Origin of the moiré superlattice scale lateral force modulation of graphene on a transition metal substrate

The moiré superlattice formed between graphene and a transition metal substrate is capable of tuning the frictional properties of graphene. For instance, a moiré superlattice scale modulation on the lateral force will be experienced by the tip of an atomic force microscope (AFM). However, the origin of this long-range force modulation still needs to be clarified. In this study, density functional theory (DFT) calculations have been carried out to investigate the indentation processes of a one-Ar-atom tip and a 10-atom Ir tip, sliding on graphene/Re(0001) and graphene/Pt(111) moiré superlattices, respectively. The calculation results indicate that the interfacial interaction between graphene and a transition metal substrate determines the morphological corrugation of graphene and the characteristics of the lateral force modulation. Moreover, when the tip-graphene interaction is strong enough, it will influence the evolutions of the adsorption energy Ead and tip sliding trajectory. Thus, the moiré superlattice scale lateral force modulation of graphene on a transition metal substrate originates from the joint effects of the graphene-substrate interfacial interaction and tip-graphene interaction.