Behavior of the Energy Spectrum and Electric Conduction of Doped Graphene

Abstract

We consider the effect of atomic impurities on the energy spectrum and electrical conductance of graphene. As is known, the ordering of atomic impurities at the nodes of a crystal lattice modifies the graphene spectrum of energy, yielding a gap in it. Assuming a Fermi level within the gap domain, the electrical conductance diverges at the ordering of graphene. Hence, we can conclude about the presence of a metal–dielectric transition. On the other hand, for a Fermi level occurring outside of the gap, we see an increase in the electrical conductance as a function of the order parameter. The analytic formulas obtained in the Lifshitz one-electron strong-coupling model, describing the one-electron states of graphene doped with substitutional impurity atoms in the limiting case of weak scattering, are compared to the results of numerical calculations. To determine the dependence of the energy spectrum and electrical conductance on the order parameter, we consider both the limiting case of weak scattering and the case of finite scattering potential. The contributions of the scattering of electrons on a vapor of atoms to the density of states and the electrical conductance of graphene with an admixture of interstitial atoms are studied within numerical methods. It is shown that an increase in the electrical conductance with the order parameter is a result of both the growth of the density of states at the Fermi level and the time of relaxation of electron states. We have demonstrated the presence of a domain of localized extrinsic states on the edges of the energy gap arising at the ordering of atoms of the admixture. If the Fermi level falls in the indicated spectral regions, the electrical conductance of graphene is significantly affected by the scattering of electrons on clusters of two or more atoms, and the approximation of coherent potential fails in this case.

Theory of Electron Correlation in Disordered Crystals

“…Such a situation is realized if graphene is placed on a potassium support. A more complex dependence of the electron energy on the wave vector in the region of the energy gap in comparison with that previously investigated in [34][35][36] in a simple two-band model is due to the effect of band hybridization.…”

“…We established that, at the potassium concentration such that the unit cell includes two carbon atoms and one potassium atom, the latter being placed on the graphene surface above a carbon atom at a distance of 0.286 nm, the energy gap is ~0.25 eV (see Figure 7b). A more complex dependence of the electron energy on the wave vector in the region of the energy gap in comparison with that previously investigated in [34][35][36] in a simple two-band model is due to the effect of band hybridization. The location of the Fermi level in the energy spectrum depends on the potassium concentration and is in the energy interval −0.36 Ry ≤ ε F ≤ Ry0.36.…”

“…where c λ ni is a discrete binary random number taking the values of 1 or 0, depending on whether an atom of type λ is at site (ni) or not, respectively (36). The joint probabilities in Equations ( 126), ( 127), (129), and (130) are defined by the following:…”

Sensitivity to strains and defects for manipulating the conductivity of graphene

“…One of Dirac electrons' most dramatic responses become apparent at the strain and defect engineering of graphene. Both the strains [1][2][3][4][5][6][7][8][9][10][11] and defects (dopants) [12][13][14][15][16][17][18][19][20][21][22] are currently known as ones of the means whereby the problem of a band gapless in graphene can be overcome. Besides, a variety of different types of point-(dopants) [23][24][25] and line-acting (grain boundaries) [26][27][28] defects is commonly an inherent feature for the graphene-based devices [29].…”