Stripe formation in electron-doped cuprates

We investigate the formation of charge domain walls in an electron-doped extended Hubbard model for the superconducting cuprates. Within an unrestricted Hartree-Fock approach, extended by slave bosons to obtain a better treatment of strong correlations, we demonstrate the occurrence of stripes in the (1,1) and (1,-1) directions having one doped electron per stripe site. The different filling, direction, and width of these electron-doped stripes with respect to those obtained in the hole-doped systems have interesting observable consequences.     

Models of bands and Fermi surfaces for electron-doped cuprates

The properties of Fermi surfaces and electron bands in electron-doped cuprates have been studied. The possible origins of a hole pocket in the nodal direction and a pseudogap at hot spots are discussed, including stripe phases and double bands in an antiferromagnetically correlated Fermi liquid. Within the framework of the mean field method, it is shown that both t-t′-t″-U Hubbard model solutions with a homogeneous antifer-romagnetic spin structure and those with a diagonal stripe structure can reproduce the fragmentar character of the Fermi surface. The appearance of hole pockets in various structures is related either to states in the lower Hubbard band or to states localized on domain walls. The behavior of a gap at the leading edge of the energy distribution of photoelectrons and its dependence on oxygen removal in the course of annealing are considered.     

Types of Fermi surface segments of cuprate stripe phases

The mean field method was used to study zones and Fermi surfaces of the stripe phases of the Hubbard model, which describes the electronic properties of cuprates. It was shown for structures with stripes parallel to bonds that the Fermi surface consisted of open surface segments and closed surfaces around hole pockets. Segments of the first type originate from quasi-one-dimensional zones of states localized on domain walls. The properties of zones in comparison with the zones observed in angle-allowed photoemission spectra and the possible influence of the corresponding two types of carriers on the dependence of the Hall constant on temperature and doping are discussed. In view of the observed magnetic quantum oscillations, the search for electron pockets was undertaken. Their formation was shown to be possible in two-layer (but not one-layer) models.     

Order and excitation in partially Gutzwiller projected t-t'-t"-J-U models

Extended t-t'-t"-J-U models in which the second-nearest-neighbor hopping (t') and third-nearest-neighbor hopping (t") are included are studied using renormalized mean field theory. The models are meant to be low-energy effective models for the Hubbard models, and hence the Heisenberg exchange integral J and Hubbard repulsion U are related by J = 4t(2)/U. The trial wavefunctions for the ground states are partially Gutzwiller projected Hartree-Fock states. The Gutzwiller projection is implemented by means of a Gutzwiller approximation, and the site double occupancy d is taken as a variational parameter. It is found that a large |t'/t| narrows the band filling range that sustains antiferromagnetism (AFM) in the ground state, enhances the d-wave singlet superconductivity (dSC) in hole overdoped systems, but suppresses the dSC in electron overdoped systems. For a system that has large |t'/t| and |t"/t'|, the superconductivity (SC) at the onset of AFM in hole doped band filling is strongly suppressed. On the excitation occurring, when an electron doped system simultaneously contains SC and AFM, the system is found to have a nodeless gap at the Fermi level. Finally, the result of this study is related to experiments on the superconducting cuprates.     

Gapless Excitation above a Domain Wall Ground State in a Flat-Band Hubbard Model

We construct a set of exact ground states with a localized ferromagnetic domain wall and with an extended spiral structure in a deformed flat-band Hubbard model in arbitrary dimensions. We show the uniqueness of the ground state for the half-filled lowest band in a fixed magnetization subspace. The ground states with these structures are degenerate with all-spin-up or all-spin-down states under the open boundary condition. We represent a spin one-point function in terms of local electron number density, and find the domain wall structure in our model. We show the existence of gapless excitations above a domain wall ground state in dimensions higher than one. On the other hand, under the periodic boundary condition, the ground state is the all-spin-up or all-spin-down state. We show that the spin-wave excitation above the all-spin-up or -down state has an energy gap because of the anisotropy     

Quantum to classical correspondence for the Fermi-acceleration model

A quantum particle which is confined to the interior of a box with infinitely high but periodically oscillating walls can have an unusual semiclassical limit: For the special case of a one-dimensional linear wall motion we show that the semiclassical domain corresponds to a classical motion in phase space where the initial momentum depends on the particle's position in the box. Another result is that quantum states which correspond to classical cycle-1 fixed points have maximum stability against the boundary induced perturbation (caused by the moving wall). Higher cycle-n fixed points are calculated by numerical bookkeeping up to n = 20. The classical motion is marginally stable. We show how a slight change in the boundary condition will lead to chaotic motion.     

Tuning the effects of Landau level mixing on anisotropic transport in quantum Hall systems

Electron-electron interactions in half-filled high Landau levels in two-dimensional electron gases in a strong perpendicular magnetic field can lead to states with anisotropic longitudinal resistance. This longitudinal resistance is generally believed to arise from broken rotational invariance, which is indicated by charge density wave order in Hartree-Fock calculations. We use the Hartree-Fock approximation to study the influence of externally tuned Landau level mixing on the formation of interaction-induced states that break rotational invariance in two-dimensional electron and hole systems. We focus on the situation when there are two non-interacting states in the vicinity of the Fermi level and construct a Landau theory to study coupled charge density wave order that can occur as interactions are tuned and the filling or mixing are varied. We consider numerically a specific example where mixing is tuned externally through Rashba spin-orbit coupling. We calculate the phase diagram and find the possibility of ordering involving coupled striped or triangular charge density waves in the two levels. Our results may be relevant to recent transport experiments on quantum Hall nematics in which Landau level mixing plays an important role.     

Scaling limit of the one-dimensional attractive Hubbard model: the non-half-filled band case

The scaling limit of the less than half-filled attractive Hubbard chain is studied. This is a continuum limit in which the particle number per lattice site, n, is kept finite (0 < n < 1) while adjusting the interaction and bandwidth in such a way that there is a finite mass gap. We construct this limit both for the spectrum and the secular equations describing the excitations. We find that similarly to the half-filled case, the limiting model has a massive and a massless sector. The structure of the massive sector is closely analogous to that of the half-filled band and consequently to the chiral invariant SU(2) Gross-Neveu (CGN) model. The structure of the massless sector differs from that of the half-filled band case: the excitations are of particle and hole type, however they are not uniquely defined. The energy and the momentum of this sector exhibits a tower structure corresponding to a conformal field theory with c = 1 and SU(2) × SU(2) symmetry. The energy-momentum spectrum and the zero temperature free energy of the states with finite density coincides with that of the half-filled case supporting the identification of the limiting model with the SU(2) symmetric CGN theory.     

Quantum well states in thin (110)-oriented Au films and k-space symmetry

We study the one- and two-dimensional extended Hubbard model by means of the Composite Operator Method within the 2-pole approximation. The fermionic propagator is computed fully self-consistently as a function of temperature, filling and Coulomb interactions. The behaviors of the chemical potential (global indicator) and of the double occupancy and nearest-neighbor density-density correlator (local indicators) are analyzed in detail as primary sources of information regarding the instability of the paramagnetic (metal and insulator) phase towards charge ordering driven by the intersite Coulomb interaction. Very rich phase diagrams (multiple first and second order phase transitions, critical points, reentrant behavior) have been found and discussed with respect to both metal-insulator and charge ordering transitions: the connections with the experimental findings relative to some manganese compounds are analyzed. Moreover, the possibility of improving the capability of describing cuprates with respect to the simple Hubbard model is discussed through the analysis of the Fermi surface and density of states features. We also report about the specific heat behavior in presence of the intersite interaction and the appearance of crossing points.Received: 2 July 2004, Published online: 12 October 2004PACS: 71.10.-w Theories and models of many-electron systems - 71.10.Fd Lattice fermion models (Hubbard model, etc.) - 71.27. + a Strongly correlated electron systems; heavy fermions     

The Fermi surface reconstruction in stripe phases of cuprates

Mean-field study of the stripe structures is conducted for a hole-doped Hubbard model. For bond-directed stripes, the Fermi surface consists of segments of an open surface and the boundaries of the hole pockets which appear in the diagonal region of momenta under certain conditions. Segments of the first type are due to one-dimensional bands of states localized on the domain walls. The relation of bands to the doping and temperature dependences of the Hall constant is discussed. In connection with the observation of quantum magnetic oscillations, a systematic search for the electron pockets has been carried out. It is shown that the formation of such pockets in bilayer models is quite possible. The article is published in the original.     

The Fermi surface reconstruction in stripe phases of cuprates

Mean-field study of the stripe structures is conducted for a hole-doped Hubbard model. For bond-directed stripes, the Fermi surface consists of segments of an open surface and the boundaries of the hole pockets which appear in the diagonal region of momenta under certain conditions. Segments of the first type are due to one-dimensional bands of states localized on the domain walls. The relation of bands to the doping and temperature dependences of the Hall constant is discussed. In connection with the observation of quantum magnetic oscillations, a systematic search for the electron pockets has been carried out. It is shown that the formation of such pockets in bilayer models is quite possible.

     

Properties of domain walls and magnetoresistance in low-doped La<Subscript>2−<Emphasis Type="Italic">y</Emphasis></Subscript>Sr<Subscript>y</Subscript>CuO<Subscript>4</Subscript>

The properties of the diagonal stripe structures of the Hubbard model are theoretically studied in relation to the incommensurate spin order and the magnetic effects detected in the dielectric phase of low-doped La_2?y Sr_yCuO₄ (y ≤ 0.05). The mean-field approximation is used to investigate the properties of the solutions with domain walls between antiphase antiferromagnetic domains that are centered on bonds. Such periodic structures with 2l sites in a unit cell are shown to have 2(l ? 1) levels in the lower and upper Hubbard subbands and two levels that are separated into the Hubbard gap and correspond to quasi-one-dimensional states localized on domain walls. The calculation results are employed to check the assumption that the low conduction of the dielectric LSCO phase occurs via the network of domain walls. The maximum relative change in the magnetoresistance during a spin-flop transition in a critical magnetic field is estimated, and the giant magnetoresistance is qualitatively explained.     

Intriguing electron correlation effects in the photoionization of metallic quantum-dot nanorings

We report detailed results on ionization in metallic quantum-dot (QD) nanorings described by the extended Hubbard model at half filling obtained by exact numerical diagonalization. In spite of very strong electron correlations, the ionization spectra are astonishingly scarce. We attribute this scarcity to a hidden quasi-symmetry, generalizing thereby similar results on optical absorption recently reported [Phys. Rev. B 75, 125323 (2007); 77, 165339 (2008)]. Numerical results indicate that this hidden quasi-symmetry of the extended Hubbard model does not evolve into a true (hidden) symmetry but remains a quasi-symmetry in the case of the restricted Hubbard model as well. Based on the observation on the number of significant ionization signals per each spatial symmetry, we claim the existence of a one-to-one map between the relevant ionization signals of the correlated half-filled nanorings and the one-hole and two-hole-one-particle processes possible in the noninteracting case. Similar to the case of optical absorption, numerous avoided crossings (anticrossings) are present in the ionization spectra, which often involve more than two states. The present results demonstrate that ionization could be a useful tool to study electron correlations in metallic QD-nanoarrays, providing information that is complementary to optical absorption.     

Ferromagnetic Domain Wall and Spiral Ground States in One-Dimensional Deformed Flat-Band Hubbard Model

We construct a set of exact ground states with a localized ferromagnetic domain wall and an extended spiral structure in a quasi-one-dimensional deformed flat-band Hubbard model. In the case of quarter filling, we show the uniqueness of the ground state with a fixed magnetization. The ground states with these structures are degenerate with the all-spin-up and all-spin-down states. This property of the degeneracy is the same as the domain wall solutions in the XXZ Heisenberg–Ising model. We derive a useful recursion relation for the normalization of the domain wall ground state. Using this recursion relation, we discuss the convergence of the ground state expectation values of arbitrary local operators in the infinite-volume limit. In the ground state of the infinite-volume system, the translational symmetry is spontaneously broken by this structure. We prove that the cluster property holds for the domain wall ground state and excited states. We also estimate bounds of the ground state expectation values of several observables, such as one- and two-point functions of spin and electron number density.     

States and energies of the periodic Hubbard model at half filling

The representation of the periodic Hubbard model in the Clifford algebra leads to explicit expressions for several families of non-trivial half-filled states in any number of dimensions. A generalization of these expressions explains the structure of the spectrum of the general Hubbard hamiltonian.     

Itinerant electron-driven chiral magnetic ordering and spontaneous quantum Hall effect in triangular lattice models

We study the Kondo Lattice and the Hubbard models on a triangular lattice. We find that at the mean-field level, these rotationally invariant models naturally support a noncoplanar chiral magnetic ordering. It appears as a weak-coupling instability at the band filling factor 3/4 due to the perfect nesting of the itinerant electron Fermi surface. This ordering is a triangular-lattice counterpart of the collinear Neel ordering that occurs on the half-filled square lattice. While the long-range magnetic ordering is destroyed by thermal fluctuations, the chirality can persist up to a finite temperature, causing a spontaneous quantum Hall effect in the absence of any externally applied magnetic field.     

d-Mott phases in one and two dimensions

We use exact diagonalization to determine the spectrum of reduced Hamiltonians based on renormalization group flows to strong coupling. For the half-filled two-leg Hubbard ladder we reproduce the known insulating d-Mott ground state with spin and charge gaps. For the saddle point regions of the two-dimensional Hubbard model near half filling we find a crossover to a similar strong coupling state, which truncates the Fermi surface near the saddle points. At lower scales d-wave superconductivity appears on the remaining Fermi surface.     

Electronic state in the 2D Hubbard model

Electronic state of the 2D Hubbard model near the half-filling is analyzed by use of the composite operator method. Doping and temperature dependence of density of states show similar behaviors obtained in numerical simulation. The weight of the upper and lower Hubbard bands at the half filling are not evenly distributed in the Brillouin zone, keeping roughly the original band distribution. With hole doping the lower Hubbard band spreads in the whole zone.     

Energetics of 2D and 3D Repulsive Hubbard Model from Their 1D Counterpart using Dimensional Scaling for an Arbitrary Band Filling

A dimensional scaling computation of the electron concentration-dependent ground-state energy for the repulsive Hubbard model is presented, a generalization of Capelle’s analysis of the 2D and 3D Hubbard Hamiltonians with half-filled bands. The computed ground-state energies are compared with the results of mean-field and density-matrix functional theories and of quantum Monte Carlo calculations. The comparison indicates that dimensional scaling yields moderately accurate ground-state energies close to and at half filling over the wide range of interaction strengths in the study. By contrast, the accuracy becomes poor at low filling for strong interactions.     

Single-hole state in half-filled 2D Hubbard model

Summary We have investigated the ground state of a single hole in the half-filled Hubbard model on a 2D square lattice using the coupled-cluster method. In particular we obtained an analytical expression of the hole energy dispersion function ɛ(k) which is consistent with earlier studies on thet-J model in the strong-coupling limit. An appreciable discrepancy on the hole energy bandwidth is, however, observed between the Hubbard model and thet-J model. We believe that this discrepancy is due to the absence of the three-site interaction term in thet-J model.