Distribution of charge carriers at strong electron–phonon interaction and “vertical dispersion” in ARPES spectra of cuprates

•Strong Frohlich electron–phonon coupling at essential carriers density is studied.•Carriers distribution admitting states with momentum uncertainty is constructed.•It describes the momentum space partition between autolocalized and free carriers.•Filled autolocalized states kill the low-momentum part of free-carriers dispersion.•This displays itself in ARPES spectra as “waterfalls” observed in cuprates.

Strong electron–phonon interaction (EPI) generating spontaneous breaking translational symmetry (polarons formation) is acknowledged in lightly doped cuprates due to interpretation of broad bands in their ARPES and optical conductivity spectra. To study systems with strong EPI at significant carrier density we construct distribution suitable for carriers with momentum uncertainty. Obtained concentrations of carriers in different states are used to predict ARPES spectra of such systems. Doping evolution of spectra calculated and “vertical dispersion” in them demonstrate the excellent qualitative and quantitative agreement with those observed in cuprates. “Vertical dispersion” in undoped and essentially doped cuprates is understood from a single viewpoint.