Symmetry breaking in the double moire superlattices of relaxed twisted bilayer graphene on hexagonal boron nitride

摘要

We study the atomic and electronic structures of the commensurate double moire superlattices in fully relaxed twisted bilayer graphene (TBG) nearly aligned with the hexagonal boron nitride (BN). The single-particle effective Hamiltonian ((H) over cap (0)) taking into account the relaxation effect and the full moire Hamiltonian introduced by BN has been built for TBG/BN. The mean-field (MF) band structures of the self-consistent Hartree-Fock (SCHF) ground states at a different number (nu) of filled flat bands relative to the charge neutrality point (CNP) are obtained based on (H) over cap (0) in the plane-wave-like basis. The single-particle flat bands in TBG/BN become separated by the opened gap at CNP due to the symmetry breaking in (H) over cap (0). We find that the broken C-2 symmetry in (H) over cap (0) mainly originates from the intralayer inversion-asymmetric structural deformation in the graphene layer adjacent to BN, which introduces spatially nonuniform modifications of the intralayer Hamiltonian. The gapped flat bands have finite Chern numbers. For TBG/BN with the magic twist angle, the SCHF ground states with vertical bar nu vertical bar = 1-3 are all insulating with narrow MF gaps. When the flat conduction bands are filled, the gap at nu = 1 is smaller than that at nu = 3, suggesting that the nontrivial topological properties associated with the flat Chern bands are more likely to be observed at nu = 3. This is similar for negative v with empty valence bands. The dependence of the electronic structure of TBG/BN on positive v is roughly consistent with recent experimental observations.