Correlation between optical phonon softening and superconducting $T_c$ in YBa${}_2$Cu${}_3$O${}_x$ 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.

Accepted for publication in J. Phys. Materials

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