Mott insulator

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Mott Insulators are a class of materials that are expected to conduct electricity under conventional band theories, but which in fact turn out to be insulators when measured. This effect is due to electron-electron interactions which are not considered in the formulation of conventional band theory.

1 History
2 Applications
3 See also
4 References

[edit] History

Although the band theory of solids had been very successful in describing various electrical properties of materials, in 1937 J H de Boer and E J W Verwey pointed out that a variety of transition metal oxides that were predicted to be conductors by band theory were in fact insulators[1]. Nevill Mott and R. Peierls then predicted that this anomaly could be explained by including interactions between electrons[2].

In 1949, in particular, Mott proposed a model for NiO as an insulator, in which conduction could be understood by the formula[3]:

(Ni²⁺O^2-)₂ $\rightarrow$ Ni³⁺O^2- + Ni¹⁺O^2-

In this situation, the formation of an energy gap preventing conduction can be understood as the competition between the Coulomb potential U between 3d electrons, and the transfer integral t of 3d electrons between neighbouring atoms (the transfer integral is a part of the tight-binding approximation). The total energy gap is then:

E_gap = U - 2zt

where z is the number of nearest neighbour atoms.

In general, Mott insulators occur when the repulsive Coulomb potential U is large enough to create an energy gap.

One of the simplest theories of Mott insulators is the Hubbard model.

[edit] Applications

Mott insulators are of growing interest in advanced physics research, and are not yet fully understood. They have applications in thin-film magnetic heterostructures and high-temperature superconductivity.