The three band Hubbard model with nearest neighbour repulsion is studied in the U=∞ limit using the large N expansion technique to order [Formula: see text]. A charge transfer (CT) instability is found like in weak coupling theory. However at small doping a major role is played by the Brinkman-Rice point. The CT instability is always associated with a diverging compressibility leading to a phase separation. The evaluation to order [Formula: see text] of the effective scattering amplitude in the Cooper channel shows the presence of superconducting instabilities in the s and d wave channel near the phase separation.
We analyze the role of the collective modes on the charge-transfer instability (CTI), phase separation, and the superconductivity in the extended Hubbard model. We show that, in the weak-coupling limit, the CTI appears when the zero-sound mode becomes unstable and the Landau stability criterion
F0s>-1 is violated, due to a coupling to the charge-transfer exciton. We also study the frequency dependence of the effective interaction, mediated by the exchange of collective modes, between the quasiparticles.
The
CuO2 sheets common to the superconducting cuprates are believed to be characterized by a charge-transfer gap in their insulating antiferromagnetic state. The three-band Hubbard model with an on-site Cu Coulomb interaction
Ud, which is large compared to the difference in energy \ensuremath{\varepsilon} between the O and Cu sites, provides a basic model for such a system. We have carried out Lanczos and Monte Carlo studies of a
CuO2 lattice described by a three-band Hubbard model. For
Ud large compared with \ensuremath{\varepsilon}, and \ensuremath{\varepsilon} comparable to or larger than the bandwidth of the lower hole band, we find strong antiferromagnetic correlations and evidence for a charge-transfer gap at a filling of one hole per Cu. The antiferromagnetic correlations decrease with either hole or electron doping, and we see that the additional holes go primarily on the O sites, while additional electrons go onto the Cu sites. For large values of the intersite Cu-O Coulomb interaction V, the hole-doped system exhibits a charge-transfer instability. As V is reduced, this is reflected as a peak in the charge-transfer susceptibility near \ensuremath{\varepsilon}+2V\ensuremath{\approxeq}
Ud, which we find is washed out by the strong Cu-O hybridization at realistic values of V. Attractive pairing interactions are found in both the d-wave and extended
s∗-wave channels near the antiferromagnetic boundary.
Exact diagonalisations of the extended two-band Hubbard model are performed. In the insulating regime it is shown that the nearest-neighbour copper-oxygen repulsion, V , leads to Frenkel excitons in the charge transfer gap at values of V of the order of copper-oxygen hybridisation, t . In the metallic regime it is shown that the static charge transfer and density-density correlation functions diverge as a function of V , indicating a charge transfer instability and phase separation. This is accompanied by a softening of the q → 0 mode of the dynamic correlation functions which is associated with the excitonic excitations responsible for the superconducting correlations observed in the proximity of the phase separation boundary described by C. Vermeulen et al. (C. Vermeulen et al. , Europhys. Lett. , 28 (1994) 653).
Understanding competing instabilities in systems with correlated fermions remains one of the holy grails of modern condensed matter physics. Among the fermionic lattice models used to this effect, the extended Hubbard model occupies a prime place due to the potential relevance of its repulsive and attractive versions for both electronic materials and artificial systems. Using the recently introduced multichannel fluctuating field approach, we address the interplay of fluctuations in the charge density wave,
s-wave superconducting, and phase separation channels in the attractive extended Hubbard model. Despite the fact that this model has been intensively studied for decades, our approach allows us to identify a phase that has not been analyzed before and which is characterized by the coexistence of collective
s-wave superconducting and phase separation fluctuations. Our findings resonate with previous observations of interplaying phase separation and superconducting phases in electronic systems, most importantly in high-temperature superconductors.
The Hubbard model including nearest-neighbor interaction is studied at
T=0 on a
d-dimensional hypercubic lattice ($d\ensuremath{\ge}3$) close to half filling. It is shown that the ground state at weak coupling is phase separated, consisting of homogeneous lower-density and antiferromagnetic or charge density wave higher-density regions. Incommensurate phases are unstable. The exact critical doping level and the exact order parameter are renormalized relative to the Hartree results. The renormalization factor at weak coupling turns out to be identical to the result found previously for the same model at half filling.