Doping dependence of critical temperature for superconductivity induced by hole-phonon interaction

To understand the nature of the high-temperature superconductors (cuprates) we have taken into consideration the interaction terms, which possess the structure of the hole-phonon (HP) and hole-hole-phonon (HHP) type. It was shown that for the high value of the HHP potential in comparison to HP, the superconducting critical temperature (TC) reaches the maximum value for the low concentration of holes, which fairly corresponds with the observed maximum of TC for hole-doped cuprates. The analysis was performed within the framework of the Eliashberg approach.