Possible effects of charge frustration in Na${}_x$CoO${}_2$: bandwidth suppression, charge orders and resurrected RVB superconductivity

Charge frustration due to further neighbor Coulomb repulsion can have dramatic effects on the electronic properties of Na${}_x$CoO${}_2$ in the full doping range. It can significantly reduce the effective mobility of the charge carriers, leading to a low degeneracy temperature ${ϵ}_F\lesssim T$. Such strongly renormalized Fermi liquid has rather unusual properties–from the point of view of the ordinary metals with ${ϵ}_F\gg T$–but similar to the properties that are actually observed in the Na${}_x$CoO${}_2$ system. For example, we show that the anomalous thermopower and Hall effect observed in Na${}_{0.7}$CoO${}_2$ 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 $x=1\mathrm{/}3$ 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.