Mott insulators are a class of materials that are expected to conduct electricity according to conventional band theories, but are actually insulators (particularly at low temperatures). These insulators fail to be correctly described by band theories of solids due to their strong electron–electron interactions, which are not considered in conventional band theory. A Mott transition is a transition from a metal to an insulator, driven by the strong interactions between electrons. One of the simplest models that can capture Mott transition is the Hubbard model. The band gap in a Mott insulator exists between bands of like character, such as 3d electron bands, whereas the band gap in charge-transfer insulators exists between anion and cation states.
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 are insulators. 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. Nevill Mott and Rudolf Peierls also in 1937 predicted the failing of band theory 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 dynamical mean field theory. Mott reviewed the subject in 1968. The subject has been thoroughly reviewed in a comprehensive paper by Masatoshi Imada, Atsushi Fujimori, and Yoshinori Tokura. A recent proposal of a "Griffiths-like phase close to the Mott transition" has been reported in the literature.
Mott criterion The Mott criterion describes the critical point of the metal–insulator transition. The criterion is
n − 1 / 3 < C a 0 ∗ , {\displaystyle n^{-1/3}<Ca_{0}^{*},}
where n {\displaystyle n} is the electron density of the material and a 0 ∗ {\displaystyle a_{0}^{*}} the effective bohr radius. The constant C {\displaystyle C} , according to various estimates, is 2.0, 2.78,4.0, or 4.2. If the criterion is satisfied (i.e. if the density of electrons is sufficiently high) the material becomes conductive (metal) and otherwise it will be an insulator.
Mottness Mottism denotes the additional component, aside from antiferromagnetic ordering, which is necessary to fully describe a 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 Vanishing of the single particle Green function along a connected surface in momentum space in the first Brillouin zone Two sign changes of the Hall coefficient as electron doping goes from n = 0 {\displaystyle n=0} to n = 2 {\displaystyle n=2} (band insulators have only one sign change at n = 1 {\displaystyle n=1} ) The presence of a charge 2 e {\displaystyle 2e} (with e < 0 {\displaystyle e<0} the charge of an electron) boson at low energies A pseudogap away from half-filling ( n = 1 {\displaystyle n=1} )
Mott transition A Mott transition is a metal-insulator transition in condensed matter. Due to electric field screening the potential energy becomes much more sharply (exponentially) peaked around the equilibrium position of the atom and electrons become localized and can no longer conduct a current. It is named after physicist Nevill Francis Mott.
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