Narrow Results

We model electron-doped high T_c materials using the t-t′-t′′-J model. This model is solved on a cluster with 32 sites using the method of exact diagonalization. Our purpose is to study the symmetry and asymmetry between hole- and electron-doped high T_c materials by comparing the results with those of the t-J model. In the electron-doped model with one charge carrier, we find a strong quasiparticle peak at (π,0). Compared to the t-J model, the bandwidth is larger, reflecting the fact that the charge carrier moves more freely in the electron-doped model. In the two-carrier model the ground state has robust d_x²-y² symmetry. This is in contrary to the two-hole t-J model whose ground state is a competition between low-energy states with d_x²-y² and p symmetries. The spatial distribution function of the carriers shows that they move almost freely on different sublattices.

The c-axis charge transport of the electron doped cobaltate is investigated within the t-J model by considering the incoherent interlayer hopping. It is shown that the c-axis charge transport of the electron doped cobaltate is essentially determined by the scattering from the in-plane fluctuation. The c-axis conductivity spectrum shows a low-energy peak and the unusual broad midinfrared band, which are qualitatively consistent with these of the doped square lattice antiferromagnet.

The incommensurate magnetic response observed in normal-state cuprate perovskites is interpreted based on the projection operator formalism and the t–J model of Cu-O planes. In agreement with experiment the calculated dispersion of maxima in the susceptibility has the shape of two parabolas with upward and downward branches which converge at the antiferromagnetic wave vector. The maxima are located at the momenta (½, ½ ± δ), (½ ± δ, ½) and at (½ ± δ, ½ ± δ), (½ ± δ, ½ ∓ δ) in the lower and upper parabolas, respectively. The upper parabola reflects the dispersion of magnetic excitations of the localized Cu spins, while the lower parabola arises due to a dip in the spin-excitation damping at the antiferromagnetic wave vector. For moderate doping this dip stems from the weakness of the interaction between the spin excitations and holes near the hot spots. The frequency dependence of the susceptibility is shown to depend strongly on the hole bandwidth and damping and varies from the shape observed in YBa₂Cu₃O_7-y to that inherent in La_2-xSr_xCuO₄.

We argue that the usual Hubbard's model produces only s-wave pairing functions and, even then, only at unphysically large values of the lumped parameter J≡4t²/U. It follows that a reliable theory of high-T_c superconductivity has to include additional features if it is to reproduce the d-wave gap. We test the effects of an alternating potential caused by a charge stripe, on the ground state of the Hubbard model in strong-coupling. If we "fine tune" we do find the d-waves. However, a better-formulated version of a three-band model yields a sturdier theory of pair formation in high-T_c superconductivity. The coupling constant g₁=t²/V factors out, hence it serves only to establish the unit of energy; the underlying Hamiltonian is universal. We outline the principal properties of this model, including the intimate relation between charge-density stripes and the d-wave pair function, its rejection of 45° stripes (checkerboard pattern), and other concerns.

Magnetic properties of the two-dimensional t-J model are reviewed. Some of these properties are close to those observed in cuprate perovskites. In particular, the magnetic response of the model is characterized by the intensive peak at the antiferromagnetic wave vector and at some transfer frequency. The peak splits into several incommensurate maxima for lower and higher frequencies. We discuss mechanisms which are responsible for these peculiarities in the model, which might also refer to cuprates.

We solve the t-J model with four holes on a 32-site lattice using exact diagonalization. This is the largest scale calculation ever reported for this model. The size of the matrix involved in this problem is about 3×10⁹ by 3×10⁹. We find that at the realistic parameter J/t = 0.3, holes in the ground state of this system are unbound. They have short range repulsion due to lowering of kinetic energy. The electron momentum distribution function resembles hole pockets. We show that in case antiferromagnetic order is strong, holes form d-wave bound pairs and there is mutual repulsion among the holes. This presumably will occur at low doping level.

The present work treats the role of ghost fields in the renormalization procedure of the Lagrangian perturbative formalism of the t–J model. We show that by introducing proper ghost field variables, the propagators and vertices can be renormalized to each order. In particular, the renormalized ferromagnetic magnon propagator coming from our previous Lagrangian formalism is studied in detail, and it is shown how the thermal softening of the magnon frequency is predicted by the model. The antiferromagnetic case is also analyzed, and the results are confronted with the previous one obtained by means of the spin-polaron theories.

By using the Hubbard -operators as field variables along with the supersymmetric version of the Faddeev–Jackiw symplectic formalism, a family of first-order constrained Lagrangians for the t-J model is found. In order to satisfy the Hubbard -operator commutation rules satisfying the graded algebra spl(2,1), the number and kind of constraints that must be included in a classical first-order Lagrangian formalism for this model are presented. The model is also analyzed via path-integral formalism, where the correlation-generating functional and the effective Lagrangian are constructed. In this context, the introduction of a proper ghost field is needed to render the model renormalizable. The perturbative Lagrangian formalism is developed and it is shown how propagators and vertices can be renormalized to each order. In particular, the renormalized ferromagnetic magnon propagator arising in the present formalism is discussed. As an example, the thermal softening of the magnon frequency is computed.

For the superconducting phase with a d-wave order parameter and zero temperature, the magnetic susceptibility of the t–J model is calculated using the Mori projection operator technique. Conditions for the appearance of an incommensurate magnetic response below the resonance frequency are identified. A fast decay of the tails of the hole coherent peaks and a weak intensity of the hole incoherent continuum near the Fermi level are enough to produce an incommensurate response using different hole dispersions established for p-type cuprates, in which such response was observed. In this case, the nesting of the itinerant-electron theory or the charge modulation of the stripe theory is unnecessary for the incommensurability. The theory reproduces the hourglass dispersion of the susceptibility maxima with their location in the momentum space similar to that observed experimentally. The upper branch of the dispersion stems from the excitations of localized spins, while the lower one is due to the incommensurate maxima of their damping. The narrow and intensive resonance peak arises if the frequency of these excitations at the antiferromagnetic momentum lies below the edge of the two-fermion continuum; otherwise the maximum is broad and less intensive.

This report proposes a graphical-like approach for simulating the Hamiltonian of the t–J model. The two spin states are modeled by the two emitting layer, the kinematics of the electrons and the causalities between the operators are satisfied through the event cone. Operators and the event cone are integrated together, and the results indicate that this approach can provide information during the evolution of the t–J model. In addition, parameters that can be accessed by this approach are consistent with general requirements on values of t and J in the t–J model. Furthermore, our approach also includes the solution with vanishing hopping amplitude (t_ij = 0) and the H_∞ solution.

The two-dimensional ferromagnetic t–J model is studied in the framework of slave-boson mean field theory. After solving the mean field self-consistent equations, we find that there exists a hole-doping region δ₁<δ<δ₂ in which p-wave superconductivity and ferromagnetism coexist. There also exists a T* line, under which pre-paired p-wave cooper pairs appear. The similarity and differences between our theoretical results and the experimental ones made for UGe₂ are compared.

Since the discovery of cuprate superconductors, the mechanism of high temperature superconductivity is still a mystery. Among the investigation tools, the electronic Raman scattering is a powerful one to probe electronic excitations in different regions of the Fermi surface of cuprate superconductors by a simple choice of the incident and scattered polarization vectors. Thus the symmetry of the superconducting Cooper pairs can be indicated. In this article we review our investigations of electronic Raman scattering in cuprate superconductors based on the t–J model within the kinetic energy driven superconductivity. The theory of electronic Raman response in cuprate superconductors is presented together with an overview of the charge-spin separation fermion-spin theory to handle the t–J model. Some theoretical results of electronic Raman response are presented in comparison with the experimental results. Special emphasize is given to the doping and temperature dependent of electronic Raman spectra.

There is a long-standing issue that the optical conductivity in normal-state of cuprate superconductors deviates the conventional Drude type marked by ${\omega }^{-2}$ dependence, exhibiting two main components from underdoping to overdoping, a narrow band peaked around zero energy and a broadband centered in the mid-infrared region called mid-infrared band. Within the renormalized t-J model and self-consistent mean field theory, we discuss the doping and energy dependence of optical conductivity in cuprate superconductors. Our results show that the appearance of the pseudogap in normal state is responsible for anomalous optical conductivity, giving rise to the mid-infrared band. In particular, in analogy to the doping dependence of pseudogap, optical conductivity is also strongly doping dependent. By increasing the doping concentration, the spectral weight of the optical conductivity suppressed strongly in underdoped region increases quickly, and the peak position of the mid-infrared band moves towards to the lower energy region, then incorporates into the narrow band centered in zero energy in the heavily overdoped region.

By considering the pseudogap effect, the doping and energy dependences of thermal conductivity in cuprate superconductors are studied. Our results show that the thermal conductivity as a function of energy exhibits a characteristic peak from underdoping to overdoping due to the presence of the pseudogap in pseudogap phase of cuprate superconductors. The thermal conductivity is strongly doping dependent. On the one hand, with increasing doping concentration, the weight of thermal conductivity increases quickly, especially the residual thermal conductivity which is in qualitative agreement with the experimental data. On the other hand, the characteristic energy corresponding to the position of the characteristic peak decreases monotonically upon increasing doping concentration, and it scales with the doping dependence of pseudogap. In particular, we have studied the doping dependence of the ratio of quasiparticle velocities normal and tangential to the Fermi surface at the nodes $v_F/v_2$. It is shown that $v_F/v_2$ increases with the increase of doping concentration. Moreover, we explain that both the residual thermal conductivity and $v_F/v_2$ increase rapidly upon the increase in doping concentration in heavily overdoped cuprate superconductors.

Based on the t-J model and slave-boson theory, we have studied the electronic structure in one-dimensional SrCuO₂ by calculating the electron spectrum. Our results show that the electron spectra are mainly composed of three parts in one-dimensional SrCuO₂, a sharp low-energy peak, a broad intermediate-energy peak and a high-energy peak. The sharp low-energy peak corresponds to the main band (MB) while the broad intermediate-energy peak and high-energy peak are associated with the shadow band (SB) and high-energy band (HB), respectively. From low-energy to intermediate-energy region, a clear two-peak structure (MB and SB) around the momentum $\mathrm{\Gamma }$ appears, and the distance between two peaks decreases along the momentum direction from $\mathrm{\Gamma }$ to $\pi /2$, then disappears at the critical momentum point $k_{\mathrm{\text{c}}}$, leaving a single peak above $k_{\mathrm{\text{c}}}$. The electron spectral function in one-dimensional SrCuO₂ is also the doping and temperature dependent. In particular, in the very low doping concentration, the HB merges into the MB. However, with the increases of the doping concentration, the HB separates from the MB and moves quickly to the high-binding energy region. The HB and MB are the direct results of the spin-charge separation while SB is the result of strong interaction between charge and spin parts. Therefore, our theoretical result predicts that the HB is more likely to be found at the low doping concentration, and it will be drowned in the background when the doping concentration is larger. Then with the temperature increases, the magnitude of the SB decreases, and it disappears at high temperature.