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We show that the changes in the electronic density of states (DOS) ingraphene induced by impurity scattering with short-range potentials arecompletely different from those caused by the long-range Coulomb potential. Thespectral weight of the state that eventually disappears into the valence band(as the strength of scattering increases) does not transform into a resonancestate. Therefore no unusual screening effects related to a redistribution ofthe density of states in the valence band are observed. The states induced bythe short-range impurities in graphene, therefore, have distinctively differentproperties compared with the long-range potential case. These properties, infact, closely resemble the case of a short-range single impurity in otherbipartite lattices, such as the square, body centered cubic, and simple cubiclattices.

Absence of a supercritical regime induced by short-range impurity scattering in gapped graphene