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 demonstrate partially coexisting pseudogap, chargedensity wave (CDW) and superconducting phases. Recently their common nature wassupposed due to similar doping dependence of their critical temperatures. Inthe CDW phase, a large frozen deformation of strongly ionic lattice isobserved. Like for a single carrier in a highly polarizable lattice, formultiple carriers in it the choice between delocalized states of all thecarriers and autolocalized states of some part of them is determined by minimumof free energy of interacting carrier and phonon fields. Applying variationalapproach, we calculate free energy of a two-liquid system of carriers withcuprates-like dispersion comprising liquid of autolocalized carriers (largepolarons and bipolarons) and Fermi liquid of delocalized carriers. Comparing itwith the free energy of pure Fermi liquid and calculating (with standardmethods of Bose-liquid theory) a temperature of superfluid transition in thelarge-bipolaron liquid we identify areas with presence of pseudogap (caused byimpact of (bi)polaron potential on delocalized quasiparticles), CDW andsuperconductivity in a phase diagram. They are in the same places as inhole-doped cuprates, and similarly to cuprates the shape of the calculatedphase diagram is stable with respect to wide-range change of the systemcharacteristics. Like in cuprates, the calculated temperature of thesuperconducting transition increases with the number of conducting planes inthe unit cell, the calculated superfluid density decreases with doping atoverdoping, and the bipolaron density (together with bipolaronic plasmonenergy) saturates at optimal doping. The results obtained allow us to discussways of increasing the temperature of the superfluid transition inlarge-bipolaron liquid and open a possibility of studying the current-carryingstate and properties of bipolaron condensate.