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Attractive non-local interactions jointly with repulsive local interaction ina microscopic modelling of electronic Fermi liquids generate a competitionbetween an enhancement of the static charge susceptibility---ultimatelysignalling charge instability and phase separation---and its correlationinduced suppression. We analyse this scenario through the investigation of theextended Hubbard model on a two-dimensional square lattice, using the spinrotation invariant slave-boson representation of Kotliar and Ruckenstein. Thequasiparticle density of states, the renormalised effective mass and the Landauparameter $F_0^s$ are presented, whereby the positivity of $F_0^s-1$constitutes a criterion for stability. Van Hove singularities in the density ofstates support possible charge instabilities. A (negative) next-nearestneighbour hopping parameter $t'$ shifts their positions and produces a tendencytowards charge instability even for low filling whereas the $t'$-controlledparticle-hole asymmetry of the correlation driven effective mass is small. Aregion of instability on account of the attractive interaction $V$ isidentified, either at half filling in the absence of strong electroniccorrelations or, in the case of large on-site interaction $U$, at densities farfrom half filling.

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