From Hubbard bands to spin-polaron excitations in the doped Mott   material Na$_x$CoO$_2$
  We investigate the excitation spectrum of strongly correlated sodium cobaltate within a realistic many-body description beyond dynamical mean-field theory (DMFT). At lower doping around $x$=0.3, rather close to Mott-critical half-filling, the single-particle spectral function of Na$_x$CoO$_2$ displays an upper Hubbard band which is captured within DMFT. Momentum-dependent self-energy effects beyond DMFT become dominant at higher doping. Around a doping level of $x\sim 0.67$, the incoherent excitations give way to finite-energy spin-polaron excitations in close agreement with optics experiments. These excitations are a direct consequence of the formation of bound states between quasiparticles and paramagnons in the proximity to in-plane ferromagnetic ordering. 
Aljoscha Wilhelm, Frank Lechermann, Hartmut Hafermann, Mikhail I.   Katsnelson and Alexander I. Lichtenstein
cond-mat.str-el