Electronic structure of lattice-relaxed hBN-encapsulated twisted bilayer graphene

Twisted bilayer graphene (tBG) on hexagonal Boron Nitride (hBN) can host the quantum anomalous Hall effect for nearly aligned moire patterns of tBG and graphene/hBN interfaces, while reproducible experimental evidence is yet to be fully established. In this study, we review the electronic structure of energetically favored magic angle-tBG and hBN heterointerface structures and demonstrate that certain commensurate double moire patterns leads to a gap opening between the valence and conduction flat bands, thereby enhancing the possibility of observing well-resolved topological bands. When the system is deposited on a bulk hBN substrate, both commensurate moire systems exhibit such gap opening. We can further tune the bands at charge neutrality through an additional encapsulation hBN layer or by applying a perpendicular electric field. Our results show that careful alignment and sliding between the moire patterns of tBG and hBN substrate can make a notable impact on the resulting device's electronic properties.