Interaction of two symmetric monovacancy defects in graphene

We investigate the interactions between two symmetric monovacancy defects in graphene grown on Ru (0001) after silicon intercalation by combining first-principles calculations with scanning tunneling microscopy (STM). First-principles calculations based on free-standing graphene show that the interaction is weak and no scattering pattern is observed when the two vacancies are located in the same sublattice of graphene, no matter how close they are, except that they are next to each other. For the two vacancies in different sublattices of graphene, the interaction strongly influences the scattering and new patterns' emerge, which are determined by the distance between two vacancies. Further experiments on silicon intercalated graphene epitaxially grown on Ru (0001) shows that the experiment results are consistent with the simulated STM images based on free-standing graphene, suggesting that a single layer of silicon is good enough to decouple the strong interaction between graphene and the Ru (0001) substrate.