Novel electronic states in Na$_x$CoO$_2$: Role of strong correlation and Na dopant order

We argue that the strong Co intra-atomic Coulomb repulsion renormalizes the crystal field splitting and the bandwidths of the $t_{2g}$ complex in Na$_x$CoO$_2$, resulting in a single band crossing the Fermi level at all doping levels $x$ explored by ARPES experiments [1]. On this basis, we study the electronic states using a minimal electron-doped, one-band Hubbard model with large $U$ on the triangular lattice. The important role played by the off-plane Na dopants is taken into account by including the ionic electrostatic potential. We find a class of charge and spin density ordered states where the system alleviates antiferromagnetic (AF) frustration via charge inhomogeneity [2]. We show that the $\sqrt{3}\times2$ Na order at $x=0.5$ causes weak $\sqrt{3} \times1$ charge order in the Co layer and the emergence of AF order with small electron and hole Fermi surface pockets [2]. This theory of the ``0.5 phase'' is consistent with neutron scattering, NMR, Shubnikov-de Haas oscillations, and transport experiments. In the sodium rich phases, the high density of off-plane Na dopants (or dilute Na vacancies), in their ordered or disordered form, increases the tendency toward carrier localization in the Co plane [3], which competes with in-plane ferromagnetic (FM) correlations described by a renormalized Stoner theory [4]. We argue that the newly discovered electronic phases associated with Na vacancy order [5,6] can be described by a useful notion of ``super-Mottness'', where strong correlation effects on the superlattice structure give rise to the competition and possible coexistence of localized magnetic moments and itinerant FM carriers. \newline \newline [1] S. Zhou, M. Gao, H. Ding, P.A. Lee, and Z. Wang, Phys. Rev. Lett. 94, 206401 (2005). \newline [2] S. Zhou and Z. Wang, Phys. Rev. Lett. 98, 076401 (2007). \newline [3] C.A. Marianetti and G. Kotliar, Phys. Rev. Lett. 98, 176405 (2007). \newline [4] M. Gao, S. Zhou, and Z. Wang, Phys. Rev. B 76, 180402 (2007). \newline [5] M. Roger, et al., Nautre, 445, 631 (2007). \newline [6] F.C. Chou, et al., arXiv:0709.0085.