Interactions between adsorbates on graphene

Interactions between adsorbates on a surface of graphene play an important role in many applications. We offer a detailed analysis of interactions between two adsorbed atoms and molecules. We compare the first principles DFT, numerical tight-binding, and analytical functional integral calculations to identify the microscopic nature of the adsorbate-adsorbate interaction and the role of different contributions. The interaction has two distinct regimes: a weak coupling regime, which is akin to RKKY (Ruderman-Kittel-Kasuya-Yosida) magnetic interaction, and a strong coupling regime which is dominated by interaction via a many-body electronic dressing ``cloud'' around each adsorbate. We show that the interplay between these two regimes provides an opportunity to manipulate the magnitude and the structure of the adsorbate-adsorbate interaction (up to complete reversal of sign) via a variety of easily accessible properties, such chemical potential via back-gating, type of an adsorbed atom, electronic configuration of an adsorbed molecule, and strain.