Strongly correlated material
Encyclopedia
Strongly correlated materials are a wide class of electronic materials that show unusual (often technologically useful) electronic and magnetic properties, such as metal-insulator transition
s or half-metal
licity. The essential feature that defines these materials is that the behavior of their electrons cannot be described effectively in terms of non-interacting entities Theoretical models of the electronic structure of strongly correlated materials must include electronic correlation
to be accurate.
Many, if not most, transition metal oxides
belong into this class which may be subdivided according to their behavior, e.g. high-Tc, spintronic materials
, Mott insulator
s, spin Peierls materials, heavy fermion
materials, quasi-low-dimensional materials, etc. The single most intensively studied effect is probably high-temperature superconductivity
in doped cuprate
s, e.g. La2-xSrxCuO4. Other ordering or magnetic phenomena and temperature-induced phase transitions in many transition-metal oxides are also gathered under the term "strongly correlated materials."
Typically, strongly correlated materials have incompletely filled d- or f-electron shells with narrow energy bands. One can no longer consider any electron
in the material as being in a "sea" of the averaged motion of the others. Each single electron
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 3d-band (the Ni atom has 8 of 10 possible 3d-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
insulator. Thus, strongly correlated materials have electronic structures that are neither simply free-electron-like nor completely ionic, but a mixture of both.
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
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.
Experimentally, 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.
Metal-insulator transition
Metal-insulator transitions are transitions from a metal to an insulator...
s or half-metal
Half-metal
A half-metal is any substance that acts as a conductor to electrons of one spin orientation, but as an insulator to those of the opposite orientation....
licity. The essential feature that defines these materials is that the behavior of their electrons cannot be described effectively in terms of non-interacting entities Theoretical models of the electronic structure of strongly correlated materials must include electronic correlation
Electronic correlation
Electronic correlation is the interaction between electrons in the electronic structure of a quantum system.- Atomic and molecular systems :...
to be accurate.
Many, if not most, transition metal oxides
Transition metal oxides
Transition metal oxides comprise a class of materials that contain transition elements and oxygen. They include insulators as well as metals. Often the same material may display both types of transport properties, hence a Metal-Insulator transition, obtained by varying either temperature or...
belong into this class which may be subdivided according to their behavior, e.g. high-Tc, spintronic materials
Spintronics
Spintronics , also known as magnetoelectronics, is an emerging technology that exploits both the intrinsic spin of the electron and its associated magnetic moment, in addition to its fundamental electronic charge, in solid-state devices.An additional effect occurs when a spin-polarized current is...
, Mott insulator
Mott insulator
Mott insulators are a class of materials that should conduct electricity under conventional band theories, but are insulators when measured...
s, spin Peierls materials, heavy fermion
Heavy Fermion
In solid-state physics, heavy fermion materials are a specific type of intermetallic compound, containing elements with 4f or 5f electrons. Electrons, a kind of fermion, found in such materials are sometimes referred to as heavy electrons...
materials, quasi-low-dimensional materials, etc. The single most intensively studied effect is probably high-temperature superconductivity
High-temperature superconductivity
High-temperature superconductors are materials that have a superconducting transition temperature above . From 1960 to 1980, 30 K was thought to be the highest theoretically possible Tc...
in doped cuprate
Cuprate
Cuprates are chemical compounds containing copper anion. Cuprates have been known for centuries and are widely used in inorganic and organic chemistry...
s, e.g. La2-xSrxCuO4. Other ordering or magnetic phenomena and temperature-induced phase transitions in many transition-metal oxides are also gathered under the term "strongly correlated materials."
Typically, strongly correlated materials have incompletely filled d- or f-electron shells with narrow energy bands. One can no longer consider any electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
in the material as being in a "sea" of the averaged motion of the others. Each single electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
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 3d-band (the Ni atom has 8 of 10 possible 3d-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
Band gap
In solid state physics, a band gap, also called an energy gap or bandgap, is an energy range in a solid where no electron states can exist. In graphs of the electronic band structure of solids, the band gap generally refers to the energy difference between the top of the valence band and the...
insulator. Thus, strongly correlated materials have electronic structures that are neither simply free-electron-like nor completely ionic, but a mixture of both.
Extensions to the LDA (LDA+U, GGA, SIC, GW, etc.) as well as simplified models Hamiltonians
Hamiltonian (quantum mechanics)
In quantum mechanics, the Hamiltonian H, also Ȟ or Ĥ, is the operator corresponding to the total energy of the system. Its spectrum is the set of possible outcomes when one measures the total energy of a system...
(e.g. Hubbard-like models
Hubbard model
The Hubbard model is an approximate model used, especially in solid state physics, to describe the transition between conducting and insulating systems...
) have been proposed and developed in order to describe phenomena that are due to strong electron correlation. Among them, Dynamical Mean Field Theory
Dynamical mean field theory
Dynamical Mean Field Theory is a method to determine the electronic structure of strongly correlated materials. In such materials, the approximation of independent electrons, which is used in Density Functional Theory and usual band structure calculations, breaks down...
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.
Experimentally, high-energy electron spectroscopies
Photoemission spectroscopy
Photoemission spectroscopy , also known as photoelectron spectroscopy, refers to energy measurement of electrons emitted from solids, gases or liquids by the photoelectric effect, in order to determine the binding energies of electrons in a substance...
, 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.
External links
- The strong-correlations puzzle - an article in Physicsworld.com.