Study of the triangular lattice tV model near x=1/3 -: art. no. 024514

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.yH(2)O. 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 root3xroot3 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 , cond-mat/0311266.) We also report a direct Gutzwiller wave function study of the spin-1/2 model.