We study the 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 · 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 ͱ 3 ϫ ͱ 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 = 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-1 2 model.

Charge frustration due to further neighbor Coulomb repulsion can have dramatic effects on the electronic properties of NaxCoO2 in the full doping range. It can significantly reduce the effective mobility of the charge carriers, leading to a low degeneracy temperature ǫF T . Such strongly renormalized Fermi liquid has rather unusual properties-from the point of view of the ordinary metals with ǫF ≫ T -but similar to the properties that are actually observed in the NaxCoO2 system. For example, we show that the anomalous thermopower and Hall effect observed in Na0.7CoO2 may be interpreted along these lines. If the repulsion is strong, it can also lead to charge order; nevertheless, away from the commensurate dopings, the configurational constraints allow some mobility for the charge carriers, i.e., there remains some "metallic" component. Finally, the particularly strong bandwidth suppression around the commensurate x = 1/3 can help resurrect the RVB superconductivity, which would otherwise not be expected near this high doping. These suggestions are demonstrated specifically for a tJ-like model with an additional nearest neighbor repulsion.

I propose a method to directly measure the space and time dependence of the pair field correlator of a pair density wave. The method is based on two separate ideas. First, we adopt the solenoid insertion method of Ref. 1 to provide the momentum in a tunnel junction. Second, we suggest the use of optimal or over-doped Bi-2201 films as a tunneling electrode with a known charge ordering wave-vector which can match the expected pair density wave wave-vectors we wish to study. The method is applicable to both fluctuating and ordered states. Potential applications are to the proposed stripe pair density wave order in LBCO and the possible pair density wave fluctuations at finite temperature or in high magnetic field in underdoped YBCO as well as other members of the cuprate family.