Charge-transfer insulators

A comparison between charge-transfer and Mott-Hubbard insulator band structures: a cuprate vs a nickelate.

Short description: Nonmetal due to charge transfer between atoms

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

dndn->dn−1dn+1,ΔE=U=Udd.

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:

dnp6->dn+1p5,ΔE=ΔCT.

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' OA2− to the ionic OA− state.[1] In this case the ligand hole is often denoted as L_.

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

## 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

dinp6djn->dinp5djn+1->din−1p6djn+1->dinp5djn+1->dinp6djn.

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

Jdd=2tdd2Udd=2tpd4ΔCT2Udd

In the charge-transfer insulator case

dinp6djn->dinp5djn+1->din+1p4djn+1->din+1p5djn->dinp6djn.

This process also yields an antiferromagnetic exchange Jpd:

Jpd=4tpd4ΔCT2⋅(2ΔCT+Upp)

The difference between these two possibilities is the intermediate state, which has one ligand hole for the first exchange (p6->p5) and two for the second (p6->p4).

The total exchange energy is the sum of both contributions:

Jtotal=2tpd4ΔCT2⋅(1Udd+1ΔCT+12Upp).

Depending on the ratio of Udd and (ΔCT+12Upp), the process is dominated by one of the terms and thus the resulting state is either Mott-Hubbard or charge-transfer insulating.[1]

## References

1. ↑ 1.0 1.1 Khomskii, Daniel I. (2014). Transition Metal Compounds. Cambridge: Cambridge University Press. doi:10.1017/cbo9781139096782. ISBN 978-1-107-02017-7. https://www.cambridge.org/core/books/transition-metal-compounds/037907D3274F602D84CFECA02A493395.
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. doi:10.1103/PhysRevLett.55.418. PMID 10032345. Bibcode: 1985PhRvL..55..418Z. https://link.aps.org/doi/10.1103/PhysRevLett.55.418.

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