Effect of impurities ordering in the electronic spectrum and conductivity of graphene

Abstract By carrying out a computation in the Lifshitz tight-binding one-electron model, we obtain the energy spectrum and electrical conductance of graphene, in the presence of substitutional impurity atoms, thus assessing the influence of the latter. In the weak-scattering approximation, we study specific features of the electron energy spectrum in the gap region having width η | δ | and centered at the point yδ, arising because of the ordering of substitutional impurity atoms on nodes of the crystal lattice. Here η is the parameter of ordering, δ is the difference of the scattering potentials of impurity atoms and carbon atoms, and y is the impurity concentration. It is shown that if the ordering parameter η is close to η max = 2 y , y 1 / 2 , the plot of the density of electron states has peaks on the edges of the energy gap. Those peaks correspond to impurity levels. As the ordering parameter η decreases, the impurity levels split into the impurity bands. The regions of localization of electron impurity states, which arise at the edges of the spectrum and edges of the energy gap, are investigated.