A Simulation Study of Atomic Resolution TEM images for Two Dimensional Single Layer and Bilayer Graphene Crystal

In a simulation study of atomic resolution transmission electron microscope images of single layer and bilayer graphene, it is demonstrated that the conventional Bloch wave formulations can be used when high-order Laue zone reflections are properly taken into account in the theory. The simulated images for bilayer graphene show 3-fold rotational lattice symmetry rather than the 6-fold one under certain conditions. This result can be understood as revealed the 3-fold rotational lattice symmetry of bilayer graphene in three dimensions along [0001]. For single layer graphene the observed phase images showing 3-fold rotational lattice symmetry were particularly noted. This phenomenon has been explained by an assumption of the re-configuration of electron density on the surface of graphene. And the matching images have been obtained as simulated with up to the second order Laue zone reflections only, reflecting the re-configuration of electrons on the surface.