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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 showed that the probability of hopping between two states of spatial separation and energy separation W has the form: [] where α −1 is the attenuation length for a hydrogen-like localised wave-function. This assumes that hopping to a state with a higher energy is the rate limiting process.
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.
At zero temperature, the Bose–Hubbard model (in the absence of disorder) is in either a Mott insulating state at small /, or in a superfluid state at large /. [8] The Mott insulating phases are characterized by integer boson densities, by the existence of an energy gap for particle-hole excitations, and by zero compressibility .
The Hubbard model introduces short-range interactions between electrons to the tight-binding model, which only includes kinetic energy (a "hopping" term) and interactions with the atoms of the lattice (an "atomic" potential). When the interaction between electrons is strong, the behavior of the Hubbard model can be qualitatively different from ...
A comparison between charge-transfer and Mott-Hubbard insulator band structures: a cuprate vs a nickelate. Nonmetal due to charge transfer between atoms 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.