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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.
Since then, these materials as well as others exhibiting a transition between a metal and an insulator have been extensively studied, e.g. by Sir Nevill Mott, after whom the insulating state is named Mott insulator. The first metal-insulator transition to be found was the Verwey transition of magnetite in the 1940s. [3]
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 superfluid is characterized by long-range phase coherence, a spontaneous breaking of the Hamiltonian's continuous U ( 1 ) {\displaystyle U(1)} symmetry, a non-zero ...
1958 – Philip W. Anderson starts developing the theory of metal-insulator transitions and Anderson localization. 1958 – John Hopfield coins the polariton in theory of Hopfield dielectric. [75] 1958–1960 – The first laser is built by Theodore Maiman at Hughes Aircraft Company, based on a patent from Townes and Arthur Leonard Schawlow. [67]
For example, the Hubbard model correctly predicts the existence of Mott insulators: materials that are insulating due to the strong repulsion between electrons, even though they satisfy the usual criteria for conductors, such as having an odd number of electrons per unit cell.
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.
The perovskite structure of BSCCO, a high-temperature superconductor and a strongly correlated material.. Strongly correlated materials are a wide class of compounds that include insulators and electronic materials, and show unusual (often technologically useful) electronic and magnetic properties, such as metal-insulator transitions, heavy fermion behavior, half-metallicity, and spin-charge ...
These are used to explore the transition between a superfluid and a Mott insulator. [60] They are also useful in studying Bose–Einstein condensation in fewer than three dimensions, for example the Lieb–Liniger model (an the limit of strong interactions, the Tonks–Girardeau gas) in 1D and the Berezinskii–Kosterlitz–Thouless transition ...