Bond versus charge disproportionation in the bismuth perovskites

We develop a theory describing a parameter based phase diagram to be associated with materials incorporating skipped valence ions. We use a recently developed tight-binding approach for the bismuthates to study the phase diagram exhibiting the crossover from a bond disproportionated (BD) to a charge disproportionated (CD) system in addition to the presence of a new metallic phase. We argue that three parameters determine the underlying physics of the BD-CD crossover when electron correlation effects are small: the hybridization between O-2p_σ and Bi-6s orbitals (t_spσ), the charge-transfer energy between Bi-6s and O-a_1g molecular orbitals (Δ), and the width of the oxygen sublattice band (W). In the BD system, we estimate an effective attractive interaction U between holes on the same O-a_1g molecular orbital. Although here we concentrate on the example of the bismuthates, the basic ideas can be directly transferred to other perovskites with negative charge-transfer energy, like ReNiO_3 (Re: rare-earth element), Ca(Sr)FeO_3, CsTIF_3 and CsTlCl_3.