Evidence of Local Lattice Match for Commensurate State of Graphene/hBN van der Waals Heterostructure with TEM Analysis

Abstract

The commensurate state of van der Waals heterostructures of two-dimensional (2D) materials takes an opportunity to overcome the inherent drawbacks on pure 2D crystals and evokes unique properties with spontaneous alternation of the periodicity in each 2D layer and 2D van der Waals superstructures [1]. However, the lattice mismatch between graphene and hBN is extremely small around 0.05 Å and the commensurate transition occurs only around the AB-stacked area where carbon atoms are located above the boron (B) atoms when graphene and hBN are aligned along almost identical orientations [2]. Therefore, it is difficult to distinguish local and uneven transitions to the commensurate state. In the present study, we propose the evidence of a local transition to the commensurate state of graphene on hexagonal boron nitride (G/hBN) through moiré superstructure analysis using dark field transmission electron microscopy (DF-TEM) [3]. The moiré fringes are locally widened and zigzagged, which manifests from local twisting and stretching in the AB-stacked configurations of the graphene lattices. Furthermore, we statistically characterize the reduced lattice mismatch as a function of a decreased twist angle. Therefore, this moiré superstructure analysis with DF-TEM can reveal the local structural variation of G/hBN even under low magnification, providing experimental evidence of the theoretically predicted relation between stacking configurations for discerning the altered electronic and optical properties of G/hBN superstructures with a low twist angle.