Correlation between optical phonon softening and superconducting T c in YBa2Cu3Ox within d-wave Eliashberg theory

Abstract We provide a mathematical description, based on d -wave Eliashberg theory, of the strong correlation between the experimentally observed softening of Raman modes associated with in-plane oxygen motions and the corresponding superconducting critical temperature T c , as a function of oxygen doping x , in YBa 2 Cu 3 O x . The theoretical model provides a direct link between physical trends of soft optical A g (in-plane) oxygen modes, the level of oxygen doping x , and the superconducting T c . Different regimes observed in the trend of T c vs doping can be related to corresponding regimes of optical phonon softening in the Raman spectra. These results provide further evidence related to the physical origin of high-temperature superconductivity in rare-earth cuprate oxides and to the significant role of electron–phonon coupling therein.