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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. Mott reviewed the ...
Having one electron per-site fills the lower band while the upper band remains empty, which suggests the system becomes an insulator. This interaction-driven insulating state is referred to as a Mott insulator. The Hubbard model is one simple model commonly used to describe metal-insulator transitions and the formation of a Mott insulator.
The bands and band gaps near the Fermi level are given special names, depending on the material: In a semiconductor or band insulator, the Fermi level is surrounded by a band gap, referred to as the band gap (to distinguish it from the other band gaps in the band structure).
The distinction between semiconductors and insulators is a matter of convention. One approach is to think of semiconductors as a type of insulator with a narrow band gap. Insulators with a larger band gap, usually greater than 4 eV, [7] are not considered semiconductors and generally do not exhibit semiconductive behaviour under practical ...
Charge-transfer insulators are a class of materials predicted to be conductors following conventional band theory, but which are in fact insulators due to a charge-transfer process. Unlike in Mott insulators , where the insulating properties arise from electrons hopping between unit cells, the electrons in charge-transfer insulators move ...
Most insulators have a large band gap. This occurs because the "valence" band containing the highest energy electrons is full, and a large energy gap separates this band from the next band above it. There is always some voltage (called the breakdown voltage) that gives electrons enough energy to be excited into this band. Once this voltage is ...
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In semiconductors, the band gap of a semiconductor can be of two basic types, a direct band gap or an indirect band gap. The minimal-energy state in the conduction band and the maximal-energy state in the valence band are each characterized by a certain crystal momentum (k-vector) in the Brillouin zone. If the k-vectors are different, the ...