Two-dimensional t-J model at moderate doping

Using the method which retains the rotation symmetry of spin components in the paramagnetic state and has no preset magnetic ordering, spectral and magnetic properties of the two-dimensional t-J model in the normal state are investigated for the ranges of hole concentrations 0 ⩽ x ⩽ 0.16 and temperatures 0.01t ⩽ T ⩽ 0.2t. The used hopping t and exchange J parameters of the model correspond to hole-doped cuprates. The obtained solutions are homogeneous which indicates that stripes and other types of phase separation are not connected with the strong electron correlations described by the model. A series of nearly equidistant maxima in the hole spectral function calculated for low T and x is connected with hole vibrations in the region of the perturbed short-range antiferromagnetic order. The hole spectrum has a pseudogap in the vicinity of (0,π) and (π, 0). For x ≈ 0.05 the shape of the hole Fermi surface is transformed from four small ellipses around (±π/2,±π/2) to two large rhombuses centered at (0, 0) and (π,π). The calculated temperature and concentration dependencies of the spin correlation length and the magnetic susceptibility are close to those observed in cuprate perovskites. These results offer explanations for the observed scaling of the static uniform susceptibility and for the changes in the spin-lattice relaxation and spin-echo decay rates in terms of the temperature and doping variations in the spin excitation spectrum of the model. Received 14 November 2002 Published online 1st April 2003 RID="a" ID="a"e-mail: alexei@fi.tartu.ee     

Critical behaviour near the metal-insulator transition of a doped Mott insulator

We have studied the critical behaviour of a doped Mott insulator near the metal-insulator transition for the infinite-dimensional Hubbard model using a linearized form of dynamical mean-field theory. The discontinuity in the chemical potential in the change from hole to electron doping, for U larger than a critical value U _c, has been calculated analytically and is found to be in good agreement with the results of numerical methods. We have also derived analytic expressions for the compressibility, the quasiparticle weight, the double occupancy and the local spin susceptibility near half-filling as functions of the on-site Coulomb interaction and the doping. Received 15 March 2001 and Received in final form 22 May 2001     

Origin and doping dependence of the photoemission pseudogap in Cu oxides

A recent report on ARPES on insulating , compared to previous data from and Dy-doped , sheds new light on the origin of the anisotropic pseudogap observed in the normal state of underdoped cuprate oxides. The energy dispersion of the insulator is attributed to strong AF correlations enhanced by the diagonal hopping between magnetic sites, which is progressively deformed by the possibility of nearest neighbour hopping, that increases with hole doping. Received 9 April 1999     

d = 3 anisotropic and d = 2 tJ models: phase diagrams, thermodynamic properties, and chemical potential shift

The anisotropic d=3 tJ model is studied by renormalization-group theory, yielding the evolution of the system as interplane coupling is varied from the isotropic three-dimensional to quasi-two-dimensional regimes. Finite-temperature phase diagrams, chemical potential shifts, and in-plane and interplane kinetic energies and antiferromagnetic correlations are calculated for the entire range of electron densities. We find that the novel τ phase, seen in earlier studies of the isotropic d=3 tJ model, persists even for strong anisotropy. While the τ phase appears at low temperatures at 30–35% hole doping away from 〈 n_i〉=1, at smaller hole dopings we see a complex lamellar structure of antiferromagnetic and disordered regions, with a suppressed chemical potential shift, a possible marker of incommensurate ordering in the form of microscopic stripes. An investigation of the renormalization-group flows for the isotropic two-dimensional tJ model also shows a clear pre-signature of the τ phase, which in fact appears with finite transition temperatures upon addition of the smallest interplane coupling.     

Spontaneous symmetry breaking approach to La2CuO4 properties: Hints for matching the Mott and Slater pictures

Special solutions of the Hartree-Fock (HF) problem for Coulomb interacting electrons described by a simple model of the Cu-O planes in La₂CuO₄ are presented. One of the mean field states obtained, is able to predict some of the most interesting properties of this material, such as its insulator character and the antiferromagnetic order. The natural appearance of pseudogaps in some states of this material is also indicated by another of the HF states obtained. These surprising results follow after eliminating spin and crystal symmetry restrictions usually imposed on the single particle HF orbitals, by employing the rotational invariant formulation of the HF scheme originally introduced by Dirac. Therefore, it is exemplified here, how up to know considered strong correlation effects, can be described by improving the HF solution of the considered system. In other words, it has been argued, that defining correlation effects as the ones shown by the system and not predicted by the HF best (lowest energy) solution, allows to explain important, up to know considered as strong correlation properties, as simple mean field ones. The discussion also helps to clarify the role of the antiferromagnetism and pseudogaps in the physical properties of the HTSC materials and indicates a promising way to start conciliating the Mott and Slater pictures in the physics of the transition metal oxides and other strongly correlated electron systems.     

Effective action for phase fluctuations in <Emphasis Type="Italic">d</Emphasis>-wave superconductors near a Mott transition

Phase fluctuations of a d-wave superconducting order parameter are theoretically studied in the context of high-T_c cuprates. We consider an extended t-J model describing electrons in a layer which also contains long-range Coulomb interactions. The constraint of having at most singly occupied sites is enforced by an additional Hubbard term. The Heisenberg interaction is decoupled by a d-wave order parameter in the particle-particle channel. Assuming first that the equilibrium state has long-range phase order, the effective action is derived perturbatively for small fluctuations within a path integral formalism, in the presence of the Coulomb and Hubbard interaction terms. In a second step, a more general derivation of is performed in terms of a gradient expansion which only assumes that the gradients of the order parameter are small whereas the value of the phase may be large. We show that in the phase-only approximation the resulting reduces in leading order in the field gradients to the perturbative one which thus allows to treat also the case without long-range phase order or vortices. Our result generalizes previous expressions for to the case of interacting electrons, is explicitly gauge invariant, and avoids problematic singular gauge transformations.     

Magnetotransport of lanthanum doped RuSr<Subscript>2</Subscript>GdCu<Subscript>2</Subscript>O<Subscript>8</Subscript> – the role of gadolinium

Strongly underdoped RuSr_1.9La_0.1GdCu₂O₈ has been comprehensively studied by dc magnetization, microwave measurements, magnetoresistivity and Hall resistivity in fields up to 9 T and temperatures down to 1.75 K. Electron doping by La reduces the hole concentration in the CuO₂ planes and completely suppresses superconductivity. Microwave absorption, dc resistivity and ordinary Hall effect data indicate that the carrier concentration is reduced and a semiconductor-like temperature dependence is observed. Two magnetic ordering transitions are observed. The ruthenium sublattice orders antiferromagnetically at 155 K in low applied magnetic fields, and the gadolinium sublattice orders antiferromagnetically at 2.8 K. The magnetoresistivity in this compound exhibits a complicated temperature dependence due to the occurence of the two magnetic orders and spin fluctuations. It is shown that the ruthenium magnetism influences the conductivity in the RuO₂ layers while the gadolinium magnetism influences the conductivity in the CuO₂ layers. The magnetoresistivity is isotropic above 4 K, but it becomes anisotropic close to the gadolinium antiferromagnetic order temperature.     

Dynamical mean-field study of the Mott transition in thin films

The correlation-driven transition from a paramagnetic metal to a paramagnetic Mott-Hubbard insulator is studied within the half-filled Hubbard model for a thin-film geometry. We consider simple-cubic films with different low-index surfaces and film thickness d ranging from d=1 (two-dimensional) up to d=8. Using the dynamical mean-field theory, the lattice (film) problem is self-consistently mapped onto a set of d single-impurity Anderson models which are indirectly coupled via the respective baths of conduction electrons. The impurity models are solved at zero temperature using the exact-diagonalization algorithm. We investigate the layer and thickness dependence of the electronic structure in the low-energy regime. Effects due to the finite film thickness are found to be the more pronounced the lower is the film-surface coordination number. For the comparatively open sc(111) geometry we find a strong layer dependence of the quasi-particle weight while it is much less pronounced for the sc(110) and the sc(100) film geometries. For a given geometry and thickness d there is a unique critical interaction strength U _c2 (d) at which all effective masses diverge and there is a unique strength U _c1 (d) where the insulating solution disappears. U _c2 (d) and U _c1 (d) gradually increase with increasing thickness eventually approaching their bulk values. A simple analytical argument explains the complete geometry and thickness dependence of U_c2. U_c1 is found to scale linearly with U_c2. Received 19 August 1998     

Flow to strong coupling in the two-dimensional Hubbard model

We extend the analysis of the renormalization group flow in the two-dimensional Hubbard model close to half-filling using the recently developed temperature flow formalism. We investigate the interplay of d-density wave and Fermi surface deformation tendencies with those towards d-wave pairing and antiferromagnetism. For a ratio of next nearest to nearest neighbor hoppings, t'/t = - 0.25, and band fillings where the Fermi surface is inside the Umklapp surface, only the d-pairing susceptibility diverges at low temperatures. When the Fermi surface intersects the Umklapp surface close to the saddle points, d-wave pairing, d-density wave, antiferromagnetic and, to a weaker extent, d-wave Fermi surface deformation susceptibilities grow together when the interactions flow to strong coupling. We interpret these findings as indications for a non-trivial strongly coupled phase with short-ranged superconducting and antiferromagnetic correlations, in close analogy with the spin liquid ground state in the well-understood two-leg Hubbard ladder. Received 23 January 2002     

Calculation of photoemission spectra of the doped Mott insulator using LDA+DMFT(QMC)

The spectral properties of La_1–xSr_xTiO₃, a doped Mott insulator with strong Coulomb correlations, are calculated with the ab initio computational scheme LDA+DMFT(QMC). It starts from the non-interacting electronic band structure as calculated by the local density approximation (LDA), and introduces the missing correlations by the dynamical mean-field theory (DMFT), using numerically exact quantum Monte-Carlo (QMC) techniques to solve the resulting self-consistent multi-band single-impurity problem. The results of the LDA+DMFT(QMC) approach for the photoemission spectra of La_1–xSr_xTiO₃ are in good agreement with experiment and represent a considerable qualitative and quantitative improvement on standard LDA calculations. Received 20 May 2000 and Received in final form 27 July 2000     

Non-perturbative conserving approximations and Luttinger's sum rule

Weak-coupling conserving approximations can be constructed by truncations of the Luttinger-Ward functional and are well known as thermodynamically consistent approaches which respect macroscopic conservation laws as well as certain sum rules at zero temperature. These properties can also be shown for variational approximations that are generated within the framework of the self-energy-functional theory without a truncation of the diagram series. Luttinger's sum rule represents an exception. We analyze the conditions under which the sum rule holds within a non-perturbative conserving approximation. Numerical examples are given for a simple but non-trivial dynamical two-site approximation. The validity of the sum rule for finite Hubbard clusters and the consequences for cluster extensions of the dynamical mean-field theory are discussed.     

Dynamical mean-field theory of a simplified double-exchange model

Simplified double-exchange model including transfer of the itinerant electrons with spin parallel to the localized spin in the same site and the indirect interaction J of kinetic type between localized spins is comprihensively investigated. The model is exactly solved in infinite dimensions. The exact equations describing the main ordered phases (ferromagnetic and antiferromagnetic) are obtained for the Bethe lattice with (z is the coordination number) in analytical form. The exact expression for the generalized paramagnetic susceptibility of the localized-spin subsystem is also obtained in analytical form. It is shown that temperature dependence of the uniform and the staggered susceptibilities has deviation from Curie-Weiss law. Dependence of Curie and Néel temperatures on itinerant-electron concentration is discussed to study instability conditions of the paramagnetic phase. Anomalous temperature behaviour of the chemical potential, the thermopower and the specific heat is investigated near the Curie point. It is found for J=0 that the system is unstable towards temperature phase separation between ferromagnetic and paramagnetic states. A phase separation connected with antiferromagnetic and the paramagnetic phases can occur only at . Zero-temperature phase diagram including the phase separation between ferromagnetic and antiferromagnetic states is given. Received 28 May 1999 and Received in final form 14 July 1999     

Breakdown of Luttinger's theorem in two-orbital Mott insulators

An analysis of Luttinger's theorem shows that – contrary to recent claims – it is not valid for a generic Mott insulator. For a two-orbital Hubbard model with two electrons per site the crossover from a non-magnetic correlated insulating phase (Mott or Kondo insulator) to a band insulator is investigated. Mott insulating phases are characterized by poles of the self-energy and corresponding zeros in the Greens functions defining a “Luttinger surface” which is absent for band insulators. Nevertheless, the ground states of such insulators with two electrons per unit cell are adiabatically connected.     

Possible propagation of the Zhang-Rice singlet as a probable Cooper channel in the CuO2 planes

The issue of how superconductivity originate in the CuO₂ planes believed to be crucial to understanding the high Tc superconducting cuprates is still an going debate. In the wake of recent experimental observations of the Zhang-Rice singlet (ZRS), its formation and propagation need to be revisited especially by using a simple approach almost at a phenomenological level. Within a highly simplified correlated variational approach (HSCVA) in this Letter, a new formation of the ZRS as constituting the ground state of a single-band t-J model of the CuO₂ planes is developed. This formation is then used to demonstrate how the ZRS can be propagated as a probable Cooper channel in the CuO₂ planes.     

Massive CP theory from a microscopic model for doped antiferromagnets

A path-integral for the t–J$t\text{–}J$ model in two dimensions is constructed based on Dirac quantization, with an action found originally by Wiegmann [P. Wiegmann, Phys. Rev. Lett. 60 (1988) 821; P. Wiegmann, Nucl. Phys. B 323 (1989) 311]. Concentrating on the low doping limit, we assume short range antiferromagnetic order of the spin degrees of freedom. Going over to a local spin quantization axis of the dopant fermions, that follows the spin degree of freedom, staggered CP¹ fields result and the constraint against double occupancy can be resolved. The staggered CP¹ fields are split into slow and fast modes, such that after a gradient expansion, and after integrating out the fast modes and the dopant fermions, a CP¹ field-theory with a massive gauge field is obtained that describes generically incommensurate coplanar magnetic structures, as discussed previously in the context of frustrated quantum antiferromagnets. Hence, the possibility of deconfined spinons is opened by doping a colinear antiferromagnet.     

Renormalization of the electron-phonon interaction: a reformulation of the BCS-gap equation

A recently developed renormalization approach is used to study the electron-phonon coupling in many-electron systems. By starting from an Hamiltonian which includes a small gauge symmetry breaking field, we directly derive a BCS-like equation for the energy gap from the renormalization approach. The effective electron-electron interaction for Cooper pairs does not contain any singularities. Furthermore, it is found that phonon-induced particle-hole excitations only contribute to the attractive electron-electron interaction if their energy difference is smaller than the phonon energy.     

Electron correlations in a C20 fullerene cluster

The ground-state properties of C₂₀ fullerene clusters are determined in the framework of the Hubbard model by using lattice density-functional theory (LDFT) and scaling approximations to the interaction-energy functional. Results are given for the ground-state energy, kinetic and Coulomb energies, local magnetic moments, and charge-excitation gap, as a function of the Coulomb repulsion U/t and for electron or hole doping δ close to half-band filling (|δ| ≤1). The role of electron correlations is analyzed by comparing the LDFT results with fully unrestricted Hartree-Fock (UHF) calculations which take into account possible noncollinear arrangements of the local spin-polarizations. The consequences of the spin-density-wave symmetry breaking, often found in UHF, and the implications of this study for more complex fullerene structures are discussed.     

Superconducting pairing in the singlet band of the Emery model

The pairing due to electron-phonon and exchange interaction in the two-band Emery model is considered. The Emery model is reduced to an effective singlet-triplet problem. The Eliashberg-equations are formulated in terms of Hubbard operators for the singlet band. The dependence of the critical temperatureT _c on the number of holesn in the doped CuO₂ plane has been calculated. The electron-phonon coupling gives rise to s-wave pairing with a maximum inT _c atn1.2. It corresponds to a maximum in the density of states for a doping value ofn=1.24. The anisotropic electron-electron coupling due to the exchange interaction produces extended s-wave pairing with a maximum atn1.05 and d-wave pairing with a maximum atn1.2.     

Thermal evolution of hole dynamics in the large-dimensional model

The dynamics of a single hole in the t - J model is solved exactly for all temperature, T, in the limit of large spatial dimensions, , using the Feenberg renormalized perturbation series. We focus in particular on single-particle spectra, together with optical and static hole conductivities. Explicit results are illustrated for a Bethe lattice, and exemplify the continuous thermal evolution of the underlying string picture from the T =0 string-pinned limit through to the paramagnetic phase. Quenched site-disorder is also readily incorporated, exact results thereby being obtained for the interplay between disorder and thermally-induced hole dynamics. Received 16 September 1998     

Phase separation in the strongly correlated Falicov-Kimball model in infinite dimensions

Phase separation in the strongly correlated Falicov-Kimball model in infinite dimensions is examined. We show that the phase separation can occur for any values of the interaction constant J^* when the site energy of the localized electrons is equal to zero. Electron-poor regions always have homogeneous state and electron-rich regions have chessboard state for , chessboard state or homogeneous state in dependence upon temperature for 0<J ^* <0.03 and homogeneous state for J ^* =0. For J ^* =0 and T=0, phase separation (segregation) occurs at .The obtained results are exact for the Bethe lattice with infinite number of the nearest neighbours. Received 1 December 1998 and Received in final form 12 April 1999