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Physical review. B, Condensed matter

Flux binding and superconductivity in thet-Jmodel

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

Published Jan 1, 1994• 10 citations
Publisher

Abstract

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 ${\mathit{k}}_{\mathit{f}}$.

DOI
10.1103/physrevb.49.607

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Physical review. B, Condensed matter•Mar 1, 1991•11 citations
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​.
A generalized slave-particle scheme is introduced to the t-J model including the non-local effects. We find a charge-spin decoupled state in which the non-local gauge fields play the roles of statistics-transmutation. As a result, the gauge fluctuation becomes massive and the electromagnetic response function exhibits the Meissner effect, like in the free-semion system, but without breaking the time-reversal and parity symmetries due to the cancellation between charge and spin degrees of freedom in the low-energy, long-wavelength regime. We also calculate the momentum distribution of electrons which shows a characteristic scale equals to the Fermi momentum kf.
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.
Using a large-N slave-boson formulation of the t-J model on the square lattice that has explicit spinon-holon decoupling of the correlated electron, we study the stability and electromagnetic response of the commensurate flux phase in the limit near half filling. A region of stability for the flux phase is found located between a dimer phase region near half filling and a fluxless metallic phase region far from half filling. The commensurate flux phase itself is found to be a superconductor of the anyon type. Furthermore, it is shown that the parity--time-reversal--violating characteristic of this phase results in a frequency-dependent Faraday effect. This effect manifests itself as a zero-field Hall effect in the low-frequency limit, where the off-diagonal conductance scales with the hole concentration. Associated with this result, it is also found that the commensurate flux phase supports a series of optical absorption peaks at energies on the order of J. Lastly, inclusion of instanton tunneling events in the effective gauge-field action results in the confinement of the spinon and holon degrees of freedom. This confinement effect, however, weakens exponentially as one approaches the Mott transition. The present results are discussed in the context of the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconducting oxides.
The electron-momentum distribution function in the t-J model is studied in the framework of the slave-particle approach. Within the decoupling scheme used in gauge-field and related theories, we treat formally phase and amplitude fluctuations as well as constraints without further approximations. Our result indicates that the electron Fermi surface observed in high-resolution angle-resolved photoemission and inverse-photoemission experiments cannot be explained within this framework, and the sum rule for the physical electron is not obeyed. A correct scaling behavior of the electron-momentum distribution function near k\ensuremath{\sim}kF{\mathit{k}}_{\mathit{F}}kF​ and k\ensuremath{\sim}3kF{\mathit{k}}_{\mathit{F}}kF​ in one dimension can be reproduced by considering the nonlocal string fields [Z. Y. Weng et al., Phys. Rev. B 45, 7850 (1992)], but the overall momentum distribution is still not correct, at least at the mean-field level.
Implication of our recent proposal [J. Phys. Soc. Jpn. 65 (1996) 687] to treat large-amplitude gauge-field fluctuations around the slave-boson mean-field theory for the t-J model has been explored in detail. By attaching gauge flux to spinons and holons and then treating them as free g-on's which respect the time-reversal symmetry, the optimum exclusion (g) and exchange (\a) statistics have been determined in the plane of doping rate and temperature. Two different relations between \a and g have been investigated, namely g=|\a| (Case1) and g=|\a|(2-|\a|) (Case2). The results indicate that slave fermion is favored at low doping while slave boson at high doping. For two dimension, in Case1 intermediate statistics are found in between, while in Case2 no intermediate statistics are found. The consequences of varying the dimensionality and strength of J have been studied also. The latter has no qualitative effect for both cases, while the former has a profound effect in Case1.
We study wave functions for generalized flux phases by the variational Monte Carlo method. Flux tubes are attached to the holes, which produce additional phase factors besides those due to the motion of electrons. The phase factors cancel each other when the electrons and holes interchange position at some special electron densities and, as a result, there are no orbital currents in these states. We investigate especially the one-third filled case and find a slightly lower kinetic energy than the original commensurate flux phase. We also calculate the chirality to confirm that time-reversal symmetry is also broken in these states. The analogy to the quantum-Hall-effect wave functions leads us to study modified forms of off-diagonal long-range order in the pair-correlation function. The existence of this long-range order is shown explicitly by variational Monte Carlo calculations and renormalized mean-field approximations. The flux phases do not have the usual off-diagonal long-range order but do have a modified form similar to that in the quantum Hall effect. The relationships to the slave-boson mean-field theories and anyon systems are also discussed.