Assessment of Fermi-liquid description for the normal state of high-Tcsuperconductors

Abstract

The applicability of Fermi-liquid theory for the normal state of the high-$T_c$ copper oxides is investigated. In the present context "Fermi-liquid theory" refers to a description in which there are two components (copper and oxygen) within the Fermi surface. This is to be contrasted with other approaches in which the Cu electrons are fully localized. Our calculations are based on a Coulomb renormalized band structure which characterizes the quasiparticle energies. This band structure arises from a variety of different but essentially equivalent mean-field techniques. The present focus is on deriving a Fermi-liquid description which combines both Coulomb-induced localization (as a precursor to the insulating state) with semirealistic band structure. The latter requires that next-nearest-neighbor oxygen-oxygen overlap integrals also be included in a tight-binding scheme. The interplay of these two effects leads to (i) a positive Hall coefficient which becomes progressively larger as the insulator is approached and reverses its sign for large doping concentration; (ii) a "pinning" of the Cu valence near the ${\mathrm{Cu}}^{2+}$ state; (iii) two important features in the density of states, one of which can be associated with the van Hove singularities and the other with band narrowing or incipient localization effects. The former occur away from the half-filled limit as a result of oxygen-oxygen overlap processes, so that the perfect nesting of the nearest-neighbor half-filled tight-binding model is significantly offset. The latter leads to a strong prediction of the theory: as in the Brinkman-Rice picture, incipient localization effects will be manifested by a progressively larger Sommerfeld coefficient $\gamma$ as the insulator is approached. This prediction needs to be tested experimentally. While transport experiments seem consistent with this behavior, more direct thermodynamic measurements are both difficult to interpret and too sample sensitive to allow clear trends to be inferred from the data. Our general conclusion is that, at present, there is no persuasive evidence to support the claim that Fermi-liquid theory is inapplicable to the copper oxides.