Three-band Hubbard Model Research Articles

Physics of the Hubbard model and high temperature superconductivity

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 CuO2 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.

Possible Collective Spin Excitation in the Spin-Triplet Superconducting State of Sr2RuO4: Multi-Band Theory

We investigate possible collective spin excitation by calculating the dynamical spin susceptibility in the spin-triplet superconducting state of Sr 2 RuO 4 . The effect of the fluctuating triplet-pairing condensate on the spin susceptibility is taken into account. The momentum and band dependences of superconducting gap structure are determined microscopically by solving the linearized Eliashberg equation for a realistic three-band Hubbard model within the perturbation theory in Coulomb interaction, and the evolution of gap magnitude below the transition temperature is determined by the standard BCS gap equation. The triplet pairing symmetry is assumed to be the most promising form: \(\mathbf{d}(\mathbf{k})\sim(k_{x}+\mathrm{i}k_{y})\hat{z}\). For small (maybe realistic) anisotropy of pairing interaction in spin space, we expect a possible low-energy spin-wave mode as a peak structure in the imaginary part of the dynamical spin susceptibility, isolated from the spin excitation continuum. The present work ...

Single-Component Molecular Metals as Multiband π–d Systems

Electronic states of single-component molecular metals M (tmdt) 2 ( M = Ni, Au) are studied theoretically. We construct an effective three-band Hubbard model for each material by numerical fitting to first-principles band calculations, while referring to molecular orbital calculations for the isolated molecules. The model consists of two kinds of base orbital for each molecule with hybridization between them, i.e., a π-character orbital for each of the two tmdt ligands, and, a p d π-orbital for M = Ni or a p d σ-orbital for M = Au centered on the metal site; this indicates that these materials can be considered as novel multiband π– d systems. We find that both orbitals contribute to realize the metallic character in Ni(tmdt) 2 . The origin of the antiferromagnetic transition observed in Au(tmdt) 2 is also discussed based on this model.

The Role of In-plane Oxygens in Optimally Doped NCCO

Within the framework of the three-band Hubbard (Emery) model of high-temperature superconductors, we find a new physical regime for the electron-doped compound NCCO at optimal doping. It is characterized by a strong renormalization of the bare copper–oxygen hopping, similar to the one on the hole-doped side, and a low value of the effective copper–oxygen splitting. After a zeroth order fit of the Fermi surface is achieved, ARPES data are reproduced by adding a simple phenomenological weak-coupling antiferromagnetic perturbation of the conduction electrons. The experimental situation corresponds to a pseudogap across the whole Fermi surface. The wide dispersive features in NCCO ARPES spectra are analogous to the hump in BSCCO. The oxygen degree of freedom dominates the band structure of both NCCO and BSCCO, however, in NCCO this cannot be demonstrated without simultaneously accounting for the antiferromagnetic scattering. The difference in Tc of the two compounds may be related in part to the difference in the calculated densities of states.

Variational cluster treatment of the three-band Hubbard model: Electron vs. hole doping

The competition between d-wave superconductivity (SC) and antiferromagnetism (AF) in the high- T C cuprates is investigated by studying the three-band Hubbard model with a minimal parameter set within the variational cluster approach (VCA). The focus is especially on the differences and similarities between the hole- and electron-doped case. While the hole-doped regime is described quite well at this simple level, additional frustrating terms in the Hamiltonian may be required for an appropriate description of electron-doped materials.

Unified description of charge and spin excitations of stripes in cuprates

We study stripes in cuprates within the one-band and the three-band Hubbard model. Magnetic and charge excitations are described within the time-dependent Gutzwiller approximation. A variety of experiments (charge profile from resonant soft X-ray scattering, incommensurability vs. doping, optical excitations, magnetic excitations, etc.) are described within the same approach.

Hole distribution in the three-band Hubbard model ofhigh-Tc cuprates

Based on the three-band Hubbard model, we studied the distance and orientation dependence ofthe interaction between two small ferromagnetic polarons induced by extra holes doped in theCuO2 plane. Through the binding energy calculation of the three-hole-doped system, we haveshown that the favourable hole distribution pattern is mainly determined by thesum of all pairs of two-hole energy changes. In the case of four-hole doping, weget a schematic phase diagram in parameter space for the stable configuration.

Metallic State of the Three-Band Hubbard Model with Super-Lattice Structure

We investigate the dynamical superlattice correlation in the two-dimensional three-band Hubbard model on the basis of the unrestricted fluctuation exchange approximation. We calculate the one-particle spectral function, the spin correlation function and the charge correlation function at finite temperature. We find that some experimental results can be reproduced consistenly by taking inhomogenous distribution of Cu 3d electrons into account. The correlation functions suggest that several kinds of instabilities with spatial inhomogenieties exist in some regions, where these instabilities significantly affect the one-particle spectral fuctions.

Charge and complex orbital ordering in [formula omitted

To discuss charge and orbital ordering in magnetite ( Fe 3 O 4 ), a spinless three-band Hubbard model was investigated by the exact diagonalization of finite size clusters and the Hartree–Fock approximation. A state with noncollinear orbital moments is obtained with both the methods. The orbital moments are not induced by the ordered spin moment via the spin–orbit interaction as usual magnetic materials but by spontaneous breaking of the time reversal symmetry within the orbital degrees of freedom. The result is consistent with a large orbital moment found in the measurements of the magnetic circular dichroism of Fe 2p X-ray absorption spectra.

Dynamical mean field theory study of a simplified model forCuO2 planes

Following previous work on Hubbard and Anderson models, we introduce a simplified three-band Hubbardmodel for CuO2 planes of high-Tc superconductors. This allows for exact evaluation of single-particle Green’s functions withinthe dynamical mean field approach. Keeping information about the lattice structurethrough the appropriate bare density of states, we study the existence of magneticsolutions, and their stability with respect to variations of the doping fraction, interactionparameters, and temperature. Normal-state properties of known superconducting cupratesare reproduced, and we show that the model has room for substantial enhancement of Néeltemperatures.

Stability of metallic stripes in the one-band extended Hubbard model

Based on an unrestricted Gutzwiller approximation (GA) we investigate static stripe configurations with regard to the orientation and periodicity in an extended one-band Hubbard model. A negative ratio between next-nearest-neighbor and nearest-neighbor hoppings, ${t}^{\ensuremath{'}}/t,$ as appropriate for cuprates, favors partially filled (metallic) stripes for both vertical and diagonal configurations. At around optimal doping diagonal stripes and site centered (SC) and bond centered (BC) vertical stripes become degenerate suggesting strong lateral and orientational fluctuations. We find that within the GA the resulting phase diagram is in agreement with experiment whereas it is not in the Hartree-Fock approximation due to a strong overestimation of the stripe filling. Results are in agreement with previous calculations within the three-band Hubbard model but with the role of SC and BC stripes interchanged.

Hidden symmetries and their consequences int2gcubic perovskites

The five-band Hubbard model for a d band with one electron per site is a model which has very interesting properties when the relevant ions are located at sites with high (e.g., cubic) symmetry. In that case, if the crystal-field splitting is large, one may consider excitations confined to the lowest threefold-degenerate ${t}_{2g}$ orbital states. When the electron hopping matrix element (t) is much smaller than the on-site Coulomb interaction energy $(U),$ the Hubbard model can be mapped onto the well-known effective Hamiltonian (at order ${t}^{2}/U)$ derived by Kugel and Khomskii (KK). Recently we have shown that the KK Hamiltonian does not support long-range spin order at any nonzero temperature due to several novel hidden symmetries that it possesses. Here we extend our theory to show that these symmetries also apply to the underlying three-band Hubbard model. Using these symmetries we develop a rigorous Mermin-Wagner construction, which shows that the three-band Hubbard model does not support spontaneous long-range spin order at any nonzero temperature and at any order in $t/U$---despite the three-dimensional lattice structure. The introduction of spin-orbit coupling does allow spin ordering, but even then the excitation spectrum is gapless due to a subtle continuous symmetry. Finally we show that these hidden symmetries dramatically simplify the numerical exact diagonalization studies of finite clusters.

On the Metal–Insulator Transitions in VO2and Ti2O3from a Unified Viewpoint

The metal–insulator (M–I) transitions in VO 2 and Ti 2 O 3 were investigated using the three-band Hubbard model in connection with the on-site exchange interaction and lattice distortions. Although these two compounds have different crystal structures, the mechanism of the phase transitions can be understood from a unified viewpoint; an increase in energy level separation among the t 2 g orbitals caused by the lattice distortion triggers an abrupt change in the electron configuration in doubly occupied sites from an S =1 Hund's coupling state to a low-spin S =0 state with much larger energy and this strongly suppresses the charge fluctuation, resulting in localization of electrons. These M–I transitions are not induced by an increase in relative strength of the Coulomb interaction against the electron hopping as in the conventional scenario of the Mott–Hubbard transition but by the level splitting among the t 2 g orbitals against the on-site exchange interaction. Switching of the nearest-neighbor spin and...

Degenerate three-band Hubbard model with anti-Hund’s rule interactions: A model forAxC60

We consider the orbitally degenerate 3-band Hubbard model with on-site interactions which favor low spin and low orbital angular momentum using standard second order perturbation theory in the large Hubbard-U limit. At even integer filling this model is a Mott insulator with a non-degenerate ground state that allows for a simple description of particle-hole excitations as well as gapped spin and orbital modes. We find that the Mott gap is generally indirect and that the single particle spectrum at low doping reappears close to even filling but rescaled by a factor 2/3 or 1/3. The model captures the basic phenomenology of the Mott insulating and metallic fullerides AxC60. This includes the existence of a smaller spin gap and larger charge gap at even integer filling, the fact that odd integer stoichiometries are generally metallic while even are insulating, as well as the rapid suppression of the density of states and superconducting transition temperatures with doping away from x=3.

A New Scenario on the Metal–Insulator Transition in VO2

The metal-insulator transition in VO2 was investigated using the three-band Hubbard model, in which the degeneracy of the 3d orbitals, the on-site Coulomb and exchange interactions, and the effects of lattice distortion were considered. A new scenario on the phase transition is proposed, where the increase in energy level separation among the t_2g orbitals caused by the lattice distortion triggers an abrupt change in the electronic configuration in doubly occupied sites from an S=1 Hund's coupling state to a spin S=0 state with much larger energy, and this strongly suppresses the charge fluctuation. Although the material is expected to be a Mott-Hubbard insulator in the insulating phase, the metal-to-insulator transition is not caused by an increase in relative strength of the Coulomb interaction against the electron hopping as in the usual Mott transition, but by the level splitting among the t_2g orbitals against the on-site exchange interaction. The metal-insulator transition in Ti2O3 can also be explained by the same scenario. Such a large change in the 3d orbital occupation at the phase transition can be detected by linear dichroic V 2p x-ray absorption measurements.

Topological doping of repulsive Hubbard models

The spin configuration induced by single holes and hole pairs doped into stoichiometric, antiferromagnetic cuprates is considered. Unrestricted Hartree–Fock calculations for the three-band Hubbard model are employed to study spin-polaron and vortex-like (meron) solutions. Meron solutions for a single hole are found to be metastable with higher energy than spin polarons. We observe that the meron solution shifts from site-centered to bond-centered as the interaction is increased. Meron–antimeron solutions for hole pairs are found to be unstable. The results are in agreement with earlier findings for the one-band Hubbard model. However, we find that the Hubbard interaction of the one-band model has to be chosen similar to the one of the three-band model to obtain comparable results, not of the order of the charge-transfer gap, as previously expected.

Lattice distortions and stripes in the underdoped region of high-Tccuprates

Superconducting and striped states under lattice distortions are investigated for high-Tc cuprates based on the quantum variational Monte Carlo method as the ground state of the two-dimensional (three-band) Hubbard model. We study the wavefunctions for the correlated condensed states: superconductivity, antiferromagnetism, inhomogeneity and their coexistent state with on-site Gutzwiller correlation. The model parameters are chosen for cuprate high-Tc superconductors such as La1−xSrxCuO4 with x < 0.125. The ground state has vertical or horizontal hole-rich arrays coexisting with incommensurate magnetism and superconductivity (SC) in the low-temperature tetragonal (LTT) phase. We show that the total energy of the inhomogeneous d-wave SC state with vertical stripes having half-filled holes is lower than that of competing spin-density wave (SDW) states. The SC order parameter oscillates according to inhomogeneity in the antiferromagnetic background, and the SC condensation energy is reduced as the doping rate decreases in the underdoped region. The decreasing tendency of the SC condensation energy with decreasing doping is in accord with that of the specific heat data. In the low-temperature orthogonal (LTO) phase the diagonal stripes are stabilized in the lightly doped region for less than 5% doping. We also examine the stability of the mixed phase of LTT–HTT coexisting with stripes.

Lattice distortions, incommensurability, and stripes in the electronic model for high-Tccuprates

Striped superconductivity (SC) with lattice distortions is investigated based on the three-band Hubbard model for high-${T}_{c}$ cuprates. A stable inhomogeneous striped state is determined in the low-temperature tetragonal phase with lattice distortions using a quantum variational Monte Carlo method. The ground state has vertical or horizontal hole-rich arrays coexisting with incommensurate magnetism and SC induced by several percents of lattice deformations. The SC order parameter oscillates according to the inhomogeneity in the antiferromagnetic background with its maxima in the hole-rich regions, and the SC condensation energy is reduced as the doping rate decreases.

Superconductivity inSr2RuO4mediated by Coulomb scattering

We investigate the superconductivity in Sr$_2$RuO$_4$ on the basis of the three-dimensional three-band Hubbard model. We propose a model with Coulomb interactions among the electrons on the nearest-neighbor Ru sites. In our model the intersite Coulomb repulsion and exchange coupling can work as the effective interaction for the spin-triplet paring. This effective interaction is enhanced by the band hybridization, which is mediated by the interlayer transfers. We investigate the possibility of this mechanism in the ground state and find that the orbital dependent spin-triplet superconductivity is more stable than the spin-singlet one for realistic parameters. This spin-triplet superconducting state has horizontal line nodes on the Fermi surface.

Inhomogeneous d-wave state and lattice distortions in the three-band Hubbard model of high-Tc cuprates

Striped superconductivity (SC) with lattice distortions is investigated based on the three-band Hubbard model of high-Tc cuprates. A stable inhomogeneous striped state is determined in the low-temperature tetragonal phase using a quantum variational Monte Carlo method. The ground state has vertical or horizontal hole-rich arrays coexisting with incommensurate magnetism and SC. The SC order parameter oscillates according to the inhomogeneity in the antiferromagnetic background with its maximum in the hole-rich region.