Long-Range Interaction Between Adatoms in Graphene

We present a theory of electron-mediated interaction between adatoms in graphene. In the case of resonant scattering, relevant for hydrogentated graphene, a long-range 1/r interaction is found. This interaction can be viewed as a fermionic analog of the Casimir interaction, in which massless fermions play the role of photons. The interaction is an attraction or a repulsion depending on whether the adatoms reside on the same sublattice or on different sublattices, with attraction dominating for adatoms randomly spread over both sublattices. The attractive nature of these forces creates an instability under which adatoms tend to aggregate.