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The family of moir\'e materials provides a powerful platform for tuninginterlayer couplings via the twist angle in systems with large spatialperiodicity. In trilayer graphene systems, interlayer couplings at the twointerfaces can possibly be tuned separately, and the competition between theseinteractions can therefore influence the electronic structure in a significantway. In this study, we investigate the electronic properties of twistedmonolayer-bilayer graphene (aAB) beyond the continuum model, usingfirst-principles calculations combined with an accurate tight-binding model. Wefind that at large twist angles, the electronic features of aAB are welldescribed by the interaction between the parabolic bands of the BernalAB-bilayer and the Dirac bands of the twisted monolayer, resulting in aspontaneous electric polarization in the former that splits the parabolicbands. As the twist angle decreases, the coupling between adjacent layers atthe twisted interface becomes dominant, which makes aAB look like twistedbilayer graphene (TBG) interacting with the outer Bernal layer. A moir\'epotential emerges in the TBG-like layers, leading to charge localization, whilethe outer Bernal layer exhibits charge delocalization with substantialsublattice polarization at the atomic scale. Furthermore, we identify narrowbands with a minimum width at a quasi-magic angle of 1.16 degrees, closelymatching the magic angle of TBG. The enhanced electron correlation expected inthese narrow bands suggests that aAB is a promising platform for exploringcorrelated electronic phenomena.

Competing interlayer interactions in twisted monolayer-bilayer graphene: From spontaneous electric polarization to quasi-magic angle