Jerzy Mizia

Equation of motion solutions to Hubbard model retaining Kondo effect

Abstract We propose a new way of analyzing the Hubbard model using equations of motion (EOM) for the higher-order Greens functions approach within the DMFT scheme. In calculating the higher order Green function we will differentiate over both times (t) and (t′). This allows us to obtain the metallic Fermi liquid at nonzero Coulomb interaction, where the three center DOS structure with two Hubbard bands and the quasiparticle resonance peak is obtained. At small Coulomb interactions and zero temperature the height of the quasiparticle resonance peak on the Fermi energy is constant similarly as in the full DMFT method with numerical (Quantum Monte Carlo) or with analytical (e.g. iterative perturbation theory) calculations.

Magnetic ordering of itinerant systems: the role of kinetic interactions

Abstract The possibility of ferromagnetic ordering is revisited in the band model. The coherent potential approximation decoupling has been used for the strong on-site Coulomb interaction. The driving forces towards the ferromagnetism are the on-site and inter-site molecular fields coming from different Coulomb interactions. Another driving force is the lowering of the kinetic energy with growing magnetic moment coming from the dependence of the hopping integrals on occupation of the neighboring sites involved in hopping. This effect is described by the hopping interaction, Δt, and by what we call the exchange–hopping interaction, tex. The exchange–hopping interaction, which is the difference in hopping integrals for different occupation of neighboring lattice sites, acts in a way analogous to the Hunds magnetic exchange interaction. The results are calculated for semi-elliptic density of states (DOS) and for the distorted semi-elliptic DOS with the maximum around the Fermi energy. They show a natural tendency towards the magnetic ordering at the end of the 3D row for the DOS with maximum density around the Fermi energy, when the hopping integrals grow with the occupation of the neighboring lattice sites.

Role of internal stresses in electronic pairing of layered superconductors

We consider an extended electronic model for superconducting ceramics. The driving force for superconductivity in a single band model is the nondiagonal Coulomb interaction (correlated hopping), Δt = (ii|1/r|ji). This driving force is supplemented by the quantum expression describing the internal local deformation of the Cu-O layers. The BCS equation is solved numerically for a single band model. It is shown that a physically reasonable set of hole-deformation coupling constants will lower significantly the band expansion coefficient, K = 8 Δt, required for superconductivity.

Appearance of antiferromagnetism and superconductivity in superconducting cuprates

Abstract We represent the superconducting ceramic compounds by the single band extended Hubbard model. We use this model for solving the simultaneous presence of antiferromagnetism and the d -wave superconductivity in the Hartree–Fock (H–F) and in the coherent potential (CP) approximation, which is applied to the on-site Coulomb repulsion U . The hopping interaction used in addition to the Coulomb repulsion causes rapid expansion of the band at carrier concentrations departing from unity. This expansion shifts the d -wave superconductivity away from the half filled point reducing its occupation range approximately to the experimental range in the YBaCuO compound. The CP approximation used for the Coulomb repulsion is justified by the large ratio of Coulomb repulsion to the effective width of perturbed density of states being reduced by the hopping interaction. The experimentally observed fast disappearance of antiferromagnetism is supported in calculations by the relatively large value of the total width of unperturbed density of states and the high values of the hopping interaction. It is shown that our model is capable of describing the electron doped compounds as well.

Antiferromagnetic ordering of itinerant systems in modified mean-field theory

Abstract This is an analysis of the itinerant model for antiferromagnetism, in which is included both on-site and inter-site electron correlations. We also consider the band degeneration, which brings into the Hamiltonian the on-site exchange interactions. The Green function technique is used and the coherent potential approximation (CPA) decoupling for the on-site Coulomb repulsion. This decoupling combined with the modified Hartree–Fock approximation for the inter-site interactions generates the change in shape of the spin bands with growing interaction constants, which is described by the correlation factors and which decreases the kinetic energy of the system. The effective Hartree field and the gain in kinetic energy due to the on-site and inter-site correlation factors drive the antiferromagnetism. The on-site and inter-site interactions act together towards the antiferromagnetism. Their cooperation decreases the interaction constants required for the antiferromagnetic ordering. This new approach allows for the antiferromagnetic instability in the purely itinerant model at the half-filling in the split band limit. This situation describes the high temperature superconducting cuprates.

Electronic pairing due to interband and intraband hopping dependence on oxygen covalency in YBaCuO superconductors

We consider the electronic extended model for the superconducting ceramics. In this model the broad electron band formed in the Cu-O plane interacts with the narrow level created by vacancies on the Cu-O chains. It has been assumed 2 that both; the interband hopping integral and the intraband hopping integral depend on the oxygen occupancy. We derive the pairing potential using the diagonalization method for the two band system and subsequently we look for the pairing terms in the remaining interactions, which are; the Coulomb on site repulsion in the broad band and the occupational difference in the intraband and interband hopping interaction. In the result we obtain the pairing potential with reduced Coulomb repulsion and with negative terms, which are proportional to the differences in the oxygen hopping integrals. The effective pairing potential is analysed for the possibility of superconducting transition. It has been shown that the high temperature << . superconductivity is possible at the reduced values of the Coulomb D t s ii 1r ri jquasi hopping term. The reduction is due to the occupational difference, DV, in the interband hopping interaction between O 2y and O 1y oxygen ions and the narrow level. The Coulomb repulsion on the narrow level also reduces required D t but at the much smaller amount. q 1998 Published by Elsevier Science B.V. All rights reserved.

The Coexistence Between Magnetic Ordering and Itinerant Electron Superconductivity

This chapter focuses on the coexistence between magnetic ordering and superconductivity. New superconducting compounds and materials quite frequently possess magnetic alignments. There is a problem of coexistence between these alignments and superconductivity (SC), especially in the high-temperature superconductors. In a majority of perovskite compounds, there are two phases, SC and AF, the presence of which depends on doping. The coexistence of AF and SC in the low-temperature superconductors has been established in materials in which different groups of electrons have been responsible for both types of ordering and the superconducting coherence length is extended over many elementary cells of the AF order. Between the phase of insulating AF and metallic SC, there is sometimes the phase of spin glass, which at present is identified rather as the diagonal stripe phase. The coexistence between magnetic phase and SC is particularly frequent in high-temperature superconductors, where the SC most likely has an electronic origin. A characteristic feature of ferromagnetic superconductors is the existence of SC only in the domain of ferromagnetic ordering. Transition to the paramagnetic state causes the disappearance of SC.

Critical Temperatures in the Three-Band Extended Hubbard Model

We investigate the three-band extended Hubbard model for the CuO 2 planes of high-temperature superconductors. We consider the limit of U = ∞ on Cu atoms and we include the nearest-neighbor Coulomb repulsion between holes on 2p x,y orbitals of oxygen and holes on 3d x2-y2 v 2 or 3d 3x2-r2 orbitals of copper (V x and V z respectively, with V x > V z ). This leads to the effective negative nearest-neighbor Coulomb interaction. Numerical analysis of this model reveals the possibility of s-wave and d-wave superconductivity arising from the difference ΔV = V z - V x . It was shown that the s-wave superconductivity is driven by ΔV and is opposed by the Coulomb repulsion on oxygen, U p , while the d-wave superconductivity is influenced only by the driving force. ΔV, This fact would enable existence of the d-wave superconductivity in many high temperature superconducting materials.

CHAPTER 7 – Itinerant Ferromagnetism

Publisher Summary This chapter focuses on the atomic elements. The atomic number of an element is equal to the number of electrons of this element. The reason is that the atomic number is equal to the number of protons in the nuclei. Every proton carries an elementary positive charge that in the neutral state of an atom has to be balanced by a negative elementary charge of electron in the electron shell. The elements are placed in seven rows corresponding to principal quantum number varying from 1 to 7. The superscript on the right denotes the actual number of electrons in the orbit. Orbits with a high-angular momentum have energy comparable with that of higher-principal quantum numbers, but low-angular momentum. When the atoms get close together, the bands formed from the orbits, which are close in energy, start overlapping. The overlapping bands are filled to the same energy, which is called the Fermi energy. It is like a liquid in connected vessels that are filled to the same level. This is why the itinerant electrons are sometimes called the Fermi liquid. The total number of electrons in overlapping bands is the same in the atomic state and in the solid state.

Band Magnetism with Inter-Site Correlations and Interactions

We introduce the Hamiltonian to describe narrow band electrons. The physics of driving forces towards ferromagnetism is re-examined. Using different approximations it has been shown that the magnetic moments created by inter-site interaction and inter-site kinetic correlation decrease quickly with temperature. As a result of these interactions and the realistic density of states (DOS) the Curie temperatures calculated after fitting magnetic moments to their low temperature values are realistic. In the past the Curie temperatures calculated using only the on-site interaction were much higher than the experimental temperatures.