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.
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 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.
Possible ordered states in the 2D extended Hubbard model with on-site (U>0) and nearest-neighbor (V) interaction are examined near half filling, with emphasis on the effect of finite V. First, the phase diagram at absolute zero is determined in the mean field approximation. For
V<0, a state where d_{x^{2}-y^{2}}-wave superconductivity (dSC), commensurate spin-density-wave (SDW) and
π-triplet pair coexist is seen to be stabilized. Here, the importance of
π-triplet pair on the coexistence of dSC and SDW is indicated. This coexistent state is hampered by the phase separation (PS), which is generally expected to occur in the presence of finite-range attractive interaction, but survives. For V>0, a state where commensurate charge-density-wave (CDW), SDW and ferromagnetism (FM) coexist is seen to be stabilized. Here, the importance of FM on the coexistence of CDW and SDW is indicated. Next, in order to examine the effects of fluctuation on each mean field ordered state, the renormalization group method for the special case that the Fermi level lies just on the saddle points, (
π,0) and (0,
π), is applied. The crucial difference from the mean field result is that superconductivity can arise even for U>0 and
V≥0, where the superconducting gap symmetry is d_{x^{2}-y^{2}}-wave for U>4V and s-wave for U<4V. Finally, the possibilities that the mean field coexistent states survive in the presence of fluctuation are discussed.
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.