Correlation between optical phonon softening and superconducting \(T_c\) in YBa\(_2\)Cu\(_3\)O\(_x\)

Abstract

We provide an extended mathematical description 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 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 mechanistically explained in terms of 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.