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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]
Without the contribution of the second term, the Hamiltonian resolves to the tight binding formula from regular band theory. Including the second term yields a realistic model that also predicts a transition from conductor to insulator as the ratio of interaction to hopping, U / t {\displaystyle U/t} , is varied.
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 ...
A common misconception occurs between centre of mass and centre of gravity.They are defined in similar ways but are not exactly the same quantity. Centre of mass is the mathematical description of placing all the mass in the region considered to one position, centre of gravity is a real physical quantity, the point of a body where the gravitational force acts.
The London equations get developed by brothers Fritz and Heinz London. Hartree introduces Hartree–Fock method. [61] 1937: Landau introduces Landau theory of phase transitions. Peierls and Nevill Francis Mott predict the breakdown of band theory in the presence of interactions. They postulate the Mott insulator.
The Seebeck coefficient (also known as thermopower, [1] thermoelectric power, and thermoelectric sensitivity) of a material is a measure of the magnitude of an induced thermoelectric voltage in response to a temperature difference across that material, as induced by the Seebeck effect. [2]
Dynamical mean-field theory, a non-perturbative treatment of local interactions between electrons, bridges the gap between the nearly free electron gas limit and the atomic limit of condensed-matter physics. [1] DMFT consists in mapping a many-body lattice problem to a many-body local problem, called an impurity model. [2]