Interplay of fractional Chern insulator and charge density wave phases in twisted bilayer graphene

Large-scale exact diagonalization reveals the competition between fractional Chern insulator and charge density wave states in a realistic spin- and valley-polarized single-band model for twisted bilayer graphene aligned with its hexagonal boron nitride substrate. While charge-ordered ground states are found across a whole range of filling fractions, consistent with experimental results in related moir\'e heterostructures, the interplay of the Berry curvature with the nontrivial single-particle dispersions may lead to the formation of topologically nontrivial correlated states at ν=1/3 as well as ν=2/5.