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Physical review. B, Condensed matter

Superconductivity, Faraday effect, and optical absorption in the commensurate flux phase of thet-Jmodel

J. P. Rodriguez, Benoît Douçot

Published Jan 1, 1992• 18 citations
Publisher

Abstract

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-${\mathit{T}}_{\mathit{c}}$ superconducting oxides.

DOI
10.1103/physrevb.45.971

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We investigate T=0 properties of the commensurate flux phases, a class of variational wave functions for the t-J model proposed recently by Anderson, Shastry, and Hristopoulos and which generalize the (1/2-flux state of Affleck and Marston away from half-filling. These states can be formally written in the quantum spin liquid form, the singlet bond amplitudes of which break the lattice translational symmetry. The supercell of the electromagnetic gauge (defining the fictitious flux) imposes the actual periodicities of the correlated wave function. Their order of commensurability with the lattice unit length is closely related to the hole density.

Physical review. B, Condensed matter•Oct 1, 1989•16 citations
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.
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​.
Both the ac conductivity and the local dynamic spin response function of the commensurate flux phase of the t-J model in two dimensions are computed near half filling. This purported anyonic superconductor shows two different zero-temperature gaps in these quantities, which correspond to the gap for quasiparticle charge excitations and quasiparticle spin excitations, respectively. In both instances, the gap exists over the entire Fermi surface. The ac conductivity also shows the expected Drude \ensuremath{\delta}-function peak with a weight that scales with the hole concentration and with an optical mass given by 2.95 in units of the band mass, (2t${)}^{\mathrm{\ensuremath{-}}1}$. This value agrees with that obtained from exact cluster calculations on the t-J model.
We consider electromagnetic response and kinetic properties of a strongly correlated two-dimensional electron system having parity- and time-reversal symmetry violating ground state. An important example of such a state is presented by a generalized flux phase of the doped Mott insulator with a fictitious magnetic field commensurate with filling. We observe that electromagnetic response functions of the compressible flux states exhibit no superconducting behaviour. Processes of spinon and holon scattering by fluctuations of a fictitious magnetic field produce a relaxation of the system. On the basis of the quantum kinetic equation we find frequency- and momentum-dependent electrical and thermal conductivities and thermopower of a generalized flux phase.
The uniform flux phases of the t-J model are studied using a slave boson representation. The gaussian fluctuations around the mean field saddle point are calculated. A key feature is the cancellation of Hall conductances of the spinons and the holons, in the limit of small doping. This cancellation leads to a pole in the global electromagnetic response function, in a mechanism which is very similar to anyon superconductivity. Our main focus has been to evaluate the Hall conductance of the global system as a function of frequency and wave vector. Using various examples, we show that because of the cancellation of the two Hall conductances in the static and long wave-length limit, the behaviour of the global system is very sensitive to lattice effects. For instance, P. Wiegmann has found that the global Hall conductance vanishes in the static and long wave length limit, if one uses the response functions for the two dimensional continuous system. However, a direct calculation of the response functions starting from the Hofstadter spectrum leads to a finite Hall conductance in the absence of an external field. We show how this formalism can be used to calculate the local magnetic field which muons are expected to measure. The electric field of the muons induces a finite Hall current which in turn creates a finite magnetic field at the muon sites. Screening of the magnetic field by the Meissner effect has been taken into account and dielectric screening as well. Preliminary results indicate that the predicted fields are approximately one order of magnitude larger than the upper bound from experimental results obtained by the Vancouver group.
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.
We investigate T=0 properties of the commensurate flux phases, a class of variational wave functions for the t-J model proposed recently by Anderson, Shastry, and Hristopoulos and which generalize the (1/2-flux state of Affleck and Marston away from half-filling. These states can be formally written in the quantum spin liquid form, the singlet bond amplitudes of which break the lattice translational symmetry. The supercell of the electromagnetic gauge (defining the fictitious flux) imposes the actual periodicities of the correlated wave function. Their order of commensurability with the lattice unit length is closely related to the hole density.