Free energy of a two-liquid system of charge carriers in strongly coupled electron and phonon fields and common nature of three phases in hole-doped cuprates.

Hole-doped cuprates exhibit partially coexisting pseudogap (PG), charge ordering (CO) and superconductivity; we show that there exists a class of systems in which they have a single nature as it has recently been supposed. Since the charge-ordered phase exhibits large frozen deformation of the lattice, we develop a method for calculating the phase diagram of a system with strong long-range (Fröhlich) electron-phonon interaction. Using a variational approach, we calculate the free energy of a two-liquid system of carriers with cuprate-like dispersion comprising a liquid of autolocalized carriers (large polarons and bipolarons) and Fermi liquid of delocalized carriers. Comparing it with the free energy of pure Fermi liquid and calculating (with standard methods of Bose liquid theory) a temperature of the superfluid transition in the large-bipolaron liquid we identify regions in the phase diagram with the presence of PG (caused by the impact of the (bi)polarons potential on delocalized quasiparticles), CO and superconductivity. They are located in the same places in the diagram as in hole-doped cuprates, and, as in the latter, the shape of the calculated phase diagram is resistant to wide-range changes in the characteristics of the system. As in cuprates, the calculated temperature of the superconducting transition increases with the number of conducting planes in the unit cell, the superfluid density decreases with doping at overdoping, the bipolaron density (and bipolaronic plasmon energy) saturates at optimal doping. Thus, the similarity of the considered system with hole-doped cuprates is not limited to the phase diagram. The results obtained allow us to discuss ways of increasing the temperature of the superfluid transition in the large-bipolaron liquid and open up the possibility of studying the current-carrying state and properties of the bipolaron condensate.

Strong long-range electron-phonon interaction as possible driving force for charge ordering in cuprates.

A model resulting in charge ordering (CO) similar to that observed in cuprate superconductors is under study. It includes strong long-range electron-phonon interaction (EPI) and high density of correlated carriers. Coexistence of large bipolarons and delocalized carriers is a feature of such system. We develop generalized variation method to calculate the bipolaron size (CO period) in the ground normal state of such system at various doping. The approach allows the revealing of a possible physical reason of strongly different doping behavior of the CO wave vector in different cuprates. Obtained doping dependences of the CO period and temperature of the CO decay demonstrate quantitative agreement with those observed in cuprates. Predicted in the suggested approach ratio of the CO wave vector to the wave vector of the high-energy anomaly (HEA) in ARPES spectrum is in consent with that in cuprates. Calculated resonant x-rays scattering on the CO emerging in the model is in good agreement with experiments on cuprates including the asymmetry of the CO peaks' cross-section. A gap arises in the spectrum of delocalized carriers near antinodal direction due to their scattering on the periodic potential created by autolocalized carriers, analogously to photon crystal effect.