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Charge instabilities of the two-dimensional Hubbard model with attractive nearest neighbour interaction

Attractive non-local interactions jointly with repulsive local interaction in a microscopic modelling of electronic Fermi liquids generate a competition between an enhancement of the static charge susceptibility---ultimately signalling charge instability and phase separation---and its correlation induced suppression. We analyse this scenario through the investigation of the extended Hubbard model on a two-dimensional square lattice, using the spin rotation invariant slave-boson representation of Kotliar and Ruckenstein. The quasiparticle density of states, the renormalised effective mass and the Landau parameter $F_0^s$ are presented, whereby the positivity of $F_0^s-1$ constitutes a criterion for stability. Van Hove singularities in the density of states support possible charge instabilities. A (negative) next-nearest neighbour hopping parameter $t'$ shifts their positions and produces a tendency towards charge instability even for low filling whereas the $t'$-controlled particle-hole asymmetry of the correlation driven effective mass is small. A region of instability on account of the attractive interaction $V$ is identified, either at half filling in the absence of strong electronic correlations or, in the case of large on-site interaction $U$, at densities far from half filling.