Phase Transitions in the Pseudospin-Electron Model

Abstract

November 18, 2018 21:48 WSPC/Trim Size: 9in x 6in for Review Volume stasyuk˙new Phase Transitions in the Pseudospin-Electron Model 3The pseudospin-electron Hamiltonian (in form (1) with inclusion only of the g-interaction) was used by Müller with the aim of describing the anharmonic vibrations in the oxygen subsystem of the high-T c superconducting crystals of the YBaCuO type. 1 The YBa 2 Cu 3 O 7−δ crystal is a typical and most studied example of such objects. The unit cell contains, besides two superconducting planes, the chain (at the δ ≪ 1 composition) elements Cu 1 -O 1 , connected by Cu 1 -O 4 -Cu 2 bridges with Cu 2 -O 2 plains through the apical oxygen ions O 4 . The vibrations of these ions along the c-axis (perpendicularly to the plains) exhibit a strong anharmonicity. Much evidence exists in support of this concept. One can mention the EXAFS data, 2,3 Raman scattering and dielectric measurements, 4,5,6,7,8,9 local polaron phenomena, 10,11 bistabilities in the normal phase region 12 as well as neutron scattering investigations 13 or the results of the first principle LAPW calculations. 14 Despite a certain ambiguity in the data, the conclusions were made about the existence of two different equilibrium positions of the O 4 ion. The local double-well picture as an approximate simplified model was supported by the oxygen O 4 vacancy effect on the positions of apical ions observed in Ref. [15].Moreover, a connection between positions of O 4 ions and electron states in Cu 2 -O 2 plains plays an important role in YBa 2 Cu 3 O 7−δ crystals. The data given in Ref. [16] point to the existence of a significant correlation between the occupancy of electron states of the Cu 2 ion and the R O4−Cu2 distance as well as to the decrease of this distance at the transition from the metallic orthorombic phase to the semiconducting one (that takes place at δ > δ * = 0.55). These and other similar facts suggest the presence of a large electron-vibrational coupling. In the pseudospin representation, when the pseudospin variable S z i = ±1/2 defines the positions of O 4 ions, it is described by the gS z i n iσ term. Consideration based on the PEM was applied to the HTSC systems starting from Refs. [1,[17][18][19][20]. Hamiltonian similar to (1) was used by Hirsch and Tang in the study of electron states in the framework of cluster calculations. In the context of the idea concerning the effect of anharmonicity on the superconducting transition temperature, 17,18,19,21 the possible connection between superconducting pairing and the lattice anharmonicity was considered by Frick et al. 22 (the quantum Monte-Carlo calculations). In what follows, the investigations of the PEM were devoted to the analysis of the electron spectrum, 23 the pseudospin and collective dynamics, 24,25 the charge and pseudospin pair correlations and the behaviour of dielectric susceptibility. 26

On the theory of high-T_c superconductivity of doped cuprates

“…This work is dedicated to the 80th birthday of Prof. I.V. Stasyuk, a renowned Ukrainian theorist, recognizing his very valuable contribution to the theory of narrow-band metals and pseudo-spin operators in the field of phase transitions in solids [23], especially of superconducting transitions [24].…”

Phase diagrams of the Bose–Fermi–Hubbard model at finite temperature

“…Models of pseudospin-electron model type are widely used in the physics of the strongly correlated electron systems. Application of such models to high-temperature superconductors allows one to describe the thermodynamics of anharmonic oxygen ion subsystem and explain the appearance of inhomogeneous states and the bistability phenomena (see [26]). Models of a lattice gas are also used at the description of ionic conductors and at the calculation of their conductivity starting from works of Mahan [27] and others [28,29].…”