Mott Criterion

	Mott Criterion The Mott criterion describes the critical point of the metal–insulator transition. The criterion is n^ < C a_0^* , where $~n$ is the electron density of the material and $a_0^$ the effective bohr radius. The constant $C$ , according to various estimates, is 2.0, 2.78,4.0, or 4.2. If the criterion is satisfied (i.e. if the density of electrons is sufficiently high) the material becomes conductive (metal) and otherwise it will be an insulator. See also Hubbard model * Bohr radius * Mott insulator Mott insulators are a class ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Critical Point (thermodynamics) In thermodynamics, a critical point (or critical state) is the end point of a phase equilibrium curve. The most prominent example is the liquid–vapor critical point, the end point of the pressure–temperature curve that designates conditions under which a liquid and its vapor can coexist. At higher temperatures, the gas cannot be liquefied by pressure alone. At the critical point, defined by a ''critical temperature'' ''T''c and a ''critical pressure'' ''p''c, phase boundaries vanish. Other examples include the liquid–liquid critical points in mixtures, and the ferromagnet–paramagnet transition (Curie temperature) in the absence of an external magnetic field. Liquid–vapor critical point Overview For simplicity and clarity, the generic notion of ''critical point'' is best introduced by discussing a specific example, the vapor–liquid critical point. This was the first critical point to be discovered, and it is still the best known and most studied one. The figu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Metal–insulator Transition Metal–insulator transitions are transitions of a material from a metal (material with good electrical conductivity of electric charges) to an insulator (material where conductivity of charges is quickly suppressed). These transitions can be achieved by tuning various ambient parameters such as temperature, pressure or, in case of a semiconductor, doping. History The basic distinction between metals and insulators was proposed by Bethe, Sommerfeld and Bloch in 1928/1929. It distinguished between conducting metals (with partially filled bands) and nonconducting insulators. However, in 1937 de Boer and Evert Verwey reported that many transition-metal oxides (such as NiO) with a partially filled d-band were poor conductors, often insulating. In the same year, the importance of the electron-electron correlation was stated by Peierls. Since then, these materials as well as others exhibiting a transition between a metal and an insulator have been extensively studied, e.g. by Si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Introduction To Solid State Physics ''Introduction to Solid State Physics'', known colloquially as ''Kittel'', is a classic condensed matter physics textbook written by American physicist Charles Kittel in 1953. The book has been highly influential and has seen widespread adoption; Marvin L. Cohen remarked in 2019 that Kittel's content choices in the original edition played a large role in defining the field of solid-state physics. It was also the first proper textbook covering this new field of physics. The book is published by John Wiley and Sons and, as of 2018, it is in its ninth edition and has been reprinted many times as well as translated into over a dozen languages, including Chinese, French, German, Hungarian, Indonesian, Italian, Japanese, Korean, Malay, Romanian, Russian, Spanish, and Turkish. In some later editions, the eighteenth chapter, titled ''Nanostructures'', was written by Paul McEuen. Along with its rival ''Ashcroft and Mermin'', the book is considered a standard textbook in condensed matter p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Hubbard Model The Hubbard model is an approximate model used to describe the transition between conducting and insulating systems. It is particularly useful in solid-state physics. The model is named for John Hubbard. The Hubbard model states that each electron experiences competing forces: one pushes it to tunnel to neighboring atoms, while the other pushes it away from its neighbors. Its Hamiltonian thus has two terms: a kinetic term allowing for tunneling ("hopping") of particles between lattice sites and a potential term reflecting on-site interaction. The particles can either be fermions, as in Hubbard's original work, or bosons, in which case the model is referred to as the "Bose–Hubbard model". The Hubbard model is a useful approximation for particles in a periodic potential at sufficiently low temperatures, where all the particles may be assumed to be in the lowest Bloch band, and long-range interactions between the particles can be ignored. If interactions between particles at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Bohr Radius The Bohr radius (''a''0) is a physical constant, approximately equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state. It is named after Niels Bohr, due to its role in the Bohr model of an atom. Its value is The number in parenthesis denotes the uncertainty of the last digits. Definition and value The Bohr radius is defined as a_0 = \frac = \frac = \frac , where * \varepsilon_0 is the permittivity of free space, * \hbar is the reduced Planck constant, * m_ is the mass of an electron, * e is the elementary charge, * c is the speed of light in vacuum, and * \alpha is the fine-structure constant. The CODATA value of the Bohr radius (in SI units) is History In the Bohr model for atomic structure, put forward by Niels Bohr in 1913, electrons orbit a central nucleus under electrostatic attraction. The original derivation posited that electrons have orbital angular momentum in integer multiples of the reduced Planck co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Mott Insulator Mott insulators are a class of materials that are expected to conduct electricity according to conventional band theories, but turn out to be insulators (particularly at low temperatures). These insulators fail to be correctly described by band theories of solids due to their strong electron–electron interactions, which are not considered in conventional band theory. A Mott transition is a transition from a metal to an insulator, driven by the strong interactions between electrons. One of the simplest models that can capture Mott transition is the Hubbard model. The band gap in a Mott insulator exists between bands of like character, such as 3d electron bands, whereas the band gap 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 Ve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]

See also