Strong On-site Repulsion Research Articles

Pseudogap Phenomena and Phase Diagram in the Two-Band Hubbard Model

High-Tc superconducting materials (HTSC) have anomalous properties such as the pseudo-gap or spin-gap etc., in Hall coefficient, 1/T1T and the density of states etc. First including effects of strong on-site repulsion between d-electrons at Cu-sites, we obtain quasi-particles with super-exchange interaction Js, whose band width tends to zero, i.e., the system goes to insulator, as the hole-doping rate tends to zero. The quasi-particles correspond to Zhang-Rice singlet states. Js larger than the band width combined with the 2-dimensional character of the system induces strong antiferro-magnetic (AF) and superconducting (SC) fluctuations. We treat effects of the AF ones in the FLEX approximation and those of the SC ones in the self-consistent t-matrix approximation to show that both fluctuations in the under-doped region start to increase at T0 as T decreases from T>>Tc, the AF ones dominate the SC ones at T>Tsg, while SC ones dominate at T<Tsg. This cross-over of the fluctuations causes the anomalous phenomena in the under-doped region. We also obtain the phase diagram of HTSC consistent to one observed in experiments.

Theory of anomalous magnon softening in ferromagnetic manganites

In metallic manganites with low Curie temperatures, a peculiar softening of the magnon spectrum close to the magnetic zone boundary has experimentally been observed. Here we present a theory of the renormalization of the magnetic excitation spectrum in colossal magnetoresistance compounds. The theory is based on the modulation of magnetic exchange bonds by the orbital degree of freedom of double-degenerate e_g electrons. The model considered is an orbitally degenerate double-exchange system coupled to Jahn-Teller active phonons which we treat in the limit of strong onsite repulsions. Charge and coupled orbital-lattice fluctuations are identified as the main origin of the unusual softening of the magnetic spectrum.

Superconductivity from doping a spin-liquid insulator: A simple one-dimensional example.

We study the phase diagram of a one-dimensional Hubbard model where, in addition to the standard nearest neighbor hopping $t$, we also include a next-to-nearest neighbor hopping $t'$. For strong enough on-site repulsion, this model has a transition at half filling from a magnetic insulator with gapless spin excitations at small $t'/t$ to a dimerized insulator with a spin gap at larger $t'/t$. We show that upon doping this model exhibits quite interesting features, which include the presence of a metallic phase with a spin gap and dominant superconducting fluctuations, in spite of the repulsive interaction. More interestingly, we find that this superconducting phase can be reached upon hole doping the magnetic insulator. The connections between this model and the two chain models, recently object of intensive investigations, are also discussed.

Superconductivity in a strongly correlated one-band system.

We study superconductivity in the extended Hubbard model with a strong on-site repulsion U and weak attractive density-density interaction ${\mathit{V}}_{\mathit{ij}}$. The electron correlation effects, beyond the weak-coupling regime of U, are included approximately by employing Hubbard decoupling approximations. The formulas for superconducting transition temperature ${\mathit{T}}_{\mathit{c}}$ of the present approach are compared to those obtained with the strong-coupling expansion and slave-boson techniques. The methods share some common features. We discuss behavior of ${\mathit{T}}_{\mathit{c}}$ for superconducting phases with s- and d-wave symmetry of the superconducting order parameter. In contrast to the mean-field treatment of U, we find that the strong on-site repulsion does not destroy superconductivity induced by ${\mathit{V}}_{\mathit{ij}}$0 even when U\ensuremath{\gg}|${\mathit{V}}_{\mathit{ij}}$|. \textcopyright{} 1996 The American Physical Society.

Doping dependence of hole-number distribution on CuO 2 plane and superconducting transition temperature of high- Tc cuprates by d xy pairing scenario

The doping dependence of the hole-number distribution on the CuO 2 plane and the superconducting transition temperature T c is investigated using the two-dimensional d-p model on the basis of a renormalized perturbation of the Fermi liquid: first forming the quasiparticles variationally by the Gutzwiller approximation taking into account the strong on-site repulsion U d at Cu sites, then treating the residual interactions among quasiparticles by the RPA. The Gutzwiller variational state describes well the electronic state around the Fermi level and accounts for the systematic doping dependence of the hole-number distribution on Cu and O sites which has been measured by Asayama et al. using the NQR technique. Then the doping dependence of T c is naturally understood by the charge-fluctuation mediated d xy pairing scenario where the role of the repulsive interaction U pd between the nearest-neighbor Cu and O sites is crucial.

Influence of long-range and strong correlation effects on the electron-phonon coupling in high-T c oxides

Calculations of the Eliashberg functionα 2F and the corresponding transport functionα 2 F for high-T c oxides are presented using a screened ionic model (rigidly shifted ionic potentials screened by charge carriers in the CuO2 planes within the RPA) for the electron-phonon coupling. It is shown that this model yields a large difference between the transport and the superconducting electron-phonon interaction due to imperfect screening and contributions beyond nearest-neighbor interactions. Using these results, the electron and the lattice heat conductivities are calculated both in the normal and the superconducting state and compared with experiment. Finally, effects due to a strong on-site electron-electron repulsion are included in leading order in an 1/N expansion, whereN is the number of spin degrees of freedom. In particular, it is shown for the infiniteU, one-band Hubbard model that correlations tend to suppressα 2 F strongly andα 2 F somewhat.

Spin correlations in semiconductor dangling bonds: Implications for the alkali-metal-covered surfaces.

It is well known that an antiferromagnetic (AF) spin arrangement within dimers provides a simple explanation of the gap in the electronic structure of the Si(100)-(2\ifmmode\times\else\texttimes\fi{}1) reconstructed surface. Taking this AF description at its face value, we explore the implications of strong Si on-site repulsions (U) for the alkali-metal-covered surface in the coverage (\ensuremath{\theta}) range up to two potassium atoms per dimer. As coverage (electron doping) increases, the substrate undergoes an insulator-metal transition which, in contrast with the U=0 situation, is gradual and due to weakening and final destruction of the AF ordering and its associated gap. The adsorption bond is strongly ionic in the low-coverage regime, with fractional ionic character (FIC) about 0.9. At \ensuremath{\theta}=0.5 (one-half of the first monolayer), however, a crossover between one-dimensional and two-dimensional behavior is found, with a steep rise of the potassium charge accompanied by a steep drop of the FIC of the bond, both signaling the formation of an occupied potassium band increasingly charged and hybridized with the Si band. This process goes on, but now slowly, along the rest of the coverage range, up to saturation, leading finally to a rather low FIC of the bond (0.28) at \ensuremath{\theta}=2. The above crossover separates the low-coverage regime, insulating and highly ionic, from the high-coverage regime where both the substrate and the adsorbate overlayer are metallic and the bonds predominantly covalent. The present model, therefore, does not sustain either the strong ionic picture along the whole coverage range or the opposite view that the transferred charge on the Si atoms is small even at low coverage.

Sign of equilibrium Hall conductivity in strongly correlated systems

We consider the equilibrium current circulating in a cylindrical geometry, perpendicular to applied magnetic and electric fields in a strongly correlated system. We show that the sign of this current is determined by the derivative of the kinetic energy with respect to the chemical potential. We present exact numerical results from diagonalization of finite clusters to support our arguments. In the case of the Hubbard model with strong on-site repulsion the sign of the equilibrium Hall conductivity is electronlike for a small number of particles and holelike close to half filling.

AHARONOV–CASHER EFFECT IN HALF-INTEGER SPIN ANTIFERROMAGNETS

The manifestation of the Aharonov–Casher effect in condensed media is considered. In the one-dimensional Hubbard model with arbitrary band filling we derived analytical expressions for the oscillating part of the ground state energy of mesoscopic ring with twisted boundary conditions which model the influence of Aharonov–Bohn (AB) and/or Aharonov–Casher (AC) fields. It is shown that in the limit of strong on-site repulsion AB-oscillations disappear for half-filled band, but the amplitude of the AC-oscillations, on the contrary, attains its maximum. The period of the AC-oscillations in this case equals hc/2 μ B (μ B is the Bohr magneton).

Failure of saturated ferromagnetism for the Hubbard model with two holes

We consider the Hubbard model on a finite set of sites with nonpositive hopping matrix elements and infinitely strong on-site repulsion. Nagaoka's theorem states that in this model the relative ground state in the sector with one unoccupied site is maximally ferromagnetic. We show that this phenomenon is a consequence of a combinatorial coincidence valid in the one-hole regime only. In the case of more than one hole there is no reason to expect maximally ferromagnetic ground states. We prove this claim for the case of two holes for models defined on a class of graphs which contains all tori that are not too small.

Correlation exponents and the metal-insulator transition in the one-dimensional Hubbard model.

The long-distance decay of correlation functions in the one-dimensional Hubbard model is determined for arbitrary band filling and correlation strength, using the exact solution of Lieb and Wu. In particular, for either infinitely strong on-site repulsion U, or in the close proximity of half filling for any U, spin-spin correlations decay like cos(2${\mathit{k}}_{\mathit{F}}$x)${\mathit{x}}^{\mathrm{\ensuremath{-}}3/2}$ ${\mathrm{ln}}^{1/2}$(x). For infinite U the results are generalized to the case of nonzero nearest-neighbor interaction. The behavior of the frequency-dependent conductivity is also discussed, in particular in the proximity of the metal-insulator transitions occurring for half and quarter filling.

Antiferromagnetic order and high-temperature superconductivity.

The nearly half-filled Hubbard model with strong on-site repulsion is used as a model for the recently discovered copper oxide high-temperature superconductors. The onset of superconductivity upon doping the half-filled lattice of La$_{2}\mathrm{Cu}$${\mathrm{O}}_{4}$ is explained in terms of the Bose-Einstein condensation of effective mass $O({m}_{e})$. These holes move freely over an antiferromagnetic background. The mechanism is very different from the BCS mechanism. A fit to data is obtained by adjusting the interplane hopping amplitude, which turns out to be extremely small, though necessary.

Attractive interaction and pairing in fermion systems with strong on-site repulsion.

It is shown that an effective attractive interaction between nearest-neighbor antiparallel spins a-rises in the Hubbard and Anderson lattice models in the limit of large on-site electron-electron repulsion. Results of Monte Carlo simulations of the Hubbard model show enhancement of anisotropic single-pairing correlations and suppression of triplet-pairing correlations. It is proposed that this interaction leads to an anisotropic singlet superconducting state in the heavy-fermion superconductors.

Thermoelectric power of 1:2 tetracyanoquinodimethanide (TCNQ) salts

A distinctive feature of a number of 1:2 tetracyanoquinodimethanide (TCNQ) salts, such as triethylammonium-${(\mathrm{TCNQ})}_{2}$ [TEA-${(\mathrm{TCNQ})}_{2}$], quinolinium-${(\mathrm{TCNQ})}_{2}$, and acridinium-${(\mathrm{TCNQ})}_{2}$ is a constant thermopower $Q\ensuremath{\simeq}\ensuremath{-}60$ \ensuremath{\mu}V/K over a wide temperature range, \ensuremath{\gtrsim} 100 K, along the highly conducting or TCNQ chain direction. These salts are characterized by $\ensuremath{\rho}$, the fraction of filled sites on the TCNQ chain \ensuremath{\simeq} \textonehalf{}. Past calculations of Beni et al. have shown that the extended Hubbard model with very strong on-site Coulomb repulsion and zero bandwidth can account for the magnitude and temperature variation of $Q$ for quinolinium-${(\mathrm{TCNQ})}_{2}$ and acridinium-${(\mathrm{TCNQ})}_{2}$. I discuss the approximation of zero bandwidth and conclude that it is not justifiable. I then show that a near-constant value close to -60 \ensuremath{\mu}V/K for temperatures \ensuremath{\gtrsim} 100 K can be obtained using a model (although not the extended Hubbard model) with two bands having nearly identical widths and scattering times and retaining the feature of very strong on-site repulsion. Near identity of the two bands is reasonable for $\ensuremath{\rho}\ensuremath{\simeq}\frac{1}{2}$. This model can also account for the magnitude and temperature variation of the conductivity of these salts over the same large temperature range.