Superconductivity in Electronic Systems with Strong Correlations
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uperconductivity in Electronic Systems with Strong Correlations N. M. Plakida* Joint Institute for Nuclear Research, Dubna, 141980 Russia *e-mail: [email protected] Received December 20, 2019; revised January 16, 2020; accepted January 29, 2020
Abstract—We report a consistent microscopic theory of superconductivity for strongly correlated electronic systems. The electronic spectrum and superconductivity are studied using the Bogoliubov–Tyablikov Green functions for the projected (Hubbard) electronic operators. The extended Hubbard model is considered where the intersite Coulomb repulsion and the electron-phonon interaction are taken into account. The d -wave pairing with high-Tc is found induced by the strong kinematical interaction of electrons with spin fluctuations that proves the spin-fluctuation mechanism of high-temperature superconductivity. DOI: 10.1134/S1063779620040577
1. INTRODUCTION Discovery of high-temperature superconductivity (HTSC) in copper-oxides (cuprates) by Bednorz and Müller [1] caused an unprecedented scientific activity in study of this extraordinary phenomenon (see, e.g., [2, 3]). In recent years intensive experimental investigations have presented detailed information concerning unconventional physical properties of cuprates. However, theoretical studies of various microscopical models have not yet brought about a commonly accepted theory of HTSC. The main problem in a theoretical study of the cuprate superconductors is that strong electron correlations there precludes from application of the conventional Fermi-liquid approach in description of their electronic structure [4]. They are Mott–Hubbard (more accurately, charge-transfer) antiferromagnetic (AF) insulators where the conduction band splits into two Hubbard subbands: the filled singly occupied by electrons and the empty one for doubly occupied electronic states. They become poor conductors when doped by holes or electrons in the corresponding subbands. To describe such strongly correlated metal one has to use the projected (Hubbard) electronic operators which are difficult to treat. Various theoretical methods were used to take into account the complicated non-Fermionic character of these operators, such as numerical simulation for finite clusters, variational approach, diagram technique, cluster approximations, slave boson (electron) representation, etc. (see, e.g., [3]). Recently we have developed a microscopic theory of spin excitations [3, 5, 6] and superconductivity [7‒11] for cuprates. We employed the equation of motion method for Bogoliubov–Tyablikov [12] Green functions (GFs) in terms of the Hubbard operators
(HOs) which enabled us to take into account rigorously the non-Fermionic character of electronic operators. An important role of the kinematical interaction for the HOs was emphasized in studying the superconductivity and the electronic spectrum. In this report we present the results of these investigations. At first we consider a model of electronic system with strong correlations and explain how the kinematical
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