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 Jan Hendrik de Boer and Evert Johannes Willem 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.