Sublattice ordering in a dilute ensemble of defects in graphene

Defects in graphene, such as vacancies or adsorbents attaching themselves to carbons, 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 dilute ensemble defects, 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.