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Several new classes of compounds can be modeled in first approximation byelectrons on the triangular lattice that interact through on-site repulsion $U$as well as nearest-neighbor repulsion $V$. This extended Hubbard model on atriangular lattice has been studied mostly in the strong coupling limit foronly a few types of instabilities. Using the extended two-particle selfconsistent approach (ETPSC), that is valid at weak to intermediate coupling, wepresent an unbiased study of the density and interaction dependent crossoverdiagram for spin and charge density wave instabilities of the normal state atarbitrary wave vector. When $U$ dominates over $V$ and electron filling islarge, instabilities are chiefly in the spin sector and are controlled mostlyby Fermi surface properties. Increasing $V$ eventually leads to chargeinstabilities. In the latter case, it is mostly the wave vector dependence ofthe vertex that determines the wave vector of the instability rather than Fermisurface properties. At small filling, non-trivial instabilities appear onlybeyond the weak coupling limit. There again, charge density wave instabilitiesare favored over a wide range of dopings by large $V$ at wave vectorscorresponding to $\sqrt(3) \times \sqrt(3)$ superlattice in real space.Commensurate fillings do not play a special role for this instability.Increasing $U$ leads to competition with ferromagnetism. At negative values of$U$ or $V$, neglecting superconducting fluctuations, one finds that chargeinstabilities are favored. In general, the crossover diagram presents a richvariety of instabilities. We also show that thermal charge-density wavefluctuations in the renormalized classical regime can open a pseudogap in thesingle-particle spectral weight, just as spin or superconducting fluctuations.

Competition between charge and spin order in the $t-U-V$ extended Hubbard model on the triangular lattice