Vibronic dispersion in the copper oxide superconductors

Abstract

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 CuO2 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 CuO2 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. We designate this entity a correlation polaron. Covalent Cu-O bonding with molecular-orbital formation occurs within the polaron, which moves in a background of ionic Cu-O bonding. Vibronic coupling at the ‘‘avoided crossover’’ from ionic to covalent bonding allows diffusional motion of uncoupled polarons without any motional enthalpy in the mobility. At temperatures T>Tl≳300 K the polarons are uncoupled and move randomly; in the narrow superconductive compositional range they condense below Tl to form a distinguishable thermodynamic phase consisting of extended vibronic states. In this ‘‘polaron liquid,’’ a distinction between bonding and antibonding states within the polarons opens a gap at the half-band position, not the Fermi energy, and some spectral weight associated with the ionic Cu-O bonding still remains at the energies of the upper and lower Hubbard bands of the parent compound.

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