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Correlated states in charge-transfer heterostructures based on rhombohedral multilayer graphene

Charge transfer is a common phenomenon in van der Waals heterostructures with proper work function mismatch, which enables electrostatic gating to control band alignment and interlayer charge distributions. This provides a tunable platform for studying coupled bilayer correlated electronic systems. Here, we theoretically investigate heterostructures of rhombohedral multilayer graphene (RMG) and an insulating substrate with gate-tunable band alignment. We first develop a self-consistent electrostatic theory for layer charge densities incorporating charge transfer, which reproduces the experimentally observed broadened and bent charge neutrality region. When the substrate's band edge has a much larger effective mass than RMG, its carriers can form a Wigner crystal at low densities. This creates a quantum superlattice that induces topological flat bands in the RMG layer, which may lead to Chern insulators driven by intralayer Coulomb interactions. Conversely, with comparable effective masses, we find an interlayer excitonic insulator state at charge neutrality stabilized by interlayer Coulomb coupling. Our work establishes these charge-transfer heterostructures as a rich platform for topological and excitonic correlated states, opening an avenue for ``charge-transferonics''.