling a double moir\'e structure. When the twist angles are similar at the two interfaces, the potential is deepened by adding the potential from the two twisted interfaces, reaching ~ 400 meV. When the twist angles are dissimilar at the two interfaces, multi-level polarization states are observed. As an example of controlling a functional layer, we demonstrate how the electrostatic potential from a twisted hBN substrate impedes exciton diffusion in a semiconductor monolayer. These findings suggest exciting opportunities for engineering properties of an adjacent functional layer using the surface potential of a twisted hBN substrate.