Na Induced Correlations in Na${}_x$CoO${}_2$

Increasing experimental evidence is building which indicates that signatures of strong correlations are present in the Na rich region of Na${}_x$CoO${}_2$ (ie. $x\approx 0.7$) and absent in the Na poor region (ie. $x\approx 0.3$). This is unexpected given that NaCoO${}_2$ is a band insulator and CoO${}_2$ has an integer filled open shell making it a candidate for strong correlations. We explain these experimental observations by presenting a minimal low-energy Hamiltonian for the cobaltates and solving it within LDA+DMFT. The Na potential is shown to be a key element in understanding correlations in this material. Furthermore, LDA calculations for the realistic Na ordering predict a \emph{binary} perturbation of the Co sites which correlates with the Na${}_1$ sites (ie. Na sites above/below Co sites).