4 research outputs found
Effects of Electron Correlation inside Disordered Crystals
No full textS.P.K. acknowledges support by the National Academy of Sciences of Ukraine (Project No.0116U002067). Calculations were performed using Latvian Super Cluster (LASC), located in the Center of Excellence at Institute of Solid State Physics, the University of Latvia, which is supported by European Union Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-Teaming. Phase two under Grant Agreement No. 739508, project CAMART2.We propose a novel approach for characterising the electron spectrum of disordered crystals constructed from a Hamiltonian of electrons as well as phonons and a diagram approach for Green’s function. The system’s electronic states were modelled by means of the multi‐band, tight-binding approach. The system’s Hamiltonian is described based on the electron wave functions at the field of the atom nucleus. Our novel approach incorporates the long‐range Coulomb interplay of electrons located in different lattice positions. Explicit interpretations of Green’s functions are derived using a diagram method.Equations are obtained for the vertex components for the mass operators of the electron–electron as well aselectron–phonon interplays. A system of equations for the spectrum of elementary excitations in the crystal is obtained, in which the vertex components for the mass operators of electron–electron as well as electron–phonon interplays are renormalised. Thismakes it possible to perform numerical computationsfor the system’s energy spectrum with a predetermined accuracy. In contrast to other approaches in which electron correlations are only taken into account in the limiting cases of an infinitely large and infinitesimal electron density, in this method, electron correlations are described in the general case of an arbitrary density. We obtained the cluster expansion of the density of states (DOS) of the disordered systems. We demon-strate that the addition of the electron‐scattering mechanismsto the clusters is decreasing. This hap-pens due to a growing number of positions in the cluster, which hang ontothe small parameter. The computing exactness is fixed by a small parameter for cluster expansion of Green’s functions of electrons as well as phonons. © 2022 by the authors. Submitted for possible open access.--//-- This is an open access article Kruchinin, S.P.; Eglitis, R.I.; Babak, V.P.; Vyshyvana, I.G.; Repetsky, S.P. Effects of Electron Correlation inside Disordered Crystals. Crystals 2022, 12, 237. https://doi.org/10.3390/cryst12020237; published under the CC BY 4.0 licence.European Union Horizon 2020 Framework Programme H2020‐WIDESPREAD‐01‐2016‐2017‐Teaming; National Academy of Sciences of Ukraine 0116U002067; Institute of Solid State Physics, University of Latvia as the Center of Excellence has received funding from the European Union’s Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under grant agreement No. 739508, project CAMART2
Theory of Electron Correlation in Disordered Crystals
No full textThis paper presents a new method of describing the electronic spectrum and electrical conductivity of disordered crystals based on the Hamiltonian of electrons and phonons. Electronic states of a system are described by the tight-binding model. Expressions for Green’s functions and electrical conductivity are derived using the diagram method. Equations are obtained for the vertex parts of the mass operators of the electron–electron and electron–phonon interactions. A system of exact equations is obtained for the spectrum of elementary excitations in a crystal. This makes it possible to perform numerical calculations of the energy spectrum and to predict the properties of the system with a predetermined accuracy. In contrast to other approaches, in which electron correlations are taken into account only in the limiting cases of an infinitely large and infinitesimal electron density, in this method, electron correlations are described in the general case of an arbitrary density. The cluster expansion is obtained for the density of states and electrical conductivity of disordered systems. We show that the contribution of the electron scattering processes to clusters is decreasing, along with increasing the number of sites in the cluster, which depends on a small parameter
Energy spectrum of graphene with adsorbed potassium atoms
No full text In the present work, we study the influence of adsorbed impurities, namely potassium atoms, on the energy spectrum of electrons in graphene. The electron states of the system are described in the frame of the self-consistent multiband strong-coupling model. It is shown that, at the ordered arrangement of potassium atoms corresponding to a minimum of the free energy, the gap arises in the energy spectrum of graphene. It is 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 equal to [Formula: see text]0.25 eV. Such situation is realized if graphene is placed on a potassium support. </jats:p
Behavior of the Energy Spectrum and Electric Conduction of Doped Graphene
No full textWe 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
