We study the superfluid properties of short-coherence-length superconductors described by the extended Hubbard model with on-site repulsive and intersite attractive interaction. We have analysed the superfluid stiffness and thermodynamic properties of the model versus electron concentration and pairing interaction on a two-dimensional square lattice with nearest- and next-nearest-neighbour hopping. The effects of phase fluctuations on anisotropic superconductivity of extended s-and d x 2 − y 2 -wave type were examined within the Kosterlitz–Thouless (KT) scenario. The KT critical temperatures were determined and compared with those from the BCS–Hartree–Fock approximation. The Uemura-type plots, i.e. the critical temperature versus zero-temperature phase stiffness, were obtained for both extended s- and d-wave pairings. The states with mixed (s ∗ and d x 2 − y 2 ) symmetry, and in particular the time-reversal breaking state of s + id symmetry, were analysed and the phase diagrams taking into account these states are presented. We also briefly discuss the crossover from BCS to local pair superconductivity for the d x 2 − y 2 -wave pairing. A comparison of the theoretical results with the experimental data, in particular those of T c versus λ −2 (0), for high- T c cuprate superconductors is made.
We study the effects of phase fluctuations in 2D short-coherence length superconductors on the basis of the extended Hubbard model with intersite attraction.In the Kosterlitz-Thouless scenario the critical temperatures for anisotropic pairings were determined and compared with the ones from BCS Hartree-Fock approximation.The Uemura-type plots, i.e. the critical temperature vs. zero temperature phase stiffness, were obtained for extended s-wave and d x 2y 2-wave pairings.We also discuss the crossover from BCS to local pair superconductivity for d-wave pairing.
Our previous mean-field study concerning superconducting pairings in the extended Hubbard model with on-site repulsive and intersite attractive interaction and arbitrary electron density is extended to include the effects of nearest-neighbor exchange (
J) and correlated hopping (
K) interaction. Detailed numerical analysis of
s-,
p-, and
d-wave pairing solutions is performed for the two-dimensional square lattice with nearest- (
t) and next-nearest- (
t2) neighbor hopping, and the resulting mutual stability phase diagrams are given as a function of band filling and the interaction parameters. Antiferromagnetic exchange can enhance both the
d-wave and the extended
s-wave pairing. If it prevails over the repulsive intersite density-density interaction, such a term can be a leading mechanism for superconductivity. However, its effects strongly depend on the band filling and the
tt2 ratio, giving in particular for
t2=0 s-wave (
d-wave) pairing as most favorable in the low (high) density limit, but increasing
t2 can even reverse this tendency. The correlated hopping term which breaks the electron-hole symmetry affects
s-wave pairing mostly. A condensation transition (phase separation), possible in the presence of the attractive density-density interaction, is also analyzed within the random-phase approximation, and stability conditions of such an electron droplet phase with respect to other types of ordering are determined as a function of the band filling for the two-dimensional square lattice.
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 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.
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.
The authors study a simple model for superconductivity based on an extended Hubbard model with on-site repulsive and inter-site attractive interaction for arbitrary electron density. The two-dimensional square lattice d-wave pairing is most stable for a nearly half-filled band. p-wave and then extended s-wave pairing become stable upon decreasing band filling. Competition between the various anisotropic pairings and antiferromagnetism as well as the effect of next-nearest-neighbour hopping is discussed. The authors relate the present model to high-T c superconducting oxides.