Ionic Hubbard model on a triangular lattice for Na_0.5CoO_2, Rb_0.5CoO_2 and K_0.5CoO_2: Mean-field slave boson theory

TL;DR

This paper develops a mean-field slave boson theory for the ionic Hubbard model on a triangular lattice, explaining the electronic phases of Na_0.5CoO_2 and related compounds, and reconciling experimental observations of charge gaps and quasiparticles.

Contribution

It introduces a novel mean-field slave boson approach to the ionic Hubbard model on a triangular lattice, analyzing phase transitions and electronic properties relevant to cobaltate materials.

Findings

Identifies metal-charge transfer insulator transition points for different hopping signs.

Proposes that a gapped heavy band coexists with an ungapped light band in Na_0.5CoO_2.

Explains experimental contradictions by band-specific gap behavior.

Abstract

We introduce 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_0.5CoO_2, Rb_0.5CoO_2, and K_0.5CoO_2. This theory has two bands of fermionic quasi-particles: 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 |Delta/t|>=1.5 for t<0, where Delta is the difference in the site energies of the two sublattices. A metal--charge transfer insulator transition occurs at |Delta/t|=5.0 for t>0 and |Delta/t|=8.0 for t<0. In the charge transfer insulator complete charge disproportionation occurs: one sublattice is filled and the other in half filled. We compare our results with exact diagonalisation calculations and experiments on Na_0.5CoO_2, and discuss the relevance of our results to Rb_0.5CoO_2 and K_0.5CoO_2. In particular we propose a resolution of seemingly contradictory experimental results on Na_0.5CoO_2. 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 1 charge carrier per 100 unit cells, remains ungapped.