Theory of Electron Correlation in Disordered Crystals
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Date
2022
Authors
Repetsky, Stanislav
Vyshyvana, Iryna
Kruchinin, Sergei
Bellucci, Stefano
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Abstract
This 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.
Description
Keywords
electronic spectrum, electrical conductivity, disordered crystals, the Hamiltonian of electrons and phonons, Green’s functions, the temperature Green’s functions, diagram technics, the mass operator of the Green’s function, density of states, free energy, article
Citation
Theory of Electron Correlation in Disordered Crystals / Stanislav P. Repetsky, Iryna G. Vyshyvana, Sergei P. Kruchinin, Stefano Bellucci // Materials. - 2022. - Vol. 15, Issue 3. - Article number 739.