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

Magnetism and ferroelectricity are essential to many forms of current technology, and the quest for multiferroic materials, where these two phenomena are intimately coupled, is of great technological and fundamental importance. Ferroelectricity and magnetism tend to be mutually exclusive and interact weakly with each other when they coexist. The exciting new development is the discovery that even a weak magnetoelectric interaction can lead to spectacular cross-coupling effects when it induces electric polarization in a magnetically ordered state. Such magnetic ferroelectricity, showing an unprecedented sensitivity to ap plied magnetic fields, occurs in 'frustrated magnets' with competing interactions between spins and complex magnetic orders. We summarize key experimental findings and the current theoretical understanding of these phenomena, which have great potential for tuneable multifunctional devices.

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Multiferroics: a magnetic twist for ferroelectricity

BiFeO3 is perhaps the only material that is both magnetic and a strong ferroelectric at room temperature. As a result, it has had an impact on the field of multiferroics that is comparable to that of yttrium barium copper oxide (YBCO) on superconductors, with hundreds of publications devoted to it in the past few years. In this Review, we try to summarize both the basic physics and unresolved aspects of BiFeO3 (which are still being discovered with several new phase transitions reported in the past few months) and device applications, which center on spintronics and memory devices that can be addressed both electrically and magnetically.

Physics and Applications of Bismuth Ferrite

Oxidative Nucleobase Modifications Leading to Strand Scission

Since the discovery of high-temperature superconductivity in cop-per oxide compounds1, there has been much effort to understand what is required for a compound to have a high transition tem-perature (Tc). Up to now, all of the families of high-Tc copper oxide superconductors have contained two-dimensional sheets of Cu–O pyramids or octahedra, and the carriers of the superconduct-ing current have been electron vacancies, or 'holes'. By contrast, we report here the discovery of a family of superconducting copper oxides in which the carriers are electrons. The new superconductors are Ce4+-doped compounds, with the formula Ln2–xCexCuO4–y, where Ln stands for the lanthanides Pr, Nd or Sm. The compounds have the Nd2CuO4 (T′-phase) structure2, which is composed of sheets of Cu–O squares (see Fig. la). This structure has no apical oxygen atoms, in contrast to the T-phase structure with Cu–O octahedra (Fig. 1b), as observed in La2–xSrxCuO4 (refs 1, 2), and the T*-phase structure with Cu–O pyramids (Fig. 1c), as in Nd2–x–z Cex Srz CuO4 (ref. 3 and Y. T. et al., manuscript in preparation).

A superconducting copper oxide compound with electrons as the charge carriers

The detailed behavior of the phase transitions was mapped out for the series R${\mathrm{NiO}}_{3}$ as a function of the rare earth (R). A sharp insulator-metal transition is observed, which depends strongly on R.Forsmall$R it occurs at a higher temperature than the antiferromagnetic ordering (measured by muon-spin relaxation). By increasing either the temperature or the size of R, an insulator-metal transition is observed, most probably caused by the closing of the charge-transfer gap, induced by increase in the electronic bandwidth.

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Systematic study of insulator-metal transitions in perovskites RNiO3 (R=Pr,Nd,Sm,Eu) due to closing of charge-transfer gap.

Samples of ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Cu}{\mathrm{O}}_{4\ensuremath{-}\ensuremath{\delta}}$ have previously shown a maximum concentration of $p=0.15$ holes per [Cu${\mathrm{O}}_{2}$] unit, because increasing $xg0.15$ normally induces compensating oxygen vacancies. Annealing samples in 100 bars of oxygen pressure fills the oxygen vacancies and greatly increases the range of accessible hole concentrations, up to $p=0.40$ (or effectively ${\mathrm{Cu}}^{+2.40}$). We find that ${T}_{c}$ is constant at \ensuremath{\simeq}36 K from $p=0.15 \mathrm{to} 0.24$, where it begins to decrease. Beyond $p\ensuremath{\simeq}0.32$, superconductivity disappears, even though the samples are more conducting.

Anomalous disappearance of high-Tc superconductivity at high hole concentration in metallic La2-xSrxCuO4.

A series of new $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{y}$-like materials are reported in which the oxygen content and the average [Cu-O] charge (or Cu valence) are separately varied over a wide range. We find a distinct boundary between samples showing anomalous insulating behavior and those with high ${T}_{c}$. These data are interpreted to demonstrate that the [Cu-O] charge in the sheets largely determines ${T}_{c}$ and that the variable oxygen content and the chains merely provide an insulating reservoir of charge.

Broader perspective on the high-temperature superconduct- ing YBa2Cu3Oy system: The real role of the oxygen content.

Bulk superconductivity is reported in T12Ca2 Ba2 Cu3 Ox with a transition to zero resistance at ≃ 125 K, the highest transition temperature (Tc) yet found. Transmission electron spectroscopy shows that the unit cell is body-centered tetragonal and contains trilayer Cu perovskitelike units separated by bilayer TI-O units. (T c in this material varies from 118 to 125 K depending on preparation conditions. A high density of perovskitelike bilayer intergrowths are observed in the 118-K material, which we speculate result in the decreased (T c. A second structure containing only bilayer perovskitelike units—TI2 Ca1 Ba2Cu2Ox—is a bulk superconductor with Tv ranging from 95 to 108 K.

Bulk superconductivity at 125 K in Tl2Ca2Ba2Cu3Ox.

We report the discovery of three new phases in the Tl-Ca-Ba-Cu-O system, Tl/sub 1/Ca/sub n//sub -1/Ba/sub 2/Cu/sub n/O/sub 2//sub n//sub +3/ (n = 1,2,3), one of which (n = 3) exhibits bulk superconductivity at approx. =110 K. The crystal structures of these new materials are closely related to that of Tl/sub 2/Ca/sub 2/Ba/sub 2/Cu/sub 3/O/sub x/, the recently discovered 125-K superconductor. All of these compounds contain Cu perovskitelike units, but whereas these are separated by bilayer Tl-O sheets in the 125-K material these are separated by monolayer Tl-O sheets in the new structures, enabling an examination of the role played by the coupling between successive Cu perovskite units on superconducting properties.

A. I. Nazzal

Papers

Systematic study of insulator-metal transitions in perovskites RNiO3 (R=Pr,Nd,Sm,Eu) due to closing of charge-transfer gap.

Anomalous disappearance of high-Tc superconductivity at high hole concentration in metallic La2-xSrxCuO4.

Broader perspective on the high-temperature superconduct- ing YBa2Cu3Oy system: The real role of the oxygen content.

Bulk superconductivity at 125 K in Tl2Ca2Ba2Cu3Ox.

Tl 1 Ca n − 1 Ba 2 Cu n O 2 n + 3 ( n = 1 , 2 , 3 ): A New Class of Crystal Structures Exhibiting Volume Superconductivity at up to ≃110 K