We review the dynamical mean-field theory of strongly correlated electron systems which is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition. This mapping is exact for models of correlated electrons in the limit of large lattice coordination (or infinite spatial dimensions). It extends the standard mean-field construction from classical statistical mechanics to quantum problems. We discuss the physical ideas underlying this theory and its mathematical derivation. Various analytic and numerical techniques that have been developed recently in order to analyze and solve the dynamical mean-field equations are reviewed and compared to each other. The method can be used for the determination of phase diagrams (by comparing the stability of various types of long-range order), and the calculation of thermodynamic properties, one-particle Green's functions, and response functions. We review in detail the recent progress in understanding the Hubbard model and the Mott metal-insulator transition within this approach, including some comparison to experiments on three-dimensional transition-metal oxides. We present an overview of the rapidly developing field of applications of this method to other systems. The present limitations of the approach, and possible extensions of the formalism are finally discussed. Computer programs for the numerical implementation of this method are also provided with this article.

Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions

We present a review of the basic ideas and techniques of the spectral density functional theory which are currently used in electronic structure calculations of strongly{correlated materials where the one{electron description breaks down. We illustrate the method with several examples where interactions play a dominant role: systems near metal{insulator transition, systems near volume collapse transition, and systems with local moments.

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Electronic structure calculations with dynamical mean-field theory

We review recent experimental work falling under the broad classification of colossal magnetoresistance (CMR), which is magnetoresistance associated with a ferromagnetic-toparamagnetic phase transition. The prototypical CMR compound is derived from the parent compound, perovskite LaMnO 3. When hole doped at a concentration of 20–40% holes/Mn ion, for instance by Ca or Sr substitution for La, the material displays a transition from a high-temperature paramagnetic insulator to a low-temperature ferromagnetic metal. Near the phase transition temperature, which can exceed room temperature in some compositions, large magnetoresistance is observed and its possible application in magnetic recording has revived interest in these materials. In addition, unusual magneto-elastic effects and charge ordering have focused attention on strong electron–phonon coupling. This coupling, which is a type of dynamic extended-system version of the Jahn–Teller effect, in conjunction with the double-exchange interaction, is also viewed as essential for a microscopic description of CMR in the manganite perovskites. Large magnetoresistance is also seen in other systems, namely Tl 2Mn2O7 and some Cr chalcogenide spinels, compounds which differ greatly from the manganite perovskites. We describe the relevant points of contrast between the various CMR materials.

REVIEW ARTICLE: Colossal magnetoresistance

Since the first days of high-Tc superconductivity, the materials science and the physics of grain boundaries in superconducting compounds have developed into fascinating fields of research. Unique electronic properties, different from those of the grain boundaries in conventional metallic superconductors, have made grain boundaries formed by high-Tc cuprates important tools for basic science. They are moreover a key issue for electronic and large-scale applications of high-Tc superconductivity. The aim of this review is to give a summary of this broad and dynamic field. Starting with an introduction to grain boundaries and a discussion of the techniques established to prepare them individually and in a well-defined manner, the authors present their structure and transport properties. These provide the basis for a survey of the theoretical models developed to describe grain-boundary behavior. Following these discussions, the enormous impact of grain boundaries on fundamental studies is reviewed, as well as high-power and electronic device applications.

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Grain boundaries in high- T c superconductors

Metal‐Insulator Transitions

We have prepared and identified as a single phase the high-temperature superconducting compound in the chemical system Y-Ba-Cu-O, an orthorhombic, distorted oxygen-deficient perovskite of stoichiometry ${\mathrm{Ba}}_{2}$${\mathrm{YCu}}_{3}$${\mathrm{O}}_{9\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ (\ensuremath{\delta}\ensuremath{\simeq}2.1). Samples exhibit zero resistance at 91 K, with a transition width of 1.5 K. The Meissner effect attains a value of 76% of the independently measured diamagnetic susceptibility. We estimate parameters that characterize this superconductor, e.g., \ensuremath{\gamma}\ensuremath{\simeq}3--5 mJ (mole Cu${)}^{\mathrm{\ensuremath{-}}1}$ ${\mathrm{K}}^{\mathrm{\ensuremath{-}}2}$. The critical current density at 77 K and H=0 exceeds 1100 A/${\mathrm{cm}}^{2}$.

https://link.aps.org/pdf/10.1103/PhysRevLett.58.1676

Bulk superconductivity at 91 K in single-phase oxygen-deficient perovskite Ba 2 YCu 3 O 9 − δ

Mott Transition in Cr-Doped V 2 O 3

We use inelastic neutron scattering to measure the spin wave dispersion throughout the Brillouin zone of the double-exchange ferromagnet La0.7Pb0.3MnO3. Magnons with energies as high as 95 meV are directly observed and an unexpectedly simple Heisenberg Hamiltonian, with solely a nearest-neighbor coupling of 8.79 +/- 0.21 meV, accounts for the entire dispersion relation. The calculated Curie temperature for this local moment Hamiltonian overestimates the measured Curie point (355 K) by only 15%. Raising temperature yields unusual broadening of the high frequency spin waves, even within the ferromagnetic phase.

Spin Waves throughout the Brillouin Zone of a Double-Exchange Ferromagnet.

In the system (${({\mathrm{V}}_{1\ensuremath{-}x}{\mathrm{Ti}}_{x})}_{2}{\mathrm{O}}_{3}$, the antiferromagnetic insulating phase is suppressed for $xg0.05$. The linear term in the heat capacity is very large ($\ensuremath{\gamma}=192\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ cal \ifmmode^\circ\else\textdegree\fi{}${\mathrm{K}}^{\ensuremath{-}2}$ per mole of ${\mathrm{V}}_{2}$${\mathrm{O}}_{3}$), and the magnetic susceptibility at 4.2\ifmmode^\circ\else\textdegree\fi{}K is 2 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}3}$ emu ${\mathrm{mole}}^{\ensuremath{-}1}$ giving a value $\frac{\ensuremath{\chi}}{\ensuremath{\gamma}}=1.8$. The results are interpreted as evidence for a strongly correlated metallic phase.

Electronic Specific Heat of Metallic Ti-Doped V 2 O 3

Measurement of spin polarization of photoelectrons from F${\mathrm{e}}_{3}$${\mathrm{O}}_{4}$ (MAG) and ${\mathrm{Li}}_{0.5}$${\mathrm{Fe}}_{2.5}$${\mathrm{O}}_{4}$ (LIF) up to $\ensuremath{\hbar}\ensuremath{\omega}=11$ eV shows that $B$-site $3d$ levels are higher in energy than $A$-site $3d$ levels. In MAG, unpolarized $2p$ electrons are not emitted up to 11 eV. Existing energy diagrams of MAG do not agree fully with the results. As a direct consequence of Hund's rule, the polarization spectra of MAG and LIF are very different because of the presence of ${\mathrm{Fe}}^{2+}$ in MAG.

J. P. Remeika

Papers

Bulk superconductivity at 91 K in single-phase oxygen-deficient perovskite Ba 2 YCu 3 O 9 − δ

Mott Transition in Cr-Doped V 2 O 3

Spin Waves throughout the Brillouin Zone of a Double-Exchange Ferromagnet.

Electronic Specific Heat of Metallic Ti-Doped V 2 O 3

Observation of Spin-Polarized Electron Levels in Ferrites