Role of anharmonicity in the high-Tcsuperconductors

It is suggested that the high-transition temperatures ($T_c\text{'}\mathrm{s}$) observed in the superconducting oxygen-deficient perovskites may be a consequence of highly anharmonic potentials. Evidence is cited which demonstrates that the harmonic approximation fails badly for ${\mathrm{Cu}}^{2+}$ ions in a ligand field with octahedral symmetry. Since Bardeen-Cooper-Schrieffer theory and its strong-coupling extensions are based on the harmonic approximation, the reasons for their failure to describe the Cu-based perovskites can now be understood. These conclusions suggest a new interpretation for the recent results in oxygen-isotope substitution experiments. This new interpretation may be consistent with an electron-lattice mechanism for superconductivity. Surprising similarities between the heme group from hemoglobin, hemocyanin, and the oxygen-deficient perovskites are discussed. Based on these ideas, the criteria for reaching high $T_c\text{'}\mathrm{s}$ in Ni-substituted perovskites are discussed. It is also suggested that nonperovskite materials, which have nearly degenerate, multiple-valley potential wells, may be potential high-$T_c$ superconductors.