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 . For the complete ordering of impurity atoms, the energy gap width equals . If the Fermi level falls in the region of the mentioned gap, then the electrical conductance 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 . At the concentration , as the ordering of impurity atoms η →1, the electrical conductance of graphene , i.e., the transition of graphene in the state of ideal electrical conductance arises.

We employ Green’s function method for describing multiband models with magnetic impurities and apply the formalism to the problem of chromium impurities adsorbed onto a carbon nanotube. Density functional theory is used to determine the bandstructure, which is then fit to a tight-binding model to allow for the subsequent Green’s function description. Electron–electron interactions, electron–phonon coupling, and disorder scattering are all taken into account (perturbatively) with a theory that involves a cluster extension of the coherent potential approximation. We show how increasing the cluster size produces more accurate results and how the final calculations converge as a function of the cluster size. We examine the spin-polarized electrical current on the nanotube generated by the magnetic impurities adsorbed onto the nanotube surface. The spin polarization increases with both increasing concentration of chromium impurities and with increasing magnetic field. Its origin arises from the strong electron correlations generated by the Cr impurities.

This paper presents a new method of describing electronic spectrum, thermodynamic potential, and electrical conductivity of disordered crystals based on the Hamiltonian of multi-electron system and diagram method for Green’s functions finding. Electronic states of a system were described by multi-band tight-binding model. The Hamiltonian of a system is defined on the basis of the wave functions of electron in the atom nucleus field. Electrons scattering on the oscillations of the crystal lattice are taken into account. The proposed method includes long-range Coulomb interaction of electrons at different sites of the lattice. Precise expressions for Green’s functions, thermodynamic potential and conductivity tensor are derived using diagram method. Cluster expansion is obtained for density of states, free energy, and electrical conductivity of disordered systems. We show that contribution of the electron scattering processes to clusters is decreasing along with increasing number of sites in the cluster, which depends on small parameter. The computation accuracy is determined by renormalization precision of the vertex parts of the mass operators of electron-electron and electron-phonon interactions. This accuracy also can be determined by small parameter of cluster expansion for Green’s functions of electrons and phonons.

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В роботі досліджено вплив адсорбованої домішки атомів Калію на елект-ронний спектер графену. Електронні стани системи описано в рамках са-моузгодженого багатозонного моделю сильного зв'язку. Показано, що при упорядкованому розташуванні атомів Калію, яке понижує енергію системи, в енергетичному спектрі графену може виникати щілина. Так, за концентрації Калію, коли на елементарну комірку приходиться два атоми Карбону і один атом Калію, який розташований на поверхні графе-ну над атомом Карбону на віддалі у 0,286 нм, величина енергетичної щі-лини складає ≅ 0,25 еВ. Така обставина реалізується, коли графен знахо-Corresponding author: Stanislav Petrovych Repetsky