Evidence of Local Commensurate State with Lattice Match of Graphene on Hexagonal Boron Nitride

Transition to a commensurate state changes the local symmetry periodicity on two-dimensional van der Waals superstructures, evoking distinctive properties far beyond individual layers. We investigate the morphology of moiré superstructures of graphene on hexagonal boron nitride (hBN) with a low twist angle (≈0°) through moiré fringe analyses with dark field transmission electron microscopy. The moiré fringes exhibit local variation, suggesting that the interaction between graphene and hBN depends on the stacking configuration and that local transition to the commensurate state occurs through the reduced crystalline mismatch (that is, by lattice stretching and twisting on the graphene lattices). This moiré superstructure analysis suggests an inventive method for studying the interaction between stacked van der Waals layers and for discerning the altered electronic and optical properties of graphene on hBN superstructures with a low twist angle, even at low magnification.