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 predicted to be conductors by band theory (because they have an odd number of electrons per unit cell) are insulators. Nevill Mott and Rudolf Peierls then (also in 1937) predicted that this anomaly can be explained by including interactions between electrons.
In 1949, in particular, Mott proposed a model for NiO as an insulator, where conduction is based on the formula
- (Ni2+O2−)2 → Ni3+O2− + Ni1+O2−.
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 neighboring atoms (the transfer integral is a part of the tight-binding approximation). The total energy gap is then
- Egap = U − 2zt,
where z is the number of nearest-neighbor 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 1963 Hubbard model. The crossover from a metal to a Mott insulator as U is increased can be predicted within the so-called Dynamical Mean Field Theory.
Read more about this topic: Mott Insulator
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