Study of the triangular lattice tV model near x = 13

We study the extended Hubbard model on a triangular lattice near doping x= 1 3 , which may be relevant for the recently discovered superconductor NaxCoO2·yH2O. By generalizing this model to N fermionic species, we formulate a meanfield description in the limit of large N. In meanfield, we find two possible phases: a renormalized Fermi liquid and a Î33Î3 charge density wave state. The transition between the two phases is driven by increasing the nearest-neighbor repulsion and is found to be first order for doping x= 1 3 , but occurs close to the point of the local instability of the uniform liquid. We also study fluctuations about the uniform meanfield state in a systematic 1 /N expansion, focusing on the residual interaction of quasiparticles and possible superconducting instabilities due to this interaction. Upon moving towards the charge density wave instability, the increasing charge fluctuations favor a particular f-wave triplet state. (This state was recently discussed by Tanaka et al., cond-mat/0311266.) We also report a direct Gutzwiller wave function study of the spin2 model.