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Physical review. B, Condensed matter

Charge excitation and the normal-state transport properties in the flux-binding phase of thet-Jmodel

Zheng-Yu Weng, D. N. Sheng, C. S. Ting

Published Oct 1, 1994• 4 citations
Publisher

Abstract

Elementary excitations are discussed in the flux-binding phase [Weng, Sheng, and Ting, Phys. Rev. B 49, 607 (1994)] of the t-J model. It is shown that the density and current constraints in the gauge-theory description will dramatically modify the charge excitations. An effective Lagrangian for the normal state of the flux-binding phase is derived, and based on it the transport properties are studied. We find that the resistivity is linearly temperature dependent with a relaxation rate \ensuremath{\Elzxh}/\ensuremath{\tau}\ensuremath{\simeq}2${\mathit{k}}_{\mathit{B}}$T, and the Hall coefficient involves a second relaxation rate with the cotangent Hall angle following a ${\mathit{T}}^{2}$ law. Furthermore, the thermopower exhibits a strong doping dependence. All these features are in good agreement with the transport measurements of the high-${\mathit{T}}_{\mathit{c}}$ copper oxide compounds.

DOI
10.1103/physrevb.50.9470

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Elementary excitations are discussed in the flux-binding phase [Weng, Sheng, and Ting, Phys. Rev. B 49, 607 (1994)] of the t-J model. It is shown that the density and current constraints in the gauge-theory description will dramatically modify the charge excitations. An effective Lagrangian for the normal state of the flux-binding phase is derived, and based on it the transport properties are studied. We find that the resistivity is linearly temperature dependent with a relaxation rate \ensuremath{\Elzxh}/\ensuremath{\tau}\ensuremath{\simeq}2kB{\mathit{k}}_{\mathit{B}}kB​T, and the Hall coefficient involves a second relaxation rate with the cotangent Hall angle following a T2{\mathit{T}}^{2}T2 law. Furthermore, the thermopower exhibits a strong doping dependence. All these features are in good agreement with the transport measurements of the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ copper oxide compounds.
A real spin-charge separation scheme is found based on a saddle-point state of the t-J model. In the one-dimensional (1D) case, such a saddle-point reproduces the correct asymptotic correlations at the strong-coupling fixed point of the model. In the two-dimensional (2D) case, the transverse gauge field confining spinon and holon is shown to be gapped at finite doping so that a spin-charge deconfinement is obtained for its first time in 2D. The gap in the gauge fluctuation disappears at half-filling limit, where a long-range antiferromagnetic order is recovered at zero temperature and spinons become confined. The most interesting features of spin dynamics and transport are exhibited at finite doping where exotic residual couplings between spin and charge degrees of freedom lead to systematic anomalies with regard to a Fermi-liquid system. In spin dynamics, a commensurate antiferromagnetic fluctuation with a small, doping-dependent energy scale is found, which is characterized in momentum space by a Gaussian peak at (\ensuremath{\pi}/a,\ensuremath{\pi}/a) with a doping-dependent width (\ensuremath{\propto} \ensuremath{\surd}\ensuremath{\delta} , \ensuremath{\delta} is the doping concentration). This commensurate magnetic fluctuation contributes a non-Korringa behavior for the NMR spin-lattice relaxation rate. There also exists a characteristic temperature scale below thich a pseudogap behavior appears in the spin dynamics. Furthermore, an incommensurate magnetic fluctuation is also obtained at a finite energy regime. In the transport, a strong-range phase intereference leads to an effective holon Lagrangian which can give rise to a series of interesting phenomena including linear-T resistivity and a T2{\mathit{T}}^{2}T2 Hall angle. We discuss the striking similarities of these theoretical features with those found in the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ cuprates and give a consistent picture for the latter. Electronic properties like Fermi surface and superconducting pairing in this framework are also discussed.
Spin fluctuations enter the calculation of the superconducting transition temperature Tc{T}_{c}Tc​ only in the next-to-leading order [i.e., in O(1/N2)]{O(1/N}^{2})]O(1/N2)] of the 1/N1/N1/N expansion of the $t\ensuremath{-}J$ model. We have calculated these terms and show that they have only little influence on the value for Tc{T}_{c}Tc​ obtained in the leading order O(1/N)O(1/N)O(1/N) in the optimal and overdoped region, i.e., for dopings larger than the instability towards a flux phase. This result disagrees with recent spin-fluctuation mediated pairing theories. The discrepancies can be traced back to the fact that in our case the coupling between electrons and spins is determined by the $t\ensuremath{-}J$ model and not adjusted and that the spin susceptibility is rather broad and structureless and not strongly peaked at low energies as in spin-fluctuation models. Relating Tc{T}_{c}Tc​ and transport we show that the effective interactions in the particle-particle and particle-hole channels are not simply related within the 1/N1/N1/N expansion by different Fermi surface averages of the same interaction as in the case of phonons or spin fluctuations. As a result, we find that large values for Tc{T}_{c}Tc​ and rather small scattering rates in the normal state as found in the experiments can easily be reconciled with each other. We also show that correlation effects heavily suppress transport relaxation rates relative to quasiparticle relaxation rates in the case of phonons but not in the case of spin fluctuations.
The Hall coefficient in the strongly correlated Fermi-liquid phase of the t-J model is studied for moderate hole concentrations. We find that the quasiparticle self-energy is strongly k dependent due to gauge-field interactions. It leads to corrections to the Fermi-surface curvature and to enhancement of the quasiparticle lifetime in the holelike region. We show that a systematic treatment of the strong local correlations to next to leading order in 1/N is sufficient to give rise to a sign change in the Hall coefficient. This effect occurs near 0.20 doping for J/t=0.2 and may be relevant to the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ materials.
A generalized slave-particle scheme is introduced to study the t-J model with nonlocal effects included. A charge-spin decoupled state is found in this scheme, in which the nonlocal gauge fields play a role of attaching fictitious quantized fluxes to the particles as an effective way to describe antiferromagnetic correlation. As a result, the gauge fluctuation is suppressed in the long-wavelength limit, which shows the stability of flux binding, and the electromagnetic response function of such a state exhibits the Meissner effect. An important consequence of the present approach is that the electron, as a combination of the charge and spin degrees of freedom, does not show time-reversal and parity-symmetry-broken behavior, in contrast to the usual anyon theory. This is consistent with experimental results. The robustness of this conclusion relies on the exactness of the constraint between the charge and spin degrees of freedom as well as the flux binding condition. We also calculate the momentum distribution of electrons, which shows a characteristic scale equal to the Fermi momentum kf{\mathit{k}}_{\mathit{f}}kf​.
Low energy properties of the metallic state of the two-dimensional t - J model are presented for second neighbor hopping with hole-doping ( ) and electron-doping ( ), with various superexchange energy J . We use a closed set of equations for the Greens functions obtained from the extremely correlated Fermi liquid theory . These equations reproduce the known low energies features of the large U Hubbard model in infinite dimensions. The density and temperature dependent quasiparticle weight, decay rate and the peak spectral heights over the Brillouin zone are calculated. We also calculate the resistivity, Hall conductivity, Hall number and cotangent Hall angle. The spectral features display high thermal sensitivity at modest T for density , implying a suppression of the effective Fermi-liquid temperature by two orders of magnitude relative to the bare bandwidth. The cotangent Hall angle exhibits a T 2 behavior at low T , followed by an interesting kink at higher T . The Hall number exhibits strong renormalization due to correlations. Flipping the sign of changes the curvature of the resistivity versus T curves between convex and concave. Our results provide a natural route for understanding the observed difference in the temperature dependent resistivity of strongly correlated electron-doped and hole-doped matter.