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Physical review. B, Condensed matter

dc transport and optical conductivity in a resonating-valence-bond crystal

Catherine Kallin, A. J. Berlinsky, W.-K. Wu

Published Mar 1, 1989• 7 citations
Publisher

Abstract

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 ${T}^{3/2}$. 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.

DOI
10.1103/physrevb.39.4267

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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.
We investigate the conductivity using Green's functions in the Tomonaga-Luttinger liquid. It is shown that the resistivity has a linear temperature dependence if we take account of the physical process that the accelerated electron decays into spinon and holon. The effect of impurity scattering becomes visible only below a crossover temperature which strongly depends on the impurity strength, energy cutoff, and spin and charge velocities. The optical conductivity is also studied and it is shown that the relaxation rate has a linear frequency dependence.
We study the response to a static electric field (charge stiffness) and the frequency-dependent conductivity of the Hubbard model in a resonant-valence-bond-type paramagnetic phase. This phase is described by means of a charge and spin rotational-invariant approach, based on a mixed fermion-boson representation of the original strongly correlated electrons. We found that the Mott transition at half filling is well described by the charge stiffness behavior, and that the values for this quantity off half filling agree reasonably well with numerical results. Furthermore, for the frequency-dependent conductivity we trace back to the origin of the band that appears inside the Hubbard gap to magnetic pair breaking. This points to a magnetic origin of the midinfrared band in high-Tc{T}_{c}Tc​ compounds.
The effects of nonmagnetic strong scatterers (unitary limit) on magnetic and transport properties are studied for resonating-valence-bond states in both the slave-boson and slave-fermion mean-field theories with the gap for the triplet excitations. In the d-wave pairing state of the slave-boson mean-field theory in two dimensions, there is no true gap for spinons, but the Anderson localization occurs, which leads to the local moment when the repulsive interaction is taken into account. In the slave-fermion mean-field theory, local moments are found bound to nonmagnetic impurities as a result of (staggered) gauge interaction. However, in both theories, localization of spinon does not appear in the resistivity, which shows the classical value for the holon.
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."
Electric resistivity is examined in the constrained Hilbert space of a doped Mott insulator, which is dictated by a non-Ioffe-Larkin composition rule due to the underlying mutual Chern-Simons topological gauge structure. In the low-temperature pseudogap phase, where holons remain condensed while spinons proliferate, charge transport is governed by chiral spinon excitation, comprising a bosonic spin-12\frac{1}{2}21​ at the core of a supercurrent vortex. It leads to vanishing resistivity with the confinement of the spinons in the superconducting phase but low-TTT divergence of the resistivity once the spinon confinement is disrupted by external magnetic fields. In the latter, the chiral spinons will generate a Hall number nH={n}_{H}=nH​= doping concentration $\ensuremath{\delta}$ and a Nernst effect to signal underlying long-range entanglement between the charge and spin degrees of freedom. Their presence is further reflected in thermodynamic quantities such as specific heat and spin susceptibility. Finally, in the high-temperature spin-disordered phase, it is shown that the holons exhibit linear-TTT resistivity by scattering with the spinons acting as free local moments, which generate randomized gauge fluxes as perceived by the charge degree of freedom.