Title: The energy spectrum and the electrical conductivity of graphene with substitution impurity
Author(s):

	S.P. Repetsky (Institute of High Technologies, Taras Shevchenko National University of Kyiv, 4-g Academician Glushkov Ave., 03022 Kyiv, Ukraine) ,
	I.G. Vyshyvana (Institute of High Technologies, Taras Shevchenko National University of Kyiv, 4-g Academician Glushkov Ave., 03022 Kyiv, Ukraine) ,
	S.P. Kruchinin (Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine, 14-b Metrolohichna St., 03143 Kyiv, Ukraine) ,
	R.M. Melnyk (National University of Kyiv-Mohyla Academy, 2 Skovorody St., 04070 Kyiv, Ukraine) ,
	A.P. Polishchuk (Aerospace Faculty, National Aviation University, 1 Kosmonavta Komarova Ave., 03058 Kyiv, Ukraine)

The effect of substitution atoms on the energy spectrum and the electrical conductivity of graphene was investigated in a Lifshitz one-electron tight-binding model. It is established that the ordering of impurity atoms results in a gap in the energy spectrum of electrons whose width depends on the order parameter and on the magnitude of the scattering potential. It is shown that if the order parameter is close to its maximum value, there are peaks associated with localized impurity states on the energy curve of the electron states density at the edges of the energy gap. At the electron concentration at which the Fermi level enters the gap region, the electrical conductivity is zero, and the metal-dielectric transition occurs. If the Fermi level falls in the region of the energy band, the electron relaxation time and electrical conductivity tend to infinity when the order parameter reaches its maximum value. The analytical calculations of the electron density and of the electrical conductivity of graphene, made in the limiting case of weak scattering, are compared with the results of the numerical calculations for different scattering potentials.

Key words: graphene, energy gap, density of states, ordering parameter, Green's function, metal-insulator transition

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