Mott insulator

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 are insulators.[4] With an odd number of electrons per unit cell, the valence band is only partially filled, so the Fermi level lies within the band. From the band theory, this implies that such a material has to be a metal. This conclusion fails for several cases, e.g. CoO, one of the strongest insulators known.[1]

Nevill Mott and Rudolf Peierls also in 1937 predicted the failing of band theory can be explained by including interactions between electrons.[5]

In 1949, in particular, Mott proposed a model for NiO as an insulator, where conduction is based on the formula[6]

(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

E_gap = 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.

Mottism denotes the additional ingredient, aside from antiferromagnetic ordering, which is necessary to fully describe a Mott insulator. In other words, we might write: antiferromagnetic order + mottism = Mott insulator.

Thus, mottism accounts for all of the properties of Mott insulators that cannot be attributed simply to antiferromagnetism.

There are a number of properties of Mott insulators, derived from both experimental and theoretical observations, which cannot be attributed to antiferromagnetic ordering and thus constitute mottism. These properties include:

• Spectral weight transfer on the Mott scale[7][8]
• Vanishing of the single particle Green function along a connected surface in momentum space in the first Brillouin zone[9]
• Two sign changes of the Hall coefficient as electron doping goes from ${\displaystyle n=0}$ to ${\displaystyle n=2}$ (band insulators have only one sign change at ${\displaystyle n=1}$)
• The presence of a charge ${\displaystyle 2e}$ (with ${\displaystyle e<0}$ the charge of an electron) boson at low energies[10][11]
• A pseudogap away from half-filling (${\displaystyle n=1}$)[12]

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 the strong correlated phenomena in high-temperature superconductivity, for example.[13][14][15][16]

This kind of insulator can become a conductor by changing some parameters, which may be composition, pressure, strain, voltage, or magnetic field. The effect is known as a Mott transition and can be used to build smaller field-effect transistors, switches and memory devices than possible with conventional materials.[17][18][19]

• Laughlin, R. B. (1997). "A Critique of Two Metals". arXiv:cond-mat/9709195.
• Anderson, P. W.; Baskaran, G. (1997). "A Critique of A Critique of Two Metals". arXiv:cond-mat/9711197.
• Jördens, Robert; Strohmaier, Niels; Günter, Kenneth; Moritz, Henning; Esslinger, Tilman (2008). "A Mott insulator of fermionic atoms in an optical lattice". Nature. 455 (7210): 204–207. arXiv:0804.4009. Bibcode:2008Natur.455..204J. doi:10.1038/nature07244. PMID 18784720. S2CID 4426395.