Charge-transfer insulators

Charge-transfer insulators are a class of materials predicted to be conductors following conventional band theory, but which are in fact insulators due to a charge-transfer process. Unlike in Mott insulators, where the insulating properties arise from electrons hopping between unit cells, the electrons in charge-transfer insulators move between atoms within the unit cell. In the Mott–Hubbard case, it's easier for electrons to transfer between two adjacent metal sites (on-site Coulomb interaction U); here we have an excitation corresponding to the Coulomb energy U with

${\displaystyle d^{n}d^{n}\rightarrow d^{n-1}d^{n+1},\quad \Delta E=U=U_{dd}}$.

In the charge-transfer case, the excitation happens from the anion (e.g., oxygen) p level to the metal d level with the charge-transfer energy Δ:

${\displaystyle d^{n}p^{6}\rightarrow d^{n+1}p^{5},\quad \Delta E=\Delta _{CT}}$.

U is determined by repulsive/exchange effects between the cation valence electrons. Δ is tuned by the chemistry between the cation and anion. One important difference is the creation of an oxygen p hole, corresponding to the change from a 'normal' ${\displaystyle {\ce {O^2-}}}$ to the ionic ${\displaystyle {\ce {O-}}}$ state.^[1] In this case the ligand hole is often denoted as ${\textstyle {\underline {L}}}$.

Distinguishing between Mott-Hubbard and charge-transfer insulators can be done using the Zaanen-Sawatzky-Allen (ZSA) scheme.^[2]