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Physical Review B

Investigation of the adequacy of the two-dimensional t−J model for high-temperature superconductivity

Gang Su

Published Sep 21, 2005• 4 citations
Publisher

Abstract

It is widely thought that the two-dimensional (2D) $t\text{\ensuremath{-}}J$ model captures essential features of the cuprate oxides. However, some recent results on the pairing correlations in this model, which were obtained by various numerical or analytical methods, are controversial. Therefore, whether the 2D $t\text{\ensuremath{-}}J$ model is really suitable for the cuprate oxides is still under debate. We argue that the 2D $t\text{\ensuremath{-}}J$ model may be inadequate for overall describing high temperature superconductivity.

DOI
10.1103/physrevb.72.092510

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It is widely thought that the two-dimensional (2D) t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model captures essential features of the cuprate oxides. However, some recent results on the pairing correlations in this model, which were obtained by various numerical or analytical methods, are controversial. Therefore, whether the 2D t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model is really suitable for the cuprate oxides is still under debate. We argue that the 2D t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model may be inadequate for overall describing high temperature superconductivity.
Theoretical ideas and experimental results concerning high-temperature superconductors are reviewed. Special emphasis is given to calculations performed with the help of computers applied to models of strongly correlated electrons proposed to describe the two-dimensional CuO2{\mathrm{O}}_{2}O2​ planes. The review also includes results using several analytical techniques. The one- and three-band Hubbard models and the $t\ensuremath{-}J$ model are discussed, and their behavior compared against experiments when available. The author found, among the conclusions of the review, that some experimentally observed unusual properties of the cuprates have a natural explanation through Hubbard-like models. In particular, abnormal features like the mid-infrared band of the optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$, the new states observed in the gap in photoemission experiments, the behavior of the spin correlations with doping, and the presence of phase separation in the copper oxide superconductors may be explained, at least in part, by these models. Finally, the existence of superconductivity in Hubbard-like models is analyzed. Some aspects of the recently proposed ideas to describe the cuprates as having a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconducting condensate at low temperatures are discussed. Numerical results favor this scenario over others. It is concluded that computational techniques provide a useful, unbiased tool for studying the difficult regime where electrons are strongly interacting, and that considerable progress can be achieved by comparing numerical results against analytical predictions for the properties of these models. Future directions of the active field of computational studies of correlated electrons are briefly discussed.
The electronic state of high-temperature cuprates is investigated on the basis of the two-dimensional Hubbard model. We investigate the three-band Hubbard model (which is sometimes called the d-p model) as well as the single-band Hubbard model. In particular, the three-band Hubbard model with d and p orbitals in the CuO 2 plane probably captures the physics of high-temperature superconductivity. Numerical studies of the two-dimensional d-p and Hubbard models have shown that they exhibit antiferromagnetism, stripes, d-wave pairing, coexistent antiferromagnetism with superconductivity, and arc spectra. They are basic phenomena seen in the high-temperature cuprates.
The class of high T c superconductors share one common structural aspect, the existence of planes of copper and oxygen ions.These planes are thought to be the source of the superconducting behaviour.They can be represented as a two-dimensional lattice of ions, which facilitates their study using numerical models.One such model is the t -J model.In most studies utilising numerical models, the planes have been considered isotropic.However, recent analysis of cuprate structure has illustrated that this may not be representative of the copper oxide planes.A number of cuprate structures exhibit different phases in which the planes are not isotropic, such as the low temperature orthorhombic and low temperature tetragonal phases.This work will examine the effects of introducing anisotropy into the t -J model in order to understand how these phases affect the results gained from numerical studies.
We have studied the behavior of pairing correlations and susceptibilities in the repulsive Hubbard model on a two-dimensional square lattice by Monte Carlo simulations. Lattice sizes up to 8\ifmmode\times\else\texttimes\fi{}8, temperatures down to T=0.083 (in units where the bandwidth W=8), interaction strengths up to U=16, and several band fillings ranging from (1/2-filled to (1/4-filled were considered. Our results suggest that the model does not exhibit superconductivity. The implications with respect to possible mechanisms for high-Tc{T}_{c}Tc​ superconductivity in oxides are discussed.
We reexamine whether the essence of high-Tc superconductivity is contained in doped Hubbard models on the square lattice by using recently developed pre-projected Gaussian-basis Monte Carlo method. The superconducting correlations of the dx2-y2 wave symmetry in the ground state at distance r decays essentially as inverse cubic of r. The upper bound of the correlation at long distances estimated by this unbiased method is 0.001, indicating that recent extensions of dynamical mean-field theories and variational methods yielded at least an order of magnitude overestimates of it. The correlations are too weak for the realistic account of the cuprate high-Tc superconductivity.
A progress report on the development of numerical and rigorous solutions of the effective two-band two-dimensional Hubbard model of the high-temperature superconductivity in cuprates [N.M. Plakida et al., PRB 51, 16599 (1995)], within the equation of motion technique of the thermodynamic Green function approach, is given. Four important consequences of the rigorous mean-field solution are worth mentioning: (1) Occurrence, both in the normal and superconducting states, of the spin-charge separation, conjectured by P.W. Anderson on intuitive grounds. (2) Origin of the static d-wave pairing in the hopping singlet conduction. (3) Complete suppression of the s-type superconducting pairing by the crystal symmetry in square two- dimensional lattices and occurrence of a residual s-type term in rectangular lattices, in agreement with the experiment. (4) The energy band hybridization in the superconducting state points to an overall displacement of the energy spectrum toward lower energies, as pointed by very precise optical measurements.