Abstract
In the one-band model of strong coupling, the influence of substitutional impurity atoms on the energy spectrum and electrical conductance of graphene is studied. It is established that the ordering of substitutional impurity atoms on nodes of the crystal lattice causes the appearance of a gap in the energy spectrum of graphene with width η|δ| centered at the point yδ, where 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. The maximum value of the parameter of ordering is {{boldsymbol{eta }}}_{{boldsymbol{max }}}{boldsymbol{=}}{bf{2}}{boldsymbol{y}}{boldsymbol{,}},{boldsymbol{y}}{boldsymbol{le }}{bf{1}}/{bf{2}}. For the complete ordering of impurity atoms, the energy gap width equals {bf{2}}{boldsymbol{y}}{boldsymbol{|}}{boldsymbol{delta }}{boldsymbol{|}}. If the Fermi level falls in the region of the mentioned gap, then the electrical conductance {{boldsymbol{sigma }}}_{{boldsymbol{alpha }}{boldsymbol{alpha }}}{boldsymbol{to }}{bf{0}} at the ordering of graphene, i.e., the metal–dielectric transition arises. If the Fermi level is located outside the gap, then the electrical conductance increases with the parameter of order η by the relation {{boldsymbol{sigma }}}_{{boldsymbol{alpha }}{boldsymbol{alpha }}}{boldsymbol{ sim }}{{boldsymbol{(}}{{boldsymbol{y}}}^{{bf{2}}}{boldsymbol{-}}frac{{bf{1}}}{{bf{4}}}{{boldsymbol{eta }}}^{{bf{2}}}{boldsymbol{)}}}^{{boldsymbol{-}}{bf{1}}}. At the concentration {boldsymbol{y}}{boldsymbol{=}}{bf{1}}{boldsymbol{/}}{bf{2}}, as the ordering of impurity atoms η →1, the electrical conductance of graphene {{boldsymbol{sigma }}}_{{boldsymbol{alpha }}{boldsymbol{alpha }}}{boldsymbol{to }}{boldsymbol{infty }}, i.e., the transition of graphene in the state of ideal electrical conductance arises.
Highlights
The recent investigations of the energy spectrum of graphene are based on the density functional theory
The numerical calculations made within the method have demonstrated the appearance of a gap in the energy spectrum of graphene caused by the presence of an impurity
New 2D-material nanomeshes based on Moiré graphene/hexagonal boron nitride bilayers were predicted, on the basis of first-principle calculations within the framework of density functional theory, with standard norm-conserving pseudo-potentials, flexible numerical LCAO double zeta + polarization orbital basis sets[2]
Summary
In work[17], the influence of the ordering of atoms on the energy spectrum and the electrical conductance of an alloy was studied analytically in the above-mentioned one-band model. No explanation about the nature of the influence of the ordering of impurities on the appearance of a gap in the energy spectrum of graphene is available until now.
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