Effect of hole doping on the electronic structure and the Fermi surface in the Hubbard model within norm-conserving cluster pertubation theory

The concentration dependences of the band structure, spectral weight, density of states, and Fermi surface in the paramagnetic state are studied in the Hubbard model within cluster pertubation theory with 2 × 2 clusters. Representation of the Hubbard X operators makes it possible to control conservation of the spectral weight in constructing cluster perturbation theory. The calculated value of the ground-state energy is in good agreement with the results obtained using nonperturbative methods such as the quantum Monte Carlo method, exact diagonalization of a 4 × 4 cluster, and the variational Monte Carlo method. It is shown that in the case of hole doping, the states in the band gap (in-gap states) lie near the top of the lower Hubbard band for large values of U and near the bottom of the upper band for small U. The concentration dependence of the Fermi surface strongly depends on hopping to second (t′) and third (t″) neighbors. For parameter values typical of HTSC cuprates, the existence of three concentration regions with different Fermi surfaces is demonstrated. It is shown that broadening of the spectral electron density with an energy resolution typical of contemporary ARPES leads to a pattern of arcs with a length depending on the concentration. Only an order-of-magnitude decrease in the linewidth makes it possible to obtain the true Fermi surface from the spectral density. The kinks associated with strong electron correlations are detected in the dispersion relation below the Fermi level.     

Electronic structure of p-type La1 ? xM x2+ MnO3 manganites in the ferromagnetic and paramagnetic phases in the LDA + GTB approach

The band structure, spectral intensity, and position of the Fermi level in doped p-type La_{1 − x} M _x/2+MnO₃ manganites (M = Sr, Ca, Ba) is analyzed using the LDA + GBT method for calculating the electronic structure of systems with strong electron correlations, taking into account antiferro-orbital ordering and using the Kugel-Khomskii ideas and real spin S = 2. The results of the ferromagnetic phase reproduce the state of a spin half-metal with 100% spin polarization at T = 0, when the spectrum is of the metal type for a quasiparticle with one spin projection and of the dielectric type for the other. It is found that the valence band becomes approximately three times narrower upon a transition to the paramagnetic phase. For the paramagnetic phase, metal properties are observed because the Fermi level is located in the valence band for any nonzero x. The dielectrization effect at the Curie temperature is possible and must be accompanied by filling of d _x orbitals upon doping. The effect itself is associated with strong electron correlations, and a complex structure of the top of the valence band is due to the Jahn-Teller effect in cubic materials.     

Anisotropic scattering rates and antiferromagnetic precursor effects in the t-t'-U Hubbard model

We have investigated the evolution of the electronic properties of the t-t'-U Hubbard model with hole doping and temperature. Due to the shape of the Fermi surface, scattering from short wavelength spin fluctuations leads to strongly anisotropic quasi-particle scattering rates at low temperatures near half-filling. As a consequence, significant variations with momenta near the Fermi surface emerge for the spectral functions and the corresponding ARPES signals. At low doping the inverse lifetime of quasiparticles on the Fermi surface is of order varying linearly in temperature from energies of order t down to a very low energy scale set by the spin fluctuation frequency while at intermediate doping a sub-linear T-dependence is observed. This behavior is possibly relevant for the interpretation of photoemission spectra in cuprate superconductors at different hole doping levels. Received 31 July 2000     

d-symmetry superconductivity due to valence bond correlations

It is shown that d-symmetry superconductivity due to valence bond correlations is possible. Valence bond correlations are compatible with antiferromagnetic spin order. In order to explictly construct a homogeneous state with the valence bond structure in the two-dimensional Hubbard model for an arbitrary doping, we have used the variational method based on unitary local transformation. Attraction between holes in the d-channel is due to modulation of hopping by the site population in course of the valence bond formation, and corresponding parameters have been calculated variationally. An important factor for the gap width is the increase in the density of states on the Fermi level due to antiferromagnetic splitting of the band. The gap width and its ratio to the T _c are 2Δ≃0.1t and 2Δ/kT _c≃4.5−4 for U/t≃8. The correspondence between the theoretical phase diagram and experimental data is discussed. The dependence of T _c on the doping δ=|n−1| and the Fermi surface shape are highly sensitive to the weak interaction t′ leading to diagonal hoppings. In the case of t′>0 and p-doping, the peak on the curve of T _c(δ) occurs at the doping δ _opt, when the energy of the flattest part of the lower Hubbard subband crosses the Fermi level at k∼(π,0). In underdoped samples with δ<δ _opt, the anisotropic pseudogap in the normal state corresponds to the energy difference |E(π,0)−μ| between this part of the spectrum and the Fermi level. Zh. éksp. Teor. Fiz. 114, 985–1005 (September 1998)     

Density of states and dispersion of quasiparticles in the Emery model: Nonlocal path-integral Monte Carlo algorithm

The spectral density of states for a 108-site Cu₃₆O₇₂ cluster in the two-dimensional three-band Emery model is reconstructed with the aid of a path integral Monte Carlo algorithm. Dispersion relations are obtained for quasiparticles in the upper Hubbard band and in the correlated-states band; this corresponds to electron and hole doping of high-T _c superconductors. The form of the isoenergy surfaces is close to the experimentally observed form and confirms the existence of singularities in the density of states near the Fermi level. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 11, 860–865 (10 June 1996)     

Remnant Fermi surface in a pseudogap regime of the two-dimensional Hubbard model at finite temperature

A precursor effect on the Fermi surface in the two-dimensional Hubbard model at finite temperatures near the antiferromagnetic instability is studied using three different itinerant approaches: the second order perturbation theory, the paramagnon theory (PT), and the two-particle self-consistent (TPSC) approach. In general, at finite temperature, the Fermi surface of the interacting electron systems is not sharply defined due to the broadening effects of the self-energy. In order to take account of those effects we consider the single-particle spectral function A(, 0) at the Fermi level, to describe the counterpart of the Fermi surface at T = 0. We find that the Fermi surface is destroyed close to the pseudogap regime due to the spin-fluctuation effects in both PT and TPSC approaches. Moreover, the top of the effective valence band is located around = (π/2,π/2) in agreement with earlier investigations on the single-hole motion in the antiferromagnetic background. A crossover behavior from the Fermi-liquid regime to the pseudogap regime is observed in the electron concentration dependence of the spectral function and the self-energy. Received 8 September 2000 and Received in final form 20 December 2000     

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     

Effects of a k⃗-dependent Hybridisation on the Fermi surface of an extended d–p Hubbard model

ABSTRACT

The topology of the Fermi surface of an extended d–p Hubbard model is investigated using Green's function technique in a n-pole approximation. The effects of the d–p hybridisation on the Fermi surface are the main focus in the present work. Nevertheless, the effects of doping, Coulomb interaction and hopping to second-nearest-neighbours on the Fermi surface, are also studied. Particularly, it is shown that the crossover from hole-like to electron-like Fermi surface (Lifshitz transition) is deeply affected by the d–p hybridisation. Moreover, the pseudogap present in the low doping regime is also affected by the hybridisation. The results show that both the doping and the hybridisation act in the sense of suppresses the pseudogap. Therefore, the systematic investigation of the Fermi surface topology, shows that not only the doping but also the hybridisation can be considered as a control parameter for both the pseudogap and the Lifshitz transition. Assuming that the hybridisation is sensitive to external pressure, the present results agree qualitatively with recent experimental data for the cuprate Nd-LSCO.     

The Kondo effect in periodic narrow-band systems

The Kondo divergences owing to interaction of current carriers with local moments in highly correlated electron systems are considered within the Hubbard and s-d exchange models with infinitely strong on-site interaction, the many-electron Hubbard representation being used. The picture of density of states containing a peak at the Fermi level is obtained. Various forms of the self-consistent approximation are used. The problem of the violation of analytical properties of the Green's function is discussed. Smearing of the “Kondo” peak owing to spin dynamics and finite temperatures is investigated. Received 25 November 1999 and Received in final form 31 January 2000     

Doping-dependent electronic structure of cuprates studied using angle-scanned photoemission

Full k -maps of the electronic structure near the Fermi level of differently doped cuprates measured with angle-scanned photoelectron spectroscopy are presented. The valence band maximum of the antiferromagnetic insulator Sr₂CuO₂Cl₂, which is taken as a representative of an undoped cuprate, and the Fermi surfaces of overdoped, optimally doped and underdoped Bi₂Sr₂CaCu₂O_8+δ high-temperature superconductors are mapped in the normal state. The results confirm the existence of large Luttinger Fermi surfaces at high doping with a Fermi surface volume proportional to (1+x), where x is the hole concentration. At very low doping, however, we find that this assumption based on Luttinger's theorem is not fulfilled. This implies a change in the topology of the Fermi surface. Furthermore the intensity of the shadow bands observed on the Fermi surface of Bi₂Sr₂CaCu₂O_8+δ as a function of the doping is discussed. Received 12 October 1999 and Received in final form 12 April 2000     

The non-Fermi-liquid nature of the metallic states of the Hubbard Hamiltonian

It has long since been argued that the metallic states of the single-band Hubbard Hamiltonian ? in two spatial dimensions (i.e. for d = 2) should be non-Fermi liquid, a possibility that would lead to the understanding of the observed anomalous behaviour of the doped copper-oxide-based superconducting compounds in their normal metallic states. Here we present a formalism which enables us to express, for arbitrary d, the behaviour of the momentum-distribution function nσ(k) pertaining to uniform metallic ground states of ? close to S _F; σ (the Fermi surface of the fermions with spin index σ, σ = ↑, ↓) in terms of a small number of constant parameters which are bound to satisfy certain inequalities implied by the requirement of the stability of the ground state of the system. These inequalities restrict the range of variation in nσ(k) for k infinitesimally inside and outside the Fermi sea pertaining to fermions with spin index σ and consequently the range of variation in the zero-temperature limit of nσ(k) for k on S _F; σ On the basis of some available accurate numerical results for nσ(k) pertaining to the Hubbard and the t-J Hamiltonian, we conclude that, at least in the strong-coupling regime, the metallic ground states of ? for d = 2 cannot be Fermi-liquid nor can they in general be purely Luttinger or marginal Fermi liquids. We further rigorously identify the pseudogap phenomenon, or 'truncation' of the Fermi surface, clearly observed in the normal states of underdoped copper-oxide-based superconductors, as corresponding to a line of resonance energies (i.e. these energies strictly do not relate to quasiparticles) located below the Fermi energy, with a concomitant suppression to zero of the jump in nσ(k) over the 'truncated' parts of the Fermi surface. Our analyses make explicit the singular significance of the non-interacting energy dispersion ε _k underlying ? in determining the low-energy spectral and transport properties of the metallic ground states of ?.     

The singlet state in the Hubbard model with U=∞

We discuss, in connection with the problem of the ground state in the Hubbard model with U=∞, the normal (nonmagnetic) N-state of a system over the entire range of electron concentrations n≤1. It is found that in a one-particle approximation, e.g., in the generalized Hartree-Fock approximation, the energy ε ₀(n) of the N-state is lower than the energy ε _FM(n) of a saturated ferromagnetic state for all values of n. Using the random phase approximation we calculate the dynamical magnetic susceptibility and show that the N-state is stable for all values of n. A formally exact representation is derived for the mass operator of the one-particle electron Green’s function, and its expression in the self-consistent Born approximation is obtained. We discuss the first Born approximation and show that when correlations are taken into account, the attenuation vanishes on the Fermi surface and the electron distribution function at T=0 acquires a Migdal discontinuity, whose magnitude depends on n. The energy of the N-state in this approximation is still lower than ε _FM(n) for n<1. We show that the spin correlation functions are isotropic, which is a characteristic feature of the singlet states of the system. We calculate the spin correlation function for the nearest neighbors in the zeroth approximation as a function of n. Finally, we conclude that the singlet state of the system in the thermodynamic limit is the ground state. Zh. éksp. Teor. Fiz. 114, 2130–2144 (December 1998)     

Spin fluctuations and ferromagnetic order in two-dimensional itinerant systems with Van Hove singularities

The quasistatic approach is used to analyze the criterion of ferromagnetism for two-dimensional (2D) systems with the Fermi level near Van Hove (VH) singularities of the electron spectrum. It is shown that the spectrum of spin excitations (paramagnons) is positively defined when the interaction between electrons and paramagnons, determined by the Hubbard on-site repulsion U, is sufficiently large. Due to incommensurate spin fluctuations near the ferromagnetic quantum phase transition, the critical interaction U_c remains finite at VH filling and exceeds considerably its value obtained from the Stoner criterion. A comparison with the functional renormalization group results and mean-field approximation which yields a phase separation is also performed.     

Theory of high-temperature superconductivity in cuprates

A microscopic theory of electronic spectrum and superconducting pairing in the high-temperature cuprate superconductors is presented. The theory is based on consideration of strong electron correlations within the Bogolyubov polar model. The Dyson equation is derived by using the equation of motion method for the thermodynamic Green functions in terms of the Hubbard operators. The self-energy is evaluated in the noncrossing approximation for electron scattering on spin and charge fluctuations induced by kinematic interaction. The theory demonstrates that a strong Coulomb repulsion results in the anomalous electronic spectrum and unconventional (d-wave) superconducting pairing with high T _c mediated by the antiferromagnetic exchange and spin fluctuations.     

Pseudogap and symmetry of superconducting order parameter in cuprates

The phase diagram, nature of the normal state pseudogap, type of the Fermi surface, and behavior of the superconducting gap in various cuprates are discussed in terms of a correlated state with valence bonds. The variational correlated state, which is a band analogue of the Anderson (RVB) states, is constructed using local unitary transformations. Formation of valence bonds causes attraction between holes in the d-channel and corresponding superconductivity compatible with antiferromagnetic spin order. Our calculations indicate that there is a fairly wide range of doping with antiferromagnetic order in isolated CuO₂ planes. The shape of the Fermi surface and phase transition curve are sensitive to the value and sign of the hopping interaction t′ between diagonal neighboring sites. In underdoped samples, the dielectrization of various sections of the Fermi boundary, depending on the sign of t′, gives rise to a pseudogap detected in photoemission spectra for various quasimomentum directions. In particular, in bismuth-and yttrium-based ceramics (t′>0), the transition from the normal state of overdoped samples to the pseudogap state of underdoped samples corresponds to the onset of dielectrization on the Brillouin zone boundary near k=(0,π) and transition from “large” to “small” Fermi surfaces. The hypothesis about s-wave superconductivity of La-and Nd-based ceramics has been revised: a situation is predicted when, notwithstanding the d-wave symmetry of the superconducting order parameter, the excitation energy on the Fermi surface does not vanish at all points of the phase space owing to the dielectrization of the Fermi boundary at k _x=± k _y. The model with orthorhombic distortions and two peaks on the curve of T _c versus doping is discussed in connection with experimental data for the yttrium-based ceramic. Zh. éksp. Teor. Fiz. 115, 649–674 (February 1999)     

Theory of the electronic structure and spin susceptibility of La2−x SrxCuO4

We solve the problem of the effect of strong electron correlations on the homogeneous spin susceptibility of current carriers in CuO₂ planes. We show that the dependence of the spin susceptibility χ(T) of high-T _c superconductors of the La_2−x Sr_xCuO₄ type on temperature and the doping index x can be explained fairly well by the two-band model suggested earlier (the singlet-correlated oxygen band plus the lower Hubbard band of copper). The model has features in common with the phenomenological t-J model but cannot be reduced to the latter completely. In contrast to the t-J model, the density of states of the oxygen holes has a peak near the bottom of the band. It is the presence of this peak together with the non-Fermi-liquid properties that explain the unusual behavior of the spin susceptibility of La_2−x Sr_xCuO₄. Zh. éksp. Teor. Fiz. 112, 1763–1777 (November 1997)     

Fluctuation-exchange study of antiferromagnetism in disordered electron-doped cuprate superconductors

On the basis of the Hubbard model, we extend the fluctuation-exchange (FLEX) approach to investigating the properties of the antiferromagnetic (AF) phase in electron-doped cuprate superconductors. Furthermore, by incorporating the effect of scatterings due to the disordered dopant atoms into the FLEX formalism, our numerical results show that the antiferromagnetic transition temperature, the onset temperature of pseudogap due to spin fluctuations, the spectral density of the single particle near the Fermi surface, and the staggered magnetization in the AF phase as a function of electron doping can consistently account for the experimental measurements.     

Kinematic mechanism of the modulation of the spectral intensity in the spatially uniform system of Hubbard fermions

Using the exact representation of the Green’s function constructed in terms of the Hubbard operators, it has been shown that the kinematic interaction that induces the spin-fluctuation processes in the spatially uniform system of Hubbard fermions leads to significant variations in the spectral intensity A(k, ω) in the Brillouin zone. As a result, the modulation of A(k, ω) appears in the Fermi contour. The sign of the hopping integral within the first coordination sphere is determined by the contour section, where A(k, ω) decreases according to the angle-resolved photoemission spectroscopy data.     

Pseudogap and the Fermi surface in the t-J model

We calculate spectral functions within the t-J model as relevant to cuprates in the regime from low to optimum doping. On the basis of equations of motion for projected operators an effective spin-fermion coupling is derived. The self-energy due to short-wavelength transverse spin fluctuations is shown to lead to a modified self-consistent Born approximation, which can explain strong asymmetry between hole and electron quasiparticles. The coupling to long-wavelength longitudinal spin fluctuations governs the low-frequency behavior and results in a pseudogap behavior, which at low doping effectively truncates the Fermi surface.     

The 3-band Hubbard-model <Emphasis Type="Italic">versus</Emphasis> the 1-band model for the high-<Emphasis Type="Bold">T</Emphasis><Subscript>c</Subscript> cuprates: Pairing dynamics,superconductivity and the ground-state phase diagram

One central challenge in high-T _c superconductivity (SC) is to derive a detailed understanding for the specific role of the Cu-d _x2-y2 and O-p _x,y orbital degrees of freedom. In most theoretical studies an effective one-band Hubbard (1BH) or t-J model has been used. Here, the physics is that of doping into a Mott-insulator, whereas the actual high-T _c cuprates are doped charge-transfer insulators. To shed light on the related question, where the material-dependent physics enters, we compare the competing magnetic and superconducting phases in the ground state, the single- and two-particle excitations and, in particular, the pairing interaction and its dynamics in the three-band Hubbard (3BH) and 1BH-models. Using a cluster embedding scheme, i.e. the variational cluster approach (VCA), we find which frequencies are relevant for pairing in the two models as a function of interaction strength and doping: in the 3BH-models the interaction in the low- to optimal-doping regime is dominated by retarded pairing due to low-energy spin fluctuations with surprisingly little influence of inter-band (p-d charge) fluctuations. On the other hand, in the 1BH-model, in addition a part comes from “high-energy” excited states (Hubbard band), which may be identified with a non-retarded contribution. We find these differences between a charge-transfer and a Mott insulator to be renormalized away for the ground-state phase diagram of the 3BH- and 1BH-models, which are in close overall agreement, i.e. are “universal”. On the other hand, we expect the differences - and thus, the material dependence to show up in the “non-universal” finite-T phase diagram (T _c-values).