Long-range adsorbate interactions mediated by two-dimensional Dirac fermions

We provide here an analytical formalism to describe the indirect interaction between adsorbed atom or molecule pairs mediated by two-dimensional (2D) Dirac fermions. We show that in contrast to the case of traditional 2D electron gas, in the 2D Dirac system, the long-range interaction behaves as 1/ r ³ decaying Friedel oscillation. This analytical formalism is fully consistent with a tight-binding numerical calculation of honeycomb lattices. Our formalism is suitable for the realistic 2D Dirac materials, such as graphene and surface states of three-dimensional topological insulators.