The origin of a$_{1g}$ and e$_g$' orderings in Na$_x$CoO$_2$

TL;DR

This study uses density functional theory to analyze the orbital energy splitting in Na_xCoO_2, revealing that Na ordering influences orbital energies and suggesting nonlocal correlations are needed to explain ARPES observations.

Contribution

It provides a detailed DFT calculation of the one-electron orbital splitting in Na_xCoO_2, incorporating Na ordering and structural effects, clarifying the origin of orbital orderings.

Findings

The energy difference _1g - _g' is negative across all Na fillings.

Na+ ions create a Coulomb field that raises the a_1g orbital energy.

Nonlocal correlation effects are necessary to explain the suppression of e_g' pockets.

Abstract

It has often been suggested that correlation effects suppress the small e_g' Fermi surface pockets of NaxCoO_2 that are predicted by LDA, but absent in ARPES measurements. It appears that within the dynamical mean field theory (DMFT) the ARPES can be reproduced only if the on-site energy of the eg' complex is lower than that of the a1g 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 meV to 315 meV in therms of the energy difference. In this work, we perform density functional theory calculations of this one-electron splitting \Delta= \epsilon_a1g-\epsilon_e_g' for the full two-layer compound, Na2xCo2O4, accounting for the effects of Na ordering, interplanar interactions and octahedral distortion. We find that \epsilon a_1g-\epsilon e_g' 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. This field disproportionately affects the a_1g orbital which protrudes farther upward from the Co plane than the e_g' orbitals. We discuss also the secondary effects of octahedral compression and multi-orbital 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.