Origin of a1g and eg' orderings in NaxCoO2

It has often been suggested that correlation effects suppress the small e(g)(') Fermi-surface pockets of NaxCoO2 that are predicted by LDA, but absent in ARPES measurements. It appears that within the dynamical mean-field theory (DMFT) the ARPES results can be reproduced only if the on-site energy of the e(g)(') complex is lower than that of the a(1g) complex at the one-electron level, prior to the addition of local correlation effects. Current estimates regarding the order of the two orbital complexes range from -200 to 315 meV in terms of the energy difference. In this work, we perform density-functional theory calculations of this one-electron splitting Delta=epsilon(a1g)-epsilon(')(eg) for the full two-layer compound, accounting for the effects of Na ordering, interplanar interactions and octahedral distortion. We find that epsilon(a1g)-epsilon(')(eg) is negative for all Na fillings and that this is primarily due to the strongly positive Coulomb field created by Na+ ions in the intercalant plane that disproportionately affects the extended a(1g) orbital. We discuss also the effects of octahedral compression and multiorbital filling on the value of Delta as a function of Na content. Our results indicate that if the e(g)(') pockets are indeed suppressed, that can only be due to nonlocal correlation effects beyond the standard DMFT.