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

Abstract

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.

Relaxation of strongly coupled electron and phonon fields after photoemission and high-energy part of ARPES spectra of cuprates

“…Finally, demonstrated broken by strong EPI translational symmetry in cuprates allows also discussion of charge ordering observed in doped cuprates [29][30][31][32][33][34] in terms of the large-radius ASs formation. Indeed, the estimated radius of the bipolaron at their maximum density in cuprates is R bip ≈ 6.5 ÷ 7 Å [46]. This value is in good agreement both with the k 0 value marking the HEA position in the momentum space [6][7][8][9][10][11] and with measured experimentally period of charge ordering ( 3.3 ÷ 4a ) [29][30][31][32][33][34] in cuprates.…”

“…Thus, the electron ASs location dictates the hole ASs one, and charge ordering period does not depend on the holes density while it is lower than n 0 . For the electron-doped systems the present approach predicts change of the charge ordering period with doping: the ASs size becomes smaller with increasing doping (an example of such dependence is presented in figure 5(a) [46]), rendering the wave vector of the charge ordering larger. Similar behavior was observed in the electron doped cuprate experimentally [34], as it is illustrated with stars in figure 5(a).…”

“…The minimum of this function yields the equilibrium bipolaron radius as function of the carrier concentration. At (ε * ) −1 = 0.3, m * = m e and ε ∞ = 3 and high carrier density R bip ≈ 6.5 ÷ 7 Å [46]. According to equation ( 5) the corresponding k 0 value is about 0.35-0.37 Å −1 .…”

“…Two different values of the critical carrier density-n 0 and n 0 -appear due to the fact that at high carrier density the bipolaron volume depends essentially on the carrier density. For example, at (ε * ) −1 = 0.3, m * = m e and ε ∞ = 3 [25] the single bipolaron radius R bip ≈ 13.5 Å [14] (we estimate it as the radius of the region, that contains 0.9 part of the polarization charge) whereas at high carrier density n n 0 the calculation yields R bip ≈ 6.5 ÷ 7 Å [46]. For clarity, let us estimate doping levels p 0 and p 0 corresponding to the carrier densities n 0 and n 0 in a system with (ε * ) −1 = 0.3, ε ∞ = 3, m * = m e .…”

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

“…broad bands in ARPES and optical spectra [21][22][23][24][25][26]) there is an important distinction between highly doped systems with the strong Fröhlich EPI and those with the strong Holstein EPI. This distinction is the possibility of coexistence of autolocalized and delocalized carriers in the former systems [35][36][37][38].…”