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

We consider photoemission from cuprate high-temperature superconductors taking into account joint relaxation of strongly coupled fields: a field of correlated electrons and phonon field. Such relaxation occurs in systems with predominantly long-range electron-phonon interaction at sufficiently high carrier concentration due to coexistence of autolocalized and delocalized carriers. A simple method to calculate analytically a high-energy part of the ARPES spectrum arising is proposed. The approach suggested yields all the high-energy spectral features like broad bands of Gaussian shape and vertical dispersion patterns being in good quantitative agreement with the experiments at any doping with both types of carriers. Demonstrated coexistence of autolocalized and delocalized carriers in cuprate superconductors is important for understanding their transport and magnetic properties. Presence of large-radius autolocalized carriers shown may be helpful in explanation of charge ordering in doped cuprates.