Band structure transformation of the avoided crossing type in impure graphene

Abstract

We show that the electronic spectrum in graphene, not unlike in other low-dimensional systems, can manifest a sharp impurity resonance near the Dirac point due to the presence of a single weakly coupled impurity described by the Fano model. It is demonstrated that, according to the established scenario, the electronic band structure of graphene undergoes a kind of transformation, specifically of the avoided crossing type, when the concentration of such short-range impurities increases. In this transformation process, main events unfold close to the impurity resonance energy, and, therefore, they relate to the most intriguing domain of the energy spectrum of graphene. The avoided crossing transformation develops in a threshold manner. Namely, it starts when the impurity concentration exceeds a critical value determined by the considerable spatial overlap of individual impurity states. Unlike former cases of such band structure transformations in low-dimensional systems, our findings unveil the formation of a new—impurity—Dirac point in the spectrum alongside the original shifted one, which doubles their number in the disordered system. The resulting electronic spectrum also features a single worthy of attention concentration broadening area or mobility gap of a substantially reduced width around the impurity resonance energy. Band edge smearing areas at old and newly formed Dirac points, where electronic states are also localized, are found to be negligibly narrow. Our analysis suggests that controlling the position of the Fermi level in the disordered system under study may allow observation of the re-entrant metal–insulator transition. The Fermi level entering and exiting the mobility gap causes the metal–insulator and insulator–metal transitions.