Dynamical mean field theory of an effective three-band model for Na${}_x$CoO${}_2$

We derive an effective Hamiltonian for highly correlated $t_{2g}$ states centered at the Co sites of Na${}_x$CoO${}_2$. The essential ingredients of the model are an O mediated hopping, a trigonal crystal-field splitting, and on-site effective interactions derived from the exact solution of a multi-orbital model in a CoO${}_6$ cluster, with parameters determined previously. The effective model is solved by dynamical mean-field theory (DMFT). We obtain a Fermi surface (FS) and electronic dispersion that agrees well with angle-resolved photoemission spectra (ARPES). Our results also elucidate the origin of the “sinking-pockets” in different doping regimes.