Study of the triangular lattice tV model near x=1/3

TL;DR

This paper investigates the extended Hubbard model on a triangular lattice near 1/3 doping, identifying phase transitions, charge density wave states, and potential superconducting instabilities through meanfield and fluctuation analyses.

Contribution

It introduces a large-N meanfield framework for the model, analyzes phase transitions, and explores superconducting tendencies near charge density wave instabilities.

Findings

First-order transition at x=1/3 doping driven by nearest neighbor repulsion

Charge fluctuations near CDW instability favor an f-wave triplet superconducting state

Gutzwiller wavefunction study supports the meanfield and fluctuation results

Abstract

We study extended Hubbard model on a triangular lattice near doping $x=1/3$, which may be relevant for the recently discovered superconductor Na$_x$CoO$_2 \cdot y$H$_2$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 $\rt3rt3$ 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 CDW instability, the increasing charge fluctuations favor a particular $f$-wave triplet state. (This state was recently discussed by Tanakaet al, cond-mat/0311266). We also report a direct Gutzwiller wavefunction study of the spin-1/2 model.