Isotope effect in high-Tcsuperconductors

Abstract

For high-${T}_{c}$ superconductors in which transition temperatures ${T}_{c}$ are reduced by doping, the oxygen isotope effect (OIE) coefficient in ${T}_{c}$ is shown to increase systematically with the pair-breaking rate and with the valence difference between the substituted and native ions. Moreover, the OIE in ${T}_{c}$ tends to zero as one approaches optimum (or ideal) stoichiometry at which the quality of the superconducting condensate is maximized. In materials with isovalent substitutions, e.g., Sr for Ba or Zn for Cu in $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$, the small OIE of the parent (unsubstituted) compound is magnified owing to pair-breaking disorder. In materials with heterovalent substitutions, e.g., La or Pr for Ba, where carrier densities are necessarily changed, pair breaking induces a much larger OIE. A seminal case is Pr-doped $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$, where data were previously misinterpreted owing to the false assumption that Pr substitutes only for Y. It is now clear, however, that the decrease in ${T}_{c}$ observed with Pr doping actually arises from pair breaking caused by Pr-on-Ba-site defects introduced during crystal growth. When $\mathrm{Pr}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ is grown correctly without such defects, ${T}_{c}$ remains unchanged (as in the case of most other rare-earth substitutions for Y). Invariance of ${T}_{c}$ under a 60% rare-earth mass increase provides strong evidence against phononic pairing mechanisms. The fact that ${T}_{c}$ drops when Pr substitutes for Ba but not for Y indicates that the superconducting hole condensate resides in the BaO layers, where pair breaking degrades ${T}_{c}$ and dramatically increases the OIE. Superconductive pairing modeled on Coulomb coupling between the hole (BaO) and the electron $(\mathrm{Cu}{\mathrm{O}}_{2})$ layers is shown to resolve the serious shortcomings inherent in approaches based on electron-phonon interactions and is found to be generally applicable. Moreover, the OIE in the magnetic penetration depth in alloys is shown to be constant, with degradation of ${T}_{c}$ up to 50%, and thus is unrelated to the OIE in ${T}_{c}$.