Photoemission modeling of a two-liquid charge-carrier system formed at strong electron–phonon coupling

Objectives. The nature of the “waterfalls” observed in the photoemission spectra of cuprate high-temperature superconductors is explained by calculating the angle-resolved photoemission spectra of systems with significant electron–phonon interaction and dispersion law characteristic of cuprates. The resulting spectrum is compared with the results of experiments on superconducting cuprates.

Methods. Photoemission spectra obtained within a two-component model, comprising a liquid of large-radius bipolarons and a Fermi liquid of delocalized charge carriers, are calculated based on Fermi’s golden rule using the bipolaron and polaron binding energies, polarization field energy, and wave functions of charge carriers in them. The approach is based on previous findings that such a two-liquid system forms the ground and weakly excited states of systems with strong Fröhlich electron–phonon interaction.

Results. Angle-resolved photoemission spectra of systems with strong electron–phonon interaction and cupratelike dispersion were calculated using the parameters of a two-fluid charge-carrier system, which were obtained by minimizing the free energy of the system. Features of the resulting spectra observed in the experimental spectra of cuprate superconductors with the corresponding doping level provide a basis to analyze their physical causes. 

Conclusions. The model used for the calculations is characterized by different energies of relaxation following the photoemission from the self-trapped state and delocalized state, which coexist and divide the momentum space in accordance with the Pauli exclusion principle under long-range strong electron–phonon interaction. This energy difference, which leads to the formation of so-called waterfalls in the angle-resolved photoemission spectra (ARPES spectra) in the nodal direction, also determines their heights. The wave vector of the waterfall is associated with the equilibrium size of bipolarons at given doping level and temperature by the uncertainty principle, as well as the change in this wave vector with varying doping level that agrees with the phenomena observed in the experimental spectra.

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