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

TL;DR

This paper explores how charge frustration from Coulomb repulsion affects Na$_x$CoO$_2$, leading to reduced bandwidth, charge ordering, and potential revival of RVB superconductivity, aligning with experimental observations.

Contribution

It demonstrates that charge frustration can cause bandwidth suppression, charge order, and revive RVB superconductivity in Na$_x$CoO$_2$ using a $tJ$-like model with repulsion.

Findings

Strong Coulomb repulsion reduces effective charge carrier mobility.

Anomalous thermopower and Hall effect explained by renormalized Fermi liquid.

Bandwidth suppression near $x=1/3$ may restore RVB superconductivity.

Abstract

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 $\epsilon_F \lesssim T$. Such strongly renormalized Fermi liquid has rather unusual properties--from the point of view of the ordinary metals with $\epsilon_F \gg T$--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 $x=1/3$ 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.