Adsorption-induced energy gap in the density of states of single-sheet graphene

On the basis of a simple model, it is shown that a monolayer of adatoms bound by an indirect exchange interaction causes the appearance of an energy gap in the density of states of a two-dimensional substrate. The character of the dependence of the $\pi$- and $\pi^*$ bands and band gap on the position of the adatom level is analyzed in detail. The occupation numbers for the monolayer of adatoms and graphene are calculated. Numerical calculations are carried out for graphane.