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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 separation. The essential feature that defines these materials is that the behavior of their
electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary partic ...
s or spinons cannot be described effectively in terms of non-interacting entities. Theoretical models of the electronic ( fermionic) structure of strongly correlated materials must include electronic ( fermionic)
correlation In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statisti ...
to be accurate. As of recently, the label quantum materials is also used to refer to strongly correlated materials, among others.


Transition metal oxides

Many transition metal oxides belong to this class which may be subdivided according to their behavior, ''e.g.'' high-Tc, spintronic materials, multiferroics, Mott insulators,
spin Peierls Spin or spinning most often refers to: * Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning * Spin, the rotation of an object around a central axis * Spin (propaganda), an intentionally b ...
materials, heavy fermion materials, quasi-low-dimensional materials, etc. The single most intensively studied effect is probably high-temperature superconductivity in doped cuprates, e.g. La2−xSrxCuO4. Other ordering or magnetic phenomena and temperature-induced
phase transition In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states ...
s in many transition-metal oxides are also gathered under the term "strongly correlated materials."


Electronic structures

Typically, strongly correlated materials have incompletely filled ''d''- or ''f''-
electron shells In chemistry and atomic physics, an electron shell may be thought of as an orbit followed by electrons around an atom's nucleus. The closest shell to the nucleus is called the "1 shell" (also called the "K shell"), followed by the "2 shell" (or ...
with narrow energy bands. One can no longer consider any
electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary partic ...
in the material as being in a " sea" of the averaged motion of the others (also known as
mean field theory In physics and probability theory, Mean-field theory (MFT) or Self-consistent field theory studies the behavior of high-dimensional random ( stochastic) models by studying a simpler model that approximates the original by averaging over degrees of ...
). Each single
electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary partic ...
has a complex influence on its neighbors. The term ''strong correlation'' refers to behavior of electrons in solids that is not well-described (often not even in a qualitatively correct manner) by simple one-electron theories such as the local-density approximation (LDA) of density-functional theory or Hartree–Fock theory. For instance, the seemingly simple material NiO has a partially filled 3''d'' band (the Ni atom has 8 of 10 possible 3''d''-electrons) and therefore would be expected to be a good conductor. However, strong Coulomb repulsion (a correlation effect) between ''d'' electrons makes NiO instead a wide-
band gap In solid-state physics, a band gap, also called an energy gap, is an energy range in a solid where no electronic states can exist. In graphs of the electronic band structure of solids, the band gap generally refers to the energy difference ( ...
insulator. Thus, ''strongly correlated materials'' have electronic structures that are neither simply free-electron-like nor completely ionic, but a mixture of both.


Theories

Extensions to the LDA (LDA+U, GGA, SIC, ''GW'', etc.) as well as simplified models Hamiltonians (e.g. Hubbard-like models) have been proposed and developed in order to describe phenomena that are due to strong electron correlation. Among them, dynamical mean field theory (DMFT) successfully captures the main features of correlated materials. Schemes that use both LDA and DMFT explain many experimental results in the field of correlated electrons.


Structural studies

Experimentally, optical spectroscopy, high-energy electron spectroscopies
resonant photoemission
and more recently resonant inelastic (hard and soft) X-ray scattering ( RIXS) and neutron spectroscopy have been used to study the electronic and magnetic structure of strongly correlated materials. Spectral signatures seen by these techniques that are not explained by one-electron density of states are often related to strong correlation effects. The experimentally obtained spectra can be compared to predictions of certain models or may be used to establish constraints to the parameter sets. One has for instance established a classification scheme of transition metal oxides within the so-called
Zaanen–Sawatzky–Allen diagram Jan Zaanen (born 17 April 1957) is professor of theoretical physics at Leiden University, the Netherlands. He is best known for his contributions to the understanding of the quantum physics of the electrons in strongly correlated material, and i ...
.


Applications

The manipulation and use of correlated phenomena has applications like superconducting magnets and in magnetic storage (CMR) technologies. Other phenomena like the metal-insulator transition in VO2 have been explored as a means to make smart windows to reduce the heating/cooling requirements of a room. Furthermore, metal-insulator transitions in Mott insulating materials like LaTiO3 can be tuned through adjustments in band filling to potentially be used to make transistors that would use conventional field effect transistor configurations to take advantage of the material's sharp change in conductivity. Transistors using metal-insulator transitions in Mott insulators are often referred to as Mott transistors, and have been successfully fabricated using VO2 before, but they have required the larger electric fields induced by ionic liquids as a gate material to operate.


See also

* Electronic correlation * Emergent behavior


References


Further reading

* * * * * * *


External links

* {{DEFAULTSORT:Strongly Correlated Material Materials science Condensed matter physics Quantum mechanics Magnetism