Study of the triangular latticetVmodel nearx=13

Abstract

We study the extended Hubbard model on a triangular lattice near doping $x=\frac{1}{3}$, which may be relevant for the recently discovered superconductor ${\mathrm{Na}}_x{\mathrm{CoO}}_2·y{\mathrm{H}}_2\mathrm{O}$. 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 $\sqrt{3}\times \sqrt{3}$ 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 $x=\frac{1}{3}$, 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 spin-$\frac{1}{2}$ model.