▎ 摘　　要

We study the stability and electronic structure of magic-angle twisted bilayer graphene on the hexagonal boron nitride (TBG/BN). Structural relaxation has been performed for commensurate supercells of the heterostructures with different twist angles (theta') and stackings between TBG and BN. We find that the slightly misaligned configuration with theta' = 0.54 degrees and the AA/AA stacking has the globally lowest total energy due to the constructive interference of the moir ' e interlayer potentials and thus the greatly enhanced relaxation in its 1x1 commensurate supercell. Gaps are opened at the Fermi level (E-F) for small supercells with the stackings that enable strong breaking of the C-2 symmetry in the atomic structure of TBG. For large supercells with theta' close to those of the 1x1 supercells, the broadened flat bands can still be resolved from the spectral functions. The theta' = 0.54 degrees is also identified as a critical angle for the evolution of the electronic structure with theta', at which the energy range of the mini-bands around E-F begins to become narrower with increasing theta' and their gaps from the dispersive bands become wider. The discovered stablest TBG/BN with a finite theta' of about 0.54 degrees and its gapped flat bands agree with recent experimental observations.