Charge-transfer insulators

Until now, when considering systems with strongly correlated electrons, we mostly discussed the properties of d-electrons themselves. However most often we are dealing not with systems with only TM elements (pure TM metals), but with different compounds containing, besides TM ions with their d-electrons, also other ions and electrons. These may be itinerant or band electrons, for example in many intermetallic compounds; some of these will be considered below, in Chapter 11. But more often we are dealing with compounds such as TM oxides, fluorides, etc., which are insulators. Still, even in this case we have in principle to include in our discussion not only the correlated d-electrons of transition metals, but also the valence s- and p-electrons of say O or F. This we have already done to some extent when we were considering the crystal field splitting of d levels in Chapter 3, in particular the p–d hybridization contribution to it, see Section 3.1 and Figs 3.5–3.8.

In some cases we can project out these other electrons and reduce the description to that containing only d-electrons, but with effective parameters determined by their interplay with say p-electrons of oxygens. In other cases, however, we have to include these electrons explicitly. This, in particular, is the case when the energy of oxygen 2p levels is close to that of d levels.