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Metal–insulator transitions are transitions of a material from a
metal A metal () is a material that, when polished or fractured, shows a lustrous appearance, and conducts electrical resistivity and conductivity, electricity and thermal conductivity, heat relatively well. These properties are all associated wit ...
(material with good
electrical conductivity Electrical resistivity (also called volume resistivity or specific electrical resistance) is a fundamental specific property of a material that measures its electrical resistance or how strongly it resists electric current. A low resistivity in ...
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 Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and eve ...
or, in case of a
semiconductor A semiconductor is a material with electrical conductivity between that of a conductor and an insulator. Its conductivity can be modified by adding impurities (" doping") to its crystal structure. When two regions with different doping level ...
, doping.


History

The basic distinction between metals and insulators was proposed by Hans Bethe,
Arnold Sommerfeld Arnold Johannes Wilhelm Sommerfeld (; 5 December 1868 – 26 April 1951) was a German Theoretical physics, theoretical physicist who pioneered developments in Atomic physics, atomic and Quantum mechanics, quantum physics, and also educated and ...
and
Felix Bloch Felix Bloch (; ; 23 October 1905 – 10 September 1983) was a Swiss-American physicist who shared the 1952 Nobel Prize in Physics with Edward Mills Purcell "for their development of new methods for nuclear magnetic precision measurements and di ...
in 1928-1929. It distinguished between conducting metals (with partially filled bands) and nonconducting insulators. However, in 1937 Jan Hendrik 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
Rudolf Peierls Sir Rudolf Ernst Peierls, (; ; 5 June 1907 – 19 September 1995) was a German-born British physicist who played a major role in Tube Alloys, Britain's nuclear weapon programme, as well as the subsequent Manhattan Project, the combined Allied ...
. 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 Magnetite is a mineral and one of the main iron ores, with the chemical formula . It is one of the iron oxide, oxides of iron, and is ferrimagnetism, ferrimagnetic; it is attracted to a magnet and can be magnetization, magnetized to become a ...
in the 1940s.


Theoretical description

The classical band structure of solid state physics predicts the
Fermi level The Fermi level of a solid-state body is the thermodynamic work required to add one electron to the body. It is a thermodynamic quantity usually denoted by ''μ'' or ''E''F for brevity. The Fermi level does not include the work required to re ...
to lie in a
band gap In solid-state physics and solid-state chemistry, a band gap, also called a bandgap or energy gap, is an energy range in a solid where no electronic states exist. In graphs of the electronic band structure of solids, the band gap refers to t ...
for insulators and in the
conduction band In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level, and thus determine the electrical conductivity of the solid. In nonmetals, the valence band is the highest range of electron energies in ...
for metals, which means metallic behavior is seen for compounds with partially filled bands. However, some compounds have been found which show insulating behavior even for partially filled bands. This is due to the electron-electron correlation, since electrons cannot be seen as noninteracting. Mott considers a lattice model with just one electron per site. Without taking the interaction into account, each site could be occupied by two electrons, one with spin up and one with spin down. Due to the interaction the electrons would then feel a strong Coulomb repulsion, which Mott argued splits the band in two. 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 The Hubbard model is an Approximation, approximate model used to describe the transition between Conductor (material), conducting and Electrical insulation, insulating systems. It is particularly useful in solid-state physics. The model is named ...
is one simple model commonly used to describe metal-insulator transitions and the formation of a Mott insulator.


Elementary mechanisms

Metal–insulator transitions (MIT) and models for approximating them can be classified based on the origin of their transition. * Mott transition: The most common transition, arising from intense electron-electron correlation. * Mott-Hubbard transition: An extension incorporating the Hubbard model, approaching the transition from the correlated paramagnetic state. * Brinkman-Rice transition: Approaching the transition from the non-interacting metallic state, where each orbital is half-filled. * Dynamical mean-field theory: A theory that accommodates both Mott-Hubbard and Brinbkman-Rice models of the transition. * Peierls transition: On some occasions, the lattice itself through electron-phonon interactions can give rise to a transition. An example of a Peierls insulator is the blue bronze K0.3MoO3, which undergoes transition at T = 180 K. * Anderson transition: When an insulator behavior in metals arises from distortions and lattice defects.


Polarization catastrophe

The polarization catastrophe model describes the transition of a material from an insulator to a metal. This model considers the electrons in a solid to act as oscillators and the conditions for this transition to occur is determined by the number of oscillators per unit volume of the material. Since every oscillator has a frequency (''ω''0) we can describe the dielectric function of a solid as, :\epsilon(\omega)= 1+\frac where ''ε''(''ω'') is the dielectric function, ''N'' is the number of oscillators per unit volume, ''ω''0 is the fundamental oscillation frequency, m is the oscillator mass, and ''ω'' is the excitation frequency. For a material to be a metal, the excitation frequency (''ω'') must be zero by definition, which then gives us the static dielectric constant, where ''ε''s is the static dielectric constant. If we rearrange equation (1) to isolate the number of oscillators per unit volume we get the critical concentration of oscillators (''N''c) at which ''ε''s becomes infinite, indicating a metallic solid and the transition from an insulator to a metal. :N_ = \frac This expression creates a boundary that defines the transition of a material from an insulator to a metal. This phenomenon is known as the polarization catastrophe. The polarization catastrophe model also theorizes that, with a high enough density, and thus a low enough molar volume, any solid could become metallic in character. Predicting whether a material will be metallic or insulating can be done by taking the ratio ''R''/''V'', where ''R'' is the molar refractivity, sometimes represented by ''A'', and ''V'' is the molar volume. In cases where ''R''/''V'' is less than 1, the material will have non-metallic, or insulating properties, while an ''R''/''V'' value greater than one yields metallic character.


See also

* *


References


Further reading

* * * http://rmp.aps.org/abstract/RMP/v70/i4/p1039_1 {{DEFAULTSORT:Metal-Insulator Transition Condensed matter physics Phase transitions