Quantum theory of solids

The investigations in the field of quantum theory of solids at ICMP are active since 70s-80s and first were aimed to develop the phase transitions theory as well as to describe the various phenomena in ferroelectric materials with the help of microscopic models with short-range interactions utilizing X-operators approach (R.R. Levitskii, I.V Stasyuk). One of the first accomplishments was the development of microscopic theory of induced optical effects in dielectric crystals (electrooptical and piezooptical effects, electro and piezo-gyration, magneto-optical effect) that helped to describe and predict the anomalies of optical properties in the vicinity of structural and ferroelectric phase transitions (I.V Stasyuk, S.S.Kotsur, R.Ya.Stetsiv, O.L.Ivankiv).

The ongoing investigations were focused on the problems of microscopic description of phase transitions and physical effects induced by short-range correlations in electronic systems with metal-insulator transition and valency-changing, high-temperature superconductors, crystals and molecular systems with hydrogen bonds, ferroelectrics, magnetics, ionic conductors and intercalated crystal structures (I.V. Stasyuk, A.M. Shvaika, R.R. Levitskii, O.V. Derzhko, T.Ye.Krokhmalskii, T.M. Verkholyak, N.I. Pavlenko, A.P. Moina, Ya.Y. Shchur, O.V.Velychko, T.S. Mysakovych).

In the theory of strongly correlated electron systems the conditions of occurrence of first and second order phase transitions between homogeneous and charge-ordered phases as well as the phase separation, transition to the superconducting state and ferroelectric instabilities in the systems with band and localized electron states have been investigated. For one and two-sublattice pseudospin-electron model the phase transitions to the different homogenous phases, the charge-ordered phase and the incommensurate phase as well as the phenomena of structural bistability depending on values of the chemical potential of electrons, asymmetry of anharmonic potentials and temperature have been described. The phase diagrams for various densities of states of conducting electrons have been obtained. It has been established that the increasing of the transversal field value (connected with the tunneling splitting) leads to the decrease of the critical temperature and then to the vanishing of the transition to incommensurate phase. For the case of strong field only the transition to the charge-ordered phase survives.

In frames of the dynamical mean field theory the approaches based on the novel diagrammatic expansions, different time decoupling and generating functional scheme have been developed. These approaches allow to construct the consistent approximate solutions both in frames of perturbation theory and non-perturbative ones. The general scheme of constructing the dynamical mean field theory equations for systems with correlated hopping has been proposed. For the asymmetric Hubbard model the features of one-particle electron and boson spectra have been investigated and the metal-insulator transition has been studied.

For the Falicov-Kimball model the exact solutions for dynamical susceptibilities have been obtained and the influence of thermally activated states on the optical conductivity spectra and the transport properties (both static and dynamical electric and thermal conductivity) in charge-ordered phase has been studied. The microscopic theory of inelastic light and X-ray scattering on the electronic excitations has been developed. The exact solution for the Falicov-Kimball model has been obtained with dynamical mean field theory. The peculiarities of resonance effects in electronic inelastic scattering in the vicinity of metal-insulator transition have been investigated.

The development of charge transfer theory for ionic conductors and crystals with superionic phases has started with the introduction of two-stage orientational-tunneling model of proton transport in chain-like molecular structures with hydrogen bonds that included strong short-range interactions of particles. This model allowed to investigate the conditions of gap opening in the spectrum and the changes of conductivity type as well as to study the dynamics of charge transfer (so-called correlated proton-electron transfer effect) along the hydrogen bond.

These ideas were used in the model for M₃H(XO₄)₂ (M=Rb, Cs, NH₄; X=S, Se) family of superionic crystals that allowed to describe the thermodynamic properties and superionic phase transitions connected with “order-disorder” and “localization-delocalization” transitions in proton subsystem and investigate the influence of orientational dynamics of XO₄ groups on the sequence of phase transitions and topology of phase diagrams. It was shown that the proton transfer mechanism is based on strong local proton-phonon interaction and effect of proton polaron. The activation energy in ferroelastic and superionic phases has been calculated and the quantitative description of the observed temperature dependencies is proposed.

Two-band pseudospin-electron model has been proposed for the description of intercalation phenomena in semiconductors. The possibility of phase separation on the phases with different concentration of ions has been analyzed. The microscopic mechanism of electret effect induced by nickel intercalation in layered crystals of gallium and indium selenates has been proposed.

The general scheme for calculation of thermodynamic and dynamic properties for spin lattice models with various types of interaction has been established. The theory of thermodynamic properties of quantum spin chains with periodically changed or random parameters as well as the theory of dynamical properties of quantum spin chains has been developed. The effects induced by the localized magnon or electron states in quantum spin or electron models on one-, two- and three-dimensional geometrically frustrated lattices (Peierls instability in strong external magnetic fields, residual entropy in ground state, universal low-temperature thermodynamics, phase transitions of geometric nature, ferromagnetism of electronic models in ground state and so on) has been studied.

In the field of complex and mixed ferroelectric systems the microscopic multi-state models with local correlations for the description of ferroelectrics with coexistence of ferro- and antiferroelectric ordering in different directions have been proposed. On this basis the theory of thermodynamic and dielectric properties of DMAAlS-DMAGaS crystals, glycine phosphite and Rochelle salt has been developed. The observed anomalies of transversal component of dielectric susceptibility of glycine phosphite crystal in transverse electric field have been described and the existence of similar effect in Rochelle salt has been predicted.

The characteristic features of structural phase transitions connected with displacement and arrangement of protons has been revealed, the interpretation of inelastic scattering and infrared absorption spectra as well as the phonon contribution into calorimetric measurements has been proposed. The results obtained for the proposed theoretical models are in good agreement with the experiments for KDP and CDP crystals.

The theory of field effects for ferroelectric crystals with hydrogen bonds that possess ferro- and antiferroelectric phase transitions as well as the ones with the proton glass phase has been developed. The effects, induced by the external electric field and external stress, have been described in frames of this theory. The satisfactory agreement with the numerous experimental data for the KDP, ADP, CDP crystals and Rochelle salt has been obtained.

For mixed ferroelectrics the phase diagrams have been obtained in frames of the cluster approach with nonequilibrium distribution of structural elements that undergo ferro- or antiferroelectric arrangement. It has been shown that it is possible to describe the dipole glass phase within the non-stochastic set of pair correlation functions for nearest neighbouring structural elements. The proposed theory is capable to describe experimentally observed properties of solid mixtures of ferroelectric crystals RbH₂PO₄ and NH₄H₂PO₄ (Rb_n(NH₄)_1-nH₂PO₄).