Vibronic dispersion in the copper oxide superconductors

Attempts to describe the normal-state electronic behavior of the copper oxide superconductors have been unable to reconcile the following observations: (i) a well-defined Fermi surface with a locus predicted by band theory, but having charge carriers of a sign predicted for a Mott-Hubbard splitting of the band; (ii) a change in sign of the carriers to that predicted by band theory, but without a significant change in the locus of the Fermi surface, on overdoping beyond the narrow superconductive compositional range; (iii) a remarkable stability of the narrow range of superconductive charge-carrier concentrations in the ${\mathrm{CuO}}_2$ sheets even in the presence of charge transfer from nonsuperconductive intergrowth layers; (iv) a dramatic sensitivity of the Néel temperature of the parent compound to oxidation of the ${\mathrm{CuO}}_2$ sheets, but the persistence of antiferromagnetic spin fluctuations into the superconductive compositions; and (v) unusual transport properties that cannot be treated within the Migdal approximation and are insensitive to high magnetic fields. To address this impasse, we propose a phenomenological polaron model based on the observation that the system must accommodate to the coexistence of ‘‘ionic’’ and ‘‘covalent’’ Cu-O bonding having different equilibrium Cu-O bond lengths.