Na$_x$CoO$_2$ in the x -> 0 Regime: Coupling of Structure and Correlation effects

The study of the strength of correlations in Na$_x$CoO$_2$ is extended to the x=0 end of the phase diagram where Mott insulating behavior has been widely anticipated. Inclusion of correlation as modeled by the LDA+U approach leads to a Mott transition in the $a_g$ subband if U is no less than U$_c$=2.5 eV. Thus U smaller than U$_c$ is required to model the metallic, nonmagnetic CoO$_2$ compound reported by Tarascon and coworkers. The orbital-selective Mott transition of the $a_g$ state, which is essentially degenerate with the $e'_{g}$ states, occurs because of the slightly wider bandwidth of the $a_g$ bands. The metal-insulator transition is found to be strongly coupled to the Co-O bond length, due to associated changes in the $t_{2g}$ bandwidth, but the largest effects occur only at a reduced oxygen height that lies below the equilibrium position.