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Physical Review Letters

Normal-state properties of the uniform resonating-valence-bond state

Naoto Nagaosa, Patrick A. Lee

Published May 14, 1990• 612 citations
Publisher

Abstract

We study a version of the uniform resonating-valence-band state in which fermions and spinless bosons are coupled by a gauge field. We show that above the Bose-Einstein temperature, the boson inverse lifetime due to scattering by the gauge field is of order kT, which suppresses the condensation temperature and leads to a linear T resistivity. The Hall number is proportional to the hole density and temperature dependent. The single-particle spectral weight exhibits a continuum plus a broadened peak. The ``Fermi surface'' area satisfies Luttinger's theorem. Comparison with the anomalous normal-state properties of oxide superconductors is made.

DOI
10.1103/physrevlett.64.2450

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We study a version of the uniform resonating-valence-band state in which fermions and spinless bosons are coupled by a gauge field. We show that above the Bose-Einstein temperature, the boson inverse lifetime due to scattering by the gauge field is of order kT, which suppresses the condensation temperature and leads to a linear T resistivity. The Hall number is proportional to the hole density and temperature dependent. The single-particle spectral weight exhibits a continuum plus a broadened peak. The ``Fermi surface'' area satisfies Luttinger's theorem. Comparison with the anomalous normal-state properties of oxide superconductors is made.
The effect of gauge fields representing the fluctuations of the local constraint and those of the phases of the bond order parameters is examined for the uniform RVB state, which is a mean-field (MF) solution of the t-J model within the slave-boson formalism. It is found that the crossover temperature for the Bose condensation of holons, T BE , below which the system may be essentially considered to be a Fermi liquid, is considerably reduced as compared with that in the MF approximation. The temperature dependences of the transport relaxation rate and the electrical resistivity are also examined
In a recent review by Anderson and co-workers, it was pointed out that an early resonating valence bond (RVB) theory is able to explain a number of unusual properties of high-temperature superconducting (SC) Cu oxides. Here we extend previous calculations to study more systematically the low-energy physical properties of the plain vanilla ddd-wave RVB state, and to compare the results with the available experiments. We use a renormalized mean-field theory combined with variational Monte Carlo and power Lanczos methods to study the RVB state of an extended $t\text{\ensuremath{-}}J$ model in a square lattice with parameters suitable for the hole-doped Cu oxides. The physical observable quantities we study include the specific heat, the linear residual thermal conductivity, the in-plane magnetic penetration depth, the quasiparticle energy at the antinode $(\ensuremath{\pi},0)$, the superconducting energy gap, the quasiparticle spectra, and the Drude weights. The traits of nodes (including kF{k}_{F}kF​, the Fermi velocity vF{v}_{F}vF​, and the velocity along Fermi surface v2{v}_{2}v2​), and the SC order parameter are studied. Comparisons of the theory and the experiments in cuprates show an overall qualitative agreement, especially on their doping dependences.
We derive the neutral fermion excitation spectrum in the resonating-valence-bond state based on a fermion-boson field theory. It is formally shown that charge-eee bosons are created upon doping while the neutral fermion excitation remains gapless, predicting a linear low-temperature specific heat $C\ensuremath{\propto}\ensuremath{\gamma}T$ in the superconducting state. Bose condensation in doped samples leads to the observed superconductivity with true "off-diagonal long-range order."
The dc transport and dynamical conductivity of a resonating-valence-bond crystal is studied at finite temperatures. The charge carriers, or holons, are assumed to be bosons which scatter inelastically with neutral spin excitations, or spinons, which are assumed to be gapless fermions. The dc resistivity arising from holon-spinon scattering in lowest order is found to vary with temperature as T3/2{T}^{3/2}T3/2. The inelastic scattering leads to a strong temperature dependence in the low-frequency conductivity and enhanced absorption in the midinfrared, in qualitative agreement with reflectivity experiments on high-temperature superconducting oxides. However, from our analysis, it appears unlikely that a single inelastic scattering mechanism can explain all the main features observed in these experiments.