Ionic Hubbard model on a triangular lattice for Na_0.5CoO₂, Rb_0.5CoO₂, and K_0.5CoO₂: Mean-field slave boson theory

We present a strongly correlated mean-field theory of the ionic Hubbard model on the triangular lattice with alternating stripes of site energy using Barnes-Coleman slave bosons. We study the paramagnetic phases of this theory at three quarters filling, where it is a model of Na_0.5CoO₂, Rb_0.5CoO₂, and K_0.5CoO₂. This theory has two bands of fermionic quasiparticles: one of which is filled or nearly filled and hence weakly correlated; the other is half-filled or nearly half-filled and hence strongly correlated. Further results depend strongly on the sign of the hopping integral t. The light band is always filled for t>0, but only becomes filled for |Δ/t|≥1.5 for t<0, where Δ is the difference in the site energies of the two sublattices. A metal-charge transfer insulator transition occurs at |Δ/t|=5.0 for t>0 and |Δ/t|=8.0 for t<0. In the charge transfer insulator complete charge disproportionation occurs: one sublattice is filled and the other is half-filled. We compare our results with exact diagonalization calculations and experiments on Na_0.5CoO₂ and discuss the relevance of our results to Rb_0.5CoO₂ and K_0.5CoO₂. We propose a resolution of seemingly contradictory experimental results on Na_0.5CoO₂. Many experiments suggest that there is a charge gap, yet quantum oscillations are observed suggesting the existence of quasiparticle states at arbitrarily low excitation energies. We argue that the heavy band is gapped while the light band, which contains less than one charge carrier per 100 unit cells, remains ungapped.