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

Band structure comparison of a Charge-Transfer Insulator vs a Mott-Hubbard Insulator.
A comparison between charge-transfer and Mott-Hubbard insulator band structures: a cuprate vs a nickelate.

.

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:

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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' to the ionic state.[1] In this case the ligand hole is often denoted as .

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

Exchange interaction

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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

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This will result in an antiferromagnetic exchange (for nondegenerate d levels) with an exchange constant  .

 

In the charge-transfer insulator case

 .

This process also yields an antiferromagnetic exchange  :

 

The difference between these two possibilities is the intermediate state, which has one ligand hole for the first exchange ( ) and two for the second ( ).

The total exchange energy is the sum of both contributions:

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Depending on the ratio of  , the process is dominated by one of the terms and thus the resulting state is either Mott-Hubbard or charge-transfer insulating.[1]


References

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  1. ^ a b Khomskii, Daniel I. (2014). Transition Metal Compounds. Cambridge: Cambridge University Press. doi:10.1017/cbo9781139096782. ISBN 978-1-107-02017-7.
  2. ^ Zaanen, J.; Sawatzky, G. A.; Allen, J. W. (1985-07-22). "Band gaps and electronic structure of transition-metal compounds". Physical Review Letters. 55 (4): 418–421. Bibcode:1985PhRvL..55..418Z. doi:10.1103/PhysRevLett.55.418. hdl:1887/5216. PMID 10032345.