Grzegorz Górski

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.

Josephson-phase-controlled interplay between correlation effects and electron pairing in a three-terminal nanostructure

We study the subgap spectrum of the interacting single-level quantum dot coupled between two superconducting reservoirs, forming the Josephson-type circuit, and additionally hybridized with a metallic normal lead. This system allows for the phase-tunable interplay between the correlation effects and the proximity-induced electron pairing resulting in the singlet-doublet (0-

Appearance of antiferromagnetism and superconductivity in superconducting cuprates

\pi

Antiferromagnetic ordering of itinerant systems in modified mean-field theory

) crossover and the phase-dependent Kondo effect. We investigate the spectral function, induced local pairing, Josephson supercurrent, and Andreev conductance in a wide range of system parameters by the numerically exact Numerical Renormalization Group and Quantum Monte Carlo calculations along with perturbative treatments in terms of the Coulomb repulsion and the hybridization term. Our results address especially the correlation effects reflected in dependencies of various quantities on the local Coulomb interaction strength as well as on the coupling to the normal lead. We quantitatively establish the phase-dependent Kondo temperature

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

\log T_{K}(\phi)\propto\cos^{2}(\phi/2)

The Coexistence Between Magnetic Ordering and Itinerant Electron Superconductivity

and show that it can be read off from the half-width of the zero-bias enhancement in the Andreev conductance in the doublet phase, which can be experimentally measured by the tunneling spectroscopy.

Critical Temperatures in the Three-Band Extended Hubbard Model

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.

Energy Harvesting in the Nonlinear Piezoelastic Systems Driven by Harmonic Excitations with Asymmetrical Shape of the Potential Energy

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.