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Monolayer graphene placed with a twist on top of AB-stacked bilayer graphenehosts topological flat bands in a wide range of twist angles. The dispersion ofthese bands and gaps between them can be efficiently controlled by aperpendicular electric field, which induces topological transitions accompaniedby changes of the Chern numbers. In the regime where the applied electric fieldinduces gaps between the flat bands, we find a relatively uniform distributionof the Berry curvature. Consequently, interaction-induced valley- and/orspin-polarized states at integer filling factors are energetically favorable.In particular, we predict a quantum anomalous Hall state at filling factor$\nu=1$ for a range of twist angles $1^\circ<\theta <1.4^\circ$. Furthermore,to characterize the response of the system to magnetic field, we computed theHofstadter butterfly and the Wannier plot, which can be used to probe thedispersion and topology of the flat bands in this material.

Topological Flat Bands and Correlated States in Twisted Monolayer-Bilayer Graphene