Moiré-localized flat bands in a family of twisted Bernal-stacked graphene multilayers

Moiré interfaces can have a dramatic effect on the properties of van der Waals materials owing to their ability to generate flat bands with nontrivial topology. In graphene-based materials, one family of twisted structures consists of three or more Bernal-stacked graphene sheets with a single rotational fault introduced at a single interface. Twisted monolayer-bilayer and bilayer-bilayer graphene form the thinnest such structures, and have been shown to host strongly correlated and topological states. Here, we extend this study to progressively thicker structures by adding additional Bernal-stacked graphene layers to both sides of the moiré interface. In studying these materials, we find unexpectedly strong similarities in the nature of their moiré flat bands, which are isolated and can be continuously deformed by a perpendicular electric field in structures as thick as six total layers. We further uncover a hierarchy of symmetry-broken and topological states in twisted monolayer-trilayer and twisted bilayer-trilayer graphene, reminiscent of those seen in twisted monolayer-bilayer and bilayer-bilayer graphene. Theoretical modeling shows that the overarching similarities across these twisted structures arise due to a localization of the low-energy states at the twisted interface.