Abstract
When adsorbents attach themselves to carbons in the honeycomb lattice of graphene, they may preferentially take positions on one of its two sublattices, thus breaking the global lattice symmetry. This leads to opening a gap in the electronic spectrum. We show that such a sublattice ordering may spontaneously occur in a low-density ensemble of adatoms adsorbed on graphene, due to the long-range interaction between them mediated by electrons. As a result sublattice-ordered domains may form, with electronic properties characteristic of a two-dimensional topological insulator.