The phase diagrams and superconducting properties of the extended Hubbard model with pair hopping interaction, i.e., the Penson-Kolb-Hubbard model are studied. The analysis of the model is performed for d-dimensional hypercubic lattices, including
d=1 and $d=\ensuremath{\infty},$ by means of the (broken symmetry) Hartree-Fock approximations and, for $d=\ensuremath{\infty},$ by the slave-boson mean-field method. For
d=1, at half filling the phase diagram is shown to consist of nine different phases including two superconducting states with center-of-mass momentum
q=0 and
q=Q $(\ensuremath{\eta}$ pairing), site and bond-located antiferromagnetic and charge-density wave states as well as three mixed phases with coexisting site and bond orderings. The stability range of the bond-type orderings shrinks with increasing lattice dimensionality d and for $d=\ensuremath{\infty}$ the corresponding diagram consists of four phases only, involving exclusively site-located orderings. Comparing the pair hopping model with the attractive Hubbard model we found in both cases gradual evolution from the BCS-like limit to the tightly bound pairs regime and a monotonic increase of the gap in the excitation spectrum with increasing coupling. However, the dynamics of electron pairs in both models is qualitatively different, which results in different dependences of condensation energies and critical temperatures on interaction parameters as well as in different electrodynamic properties, especially in a strong coupling regime.
We study the extended Hubbard model with on-site density-density U and intersite pair hopping J interactions, i.e. the Penson-Kolb-Hubbard model.This report focuses mainly on the properties of the model at T ≥ 0 in the case of repulsive J (J < 0) which may stabilize superconductivity with η-pairing.The analysis is performed within the (broken symmetry) Hartree-Fock approximation for arbitrary interaction parameters (J < 0 and U ) and electron concentration (0 < n < 2) on the d = 2 square lattice.The phase diagrams of the model at T = 0 and at finite temperatures are examined taking into account magnetic and charge-ordered phases and superconducting states with η-and s-wave pairing.
We present the analysis of paramagnetic eects of magnetic eld (B) (Zeeman term) in the zero-bandwidth limit of the extended Hubbard model for arbitrary chemical potential µ and electron density n.The eective Hamiltonian considered consists of the on-site interaction U and the intersite charge exchange term I, determining the hopping of electron pairs between nearest-neighbour sites.The model has been analyzed within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-eld approximation (rigorous in the limit of innite dimensions d → +∞).In this report we focus on metastable phases as well as phase separated states involving superconducting and nonordered phases and determine their ranges of occurrence for U/I0 = 1.05 (I0 = zI) in the presence of magnetic eld B = 0. Our investigations of the general case for arbitrary U/I0 show that, depending on the values of interaction parameters (for xed n), the phase separating state can occur in higher elds than the homogeneous superconducting phase (eld-induced phase separated).Moreover, a rst-order superconductingnonordered transition occurs between metastable phases and these metastable phases can exist inside the regions of the phase separated state stability.Such behaviour is associated with the presence of tricritical line on the phase diagrams of the system.
We have studied the extended Hubbard model with pair hopping in the atomic limit for arbitrary electron density and chemical potential. The Hamiltonian considered consists of (i) the effective on-site interaction U and (ii) the intersite charge exchange interactions I, determining the hopping of electron pairs between nearest-neighbour sites. The model can be treated as a simple effective model of a superconductor with very short coherence length in which electrons are localized and only electron pairs have a possibility of transferring. The phase diagrams and thermodynamic properties of this model have been determined within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. We have also obtained rigorous results for a linear chain (d = 1) in the ground state. Moreover, at T = 0 some results derived within the random phase approximation (and the spin-wave approximation) for d = 2 and 3 lattices and within the low-density expansions for d = 3 lattices are presented. Our investigation of the general case (as a function of the electron concentration n and as a function of the chemical potential μ) shows that, depending on the values of interaction parameters, the system can exhibit not only the homogeneous phases, superconducting (SS) and nonordered (NO), but also the phase separated states (PS: SS-NO). The system considered exhibits interesting multicritical behaviour including tricritical points.
We study the ground state phase diagrams of the extended Hubbard model with the pairhopping interaction J, i.e. the PensonKolbHubbard model.We concentrate on the case of attractive J (J > 0) which can stabilise s-wave pairing superconductivity in the system and competes with the on-site repulsive U .The evolution of the phase diagrams and order parameters for arbitrary electron density and representative values of the interaction parameters are analyzed within the (broken symmetry) HartreeFock approximation.The calculations are performed for the case of nearest-neighbors electron hopping t on the d = 2 square lattice.
We study
s-wave superconductivity in the two-dimensional square-lattice attractive Hubbard Hamiltonian for various inhomogeneous patterns of interacting sites. Using the Bogoliubov--de Gennes mean-field approximation, we obtain the phase diagram for inhomogeneous patterns in which the on-site attractive interaction
Ui between the electrons takes on two values
Ui=0 and $\ensuremath{-}U∕(1\ensuremath{-}f)$ (with
f the concentration of noninteracting sites) as a function of average electron occupation per site,
n, and study the evolution of the phase diagram as
f varies. In certain regions of the phase diagram, inhomogeneity results in a larger zero-temperature average pairing amplitude (order parameter) and also a higher superconducting critical temperature
Tc, relative to a uniform system with the same mean interaction strength (${U}_{i}=\ensuremath{-}U$ on all sites). These effects are observed for stripes, checkerboard, and even random patterns of the attractive centers, suggesting that the pattern of inhomogeneity is unimportant. The phase diagrams also include regions where superconductivity is obliterated due to the formation of various charge-ordered phases. The enhancement of
Tc due to inhomogeneity is robust as long as the electron doping per site,
n, is less than twice the fraction of interacting sites $[2(1\ensuremath{-}f)]$ regardless of the pattern. We also show that for certain inhomogeneous patterns, when $n=2(1\ensuremath{-}f)$, increasing temperature can work against the stability of existing charge-ordered phases for large
f and, as a result, enhance
Tc.