We discuss the density-density response functions and the collective excitation spectrum for the extended Hubbard model with on-site attraction and arbitrary electron density, in the superconducting ground state.For the short-range intersite interaction we find the sound wave-like modes with the velocity interpolating smoothly between the weak (v 2Zt, |UD <2Zt) and strong coupling (v > 2Zt) limits.The latter agrees with the results obtained from an effective pseudospin Hamiltonian valid in the strong coupling limit.In the weak coupling regime, we obtain that apart from a commensurate charge density wave instability, an increase in the intersite Coułomb repulsion can give rise to a charge density wave incommensurate with the lattice period, away from half-frlling.The ground state phase diagram for 2D square lattice, including singlet superconducting ground state, electronic droplet formation, and charge density waves is determined.It is also shown that the energy of collective excitations evolves smoothly from weak to strong coupling limit for a 2D lattice, in the case of a long-range Coulomb interaction.Finally, the mode coupling effects in the frequency behavior of the density-density response functions are analyzed.
By use of a diagrammatic method we determine the density-density response functions in the random-phase approximation (RPA) and the collective-excitation spectrum for the extended Hubbard model with on-site attraction and arbitrary electron density, in the superconducting ground state. The energy of the collective modes, given by the poles of these response functions, is found to be a linear function of the wave vector (for small k and short-range intersite interaction) with the velocity interpolating smoothly between the weak- (\ensuremath{\propto}2zt, \ensuremath{\Vert}U\ensuremath{\Vert}\ensuremath{\ll}2zt) and strong-coupling (\ensuremath{\propto}
zt2/\ensuremath{\Vert}U\ensuremath{\Vert}, \ensuremath{\Vert}U\ensuremath{\Vert}\ensuremath{\gg}2zt) limits. The latter agrees with the results obtained from an effective pseudospin Hamiltonian valid in the strong-coupling limit. The numerical analysis for a two-dimensional (2D) square lattice shows the occurrence of a rotonlike minima near the zone boundary. In the weak-coupling regime we find that apart from a commensurate charge-density-wave (CDW) instability, an increase in the intersite Coulomb repulsion can give rise to a CDW incommensurate with the lattice period, away from half-filling. The resulting phase diagram for the 2D square lattice, including a singlet superconducting ground state, electronic-droplet formation, and CDW's, is determined. Finally, the effects of a long-range Coulomb interaction are analyzed briefly and it is shown that the energy of collective excitations evolves smoothly from the weak- to the strong-coupling limit for a 2D lattice.
Abstract The possibility of the superconducting transition in the repulsive Hubbard model on a square lattice is studied using the ladder approximation of the strong coupling diagram technique. The t – U and t – t ′– t ″– U models are considered in the regime of strong correlations, for the on-site Coulomb repulsion U = 8 t , in the range of temperatures 0.02 t ≲ T ≲ 0.3 t . To avoid the influence of the phase separation and size effects the calculations are performed in an infinite crystal, in the part of the phase diagram without inhomogeneities, for the electron concentration n ¯ = 0.92 . Solutions of the Eliashberg equation for singlet and triplet pairing, which are transformed according to one-dimensional representations of the lattice point group D 4 , are considered. For both models and all considered symmetries, eigenvalues of the Eliashberg equation are less than unity and demonstrate no upward trend with decreasing temperature. This result points to the absence of superconductivity in the Hubbard model in the strong-coupling regime. We discuss the reason for the small eigenvalue of the Eliashberg equation in the case of the singlet d x 2 − y 2 pairing.
We demonstrate the possibility of triplet p-wave pairing at low electron density a large number of models such as 3D and 2D Fermi-gas models with hard-core repulsion, 3D and 2D Hubbard models, and the Shubin-Vonsovsky model. The critical temperature for p-wave pairing can be considerably higher in the spin-polarized case or even in a two-band situation at low density and can reach experimentally observable values of 1–5 K. We also discuss briefly the d-wave pairing and high-Tc superconductivity with Tc ∼ 100 K which arise in the extended Hubbard model and in the generalized t-J model when close to half-filling.
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 phase diagram of the extended Hubbard model on a two-dimensional square lattice, including on-site (
U) and nearest-neighbor (
V) interactions, at weak couplings. We show that the charge-density wave phase that is known to occur at half filling when
4V>U gives way to a
dxy-wave superconducting instability away from half filling, when the Fermi surface is not perfectly nested, and for sufficiently large repulsive
V and a range of on-site repulsive interaction
U. In addition, when nesting is further suppressed and in the presence of a nearest-neighbor attraction, a triplet time-reversal breaking
(px+ipy)-wave pairing instability emerges, competing with the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ pairing state that is known to dominate at fillings just slightly away from half. At even smaller fillings, where the Fermi surface no longer presents any nesting, the
(px+ipy)-wave superconducting phase dominates in the whole regime of on-site repulsions and nearest-neighbor attractions, while
dxy pairing occurs in the presence of on-site attraction. Our results suggest that zero-energy Majorana fermions can be realized on a square lattice in the presence of a magnetic field. For a system of cold fermionic atoms on a two-dimensional square optical lattice, both an on-site repulsion and a nearest-neighbor attraction would be required, in addition to rotation of the system to create vortices. We discuss possible ways of experimentally engineering the required interaction terms in a cold atom system.