Impurity Ordering Effects on Graphene Electron Properties

Abstract

The impurity ordering effects on graphene electron properties within a one-band model of strong coupling are studied. We carried out analytical and numerical calculations of the energy spectrum of electrons in the cases of low and high orderings. The limiting case of weak scattering for the varying degrees of scattering potential is analyzed. The ordering of impurity atoms causes the appearance of a gap in the energy spectrum of electrons. The gap width is proportional to the ordering parameter and the scattering potential for moderate magnitudes of the latter, but, as the scattering potential increases, its more complex behavior is observed. It is established that the regions of localization of electronic states are at the edges of the gap and the edges of the energy spectrum. The case of weak scattering potential allows the analytic investigation at the gap edges. Within the Lifshitz one-electron tight-binding model, the electrical conductivity of graphene is investigated. When the Fermi level enters the gap region of the energy spectrum, the electrical conductivity becomes zero, and the metal-dielectric transition occurs. If the Fermi level is in the region of the energy band, the electron relaxation time and electrical conductivity go to infinity, when the order parameter reaches its maximum value.