Mott insulators are a class of materials that should conduct electricity under conventional band theories, but are in fact insulators when measured. This effect is due to electron–electron interactions, which are not considered in conventional band theory. The bandgap in a Mott insulator exists between bands of like character, such as 3d character, whereas the bandgap in charge transfer insulators exists between anion and cation states, such as between O 2p and Ni 3d bands in NiO.
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. Nevill Mott and Rudolf Peierls then 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 In this situation, the formation of an energy gap preventing conduction can be understood as the competition between the Coulomb potentialU between 3d electrons and the transfer integral t of 3d electrons between neighboring atoms. The total energy gap is then 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 simplesttheories 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.
Mottness
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:
Mott insulators are of growing interest in advanced physics research, and are not yet fully understood. They have applications in thin-filmmagnetic heterostructures and the strong correlated phenomena in high-temperature superconductivity, for example. 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.
