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The effect of substitution atoms on the energy spectrum and the electricalconductivity of graphene was investigated in a Lifshitz one-electrontight-binding model. It is established that the ordering of impurity atomsresults in a gap in the energy spectrum of electrons whose width depends on theorder parameter and on the magnitude of the scattering potential. It is shownthat if the order parameter is close to its maximum value, there are peaksassociated with localized impurity states on the energy curve of the electronstates density at the edges of the energy gap. At the electron concentration atwhich the Fermi level enters the gap region, the electrical conductivity iszero, and the metal-dielectric transition occurs. If the Fermi level falls inthe region of the energy band, the electron relaxation time and electricalconductivity tend to infinity when the order parameter reaches its maximumvalue. The analytical calculations of the electron density and of theelectrical conductivity of graphene, made in the limiting case of weakscattering, are compared with the results of the numerical calculations fordifferent scattering potentials.

The energy spectrum and the electrical conductivity of graphene with substitution impurity