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

$d^nd^n \rightarrow d^d^, \quad \Delta E = U = U_$.

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:

$d^np^6 \rightarrow d^p^, \quad \Delta E = \Delta_$.

''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' O^2- to the ionic O- state. In this case the ligand hole is often denoted as $\underline$.

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

Exchange Interaction

Analogous to Mott insulators we also have to consider superexchange in charge-transfer insulators. One contribution is similar to the Mott case: the hopping of a ''d'' electron from one transition metal site to another and then back the same way. This process can be written as

$d^n_ip^6d^n_j \rightarrow d^n_ip^5d^_j \rightarrow d^_ip^6d^_j \rightarrow d^n_ip^5d^_j \rightarrow d^n_ip^6d^n_j$.

This will result in an antiferromagnetic exchange (for nondegenerate ''d'' levels) with an exchange constant $J = J_$.

$J_ = \frac = \cfrac$

In the charge-transfer insulator case

$d^n_i p^6d^n_j \rightarrow d^n_i p^5d^_j \rightarrow d^_i p^4d^_j \rightarrow d^_i p^5d^n_j \rightarrow d^n_i p^6d^n_j$.

This process also yields an antiferromagnetic exchange $J_$:

$J_ = \cfrac$

The difference between these two possibilities is the intermediate state, which has one ligand hole for the first exchange ($p^6\rightarrow p^5$) and two for the second ($p^6\rightarrow p^4$).

The total exchange energy is the sum of both contributions:

$J_ = \cfrac \cdot \left(\cfrac + \cfrac\right)$.

Depending on the ratio of $U_\text \left(\Delta_+\tfracU_\right)$, the process is dominated by one of the terms and thus the resulting state is either Mott-Hubbard or charge-transfer insulating.

References

{{DEFAULTSORT:Charge Transfer Insulators
Quantum phases
Electronic band structures