Moiré commensurability and the quantum anomalous Hall effect in twisted bilayer graphene on hexagonal boron nitride

The quantum anomalous Hall effect sometimes occurs in twisted bilayer graphene when it is nearly aligned with an encapsulating hexagonal boron nitride (hBN) layer. The authors argue that the quantum anomalous Hall effect is likely only when the graphene/graphene and graphene/hBN moir\'e patterns are nearly commensurate. This picture gives rise to the series of ``Hall windows'' in the twist-angle space illustrated here.