  Electronic and transport properties of Graphene, a one-atom thick crystalline
material, are sensitive to the presence of atoms adsorbed on its surface. An
ensemble of randomly positioned adatoms, each serving as a scattering center,
leads to the Bolzmann-Drude diffusion of charge determining the resistivity of
the material. An important question, however, is whether the distribution of
adatoms is always genuinely random. In this Article we demonstrate that a
dilute adatoms on graphene may have a tendency towards a spatially correlated
state with a hidden Kekule mosaic order. This effect emerges from the
interaction between the adatoms mediated by the Friedel oscillations of the
electron density in graphene. The onset of the ordered state, as the system is
cooled below the critical temperature, is accompanied by the opening of a gap
in the electronic spectrum of the material, dramatically changing its transport
properties.
