Quantum Anomalous Hall Effect of Twisted Bilayer Graphene/Hexagonal Boron Nitride Double-Moiré Structures

Twisted bilayer graphene (tBG) nearly aligned with a hexagonal boron nitride (hBN) substrate hosts two moiré patterns and sometimes shows quantum anomalous Hall effects (QAHE). The influence of hBN on low-energy states in tBG has normally been approximated by a spatially uniform sublattice-asymmetric potential, in spite of the fact that moiré periodic terms in the Hamiltonian are estimated to be equally large. I will present a study of the QAHE of tBG/hBN trilayers using a double-moiré model. I will first identify a series of twist-angle pairs at which the two moiré patterns are commensurate, allowing moiré band theory to be applied, and then illustrate the significant effect of rigid in-plane hBN translation on the moiré band structures and Chern numbers. Using this information, I will discuss the anomalous Hall properties of general tBG/hBN trilayers in two regimes: i) when the twist-angle pair is close to a commensurate point, so that a supermoiré pattern arises between the two patterns; ii) when the twist-angle pair is far from a commensurate point, creating a disorder-like effect. Finally, I will suggest a number of possible experiments that could verify the proposed critical role of the G/hBN moiré pattern.