Strongly correlated material

Strongly correlated materials are a wide class of materials that show unusual (often technologically useful) electronic and magnetic properties, such as metal-insulator transitions or half-metallicity.

Electron correlations are those effects which are not captured by Hartree-Fock theory. If these effects are large and particularly when Hartree-Fock gives a qualitatively incorrect results one refers to a material as strongly correlated.

The most commonly known strongly correlated materials are high-temperature superconductors which exhibit interesting conductive properties.

Many, if not most, transition metal oxides belong into this class which may be subdivided according to their behavior, e.g. high Tc superconductors, spintronic materials, Mott insulators, spin Peierls 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. La_2-xSr_xCuO₄. 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 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 LDA (LDA+U, GGA, SIC, GW, etc.) as well as simplified model Hamiltonians (e.g. Hubbard-like models) have been proposed and developed in order to describe phenomena that are due to strong electron correlation.

Experimentally, high-energy electron spectroscopies, and more recently resonant inelastic (hard and soft) x-ray scattering 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.