Isotope Effect in High-T_c Superconductors

Isotope Effect in High-T_C Superconductors, D. R. Harshman J. D. Dow and A. T. Fiory [slides]

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 YBa₂Cu₃O_7−δ, 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 YBa₂Cu₃O_7−δ, 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 PrBa₂Cu₃O_7−δ 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 CuO₂ 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.

D. R. Harshman, J. D. Dow and A. T. Fiory, Phys. Rev. B 77, 024523 (2008).

Variation of the oxygen isotope effect parameter with normalized transition temperatures for Pr-, La-, Zn- and Sr-doped YBa2Cu3O7−δ. The dashed curve is the isovalent pair breaking theory, applicable for Zn and Sr substitutions. The solid curve is the heterovalent theory, applicable for La and Pr substitutions.

Exponent of the oxygen isotope effect in the superconducting transition, α0, plotted against the Meissner-effect fraction for Pr-doped YBa2Cu3O7−δ (fraction is equal to unity when undoped). Labels denote TC and Pr fraction x per formula unit for each datum. The dashed curve is a guide to the eye.

Reply to “Comment on ‘Isotope effect in high-T_C superconductors’ ” [arXiv] Our paper on the isotope effect in high-temperature superconductors with cation substitutions presents a comprehensive analysis rooted completely in the experimental evidence. In this Reply we show that pairbreaking disorder, isotope effects, doping-induced variations in T_C and in the magnetic penetration depth, Coulomb’s law, and Anderson’s theorem are treated with correct physical and mathematical fundamentals. In contrast, the theory fostered in the Comment by Alexandrov and Zhao contradicts several specific experimental facts, eight of which are briefly discussed. Their Comment also uncritically repeats a previously discredited assertion of an isotope effect in the superconducting carrier mass, incorrectly assumes that cation doping continuously varies intrinsic superconducting parameters, unjustifiably assigns importance to data from samples with serious quality problems, and renders a false estimate of the pair-breaking strength.

D. R. Harshman, J. D. Dow and A. T. Fiory, Phys. Rev. B 80, 136502 (2009).