In the light of the tremendous progress that has been made in raising the transition temperature of the copper oxide superconductors (for a review, see ref. 1), it is natural to wonder how high the transition temperature, Tc, can be pushed in other classes of materials. At present, the highest reported values of Tc for non-copper-oxide bulk superconductivity are 33 K in electron-doped CsxRbyC60 (ref. 2), and 30 K in Ba1-xKxBiO3 (ref. 3). (Hole-doped C60 was recently found4 to be superconducting with a Tc as high as 52 K, although the nature of the experiment meant that the supercurrents were confined to the surface of the C60 crystal, rather than probing the bulk.) Here we report the discovery of bulk superconductivity in magnesium diboride, MgB2. Magnetization and resistivity measurements establish a transition temperature of 39 K, which we believe to be the highest yet determined for a non-copper-oxide bulk superconductor.

Superconductivity at 39 K in magnesium diboride

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

First-principles band theory, properly augmented by topological considerations, has provided a remarkably successful framework for predicting new classes of topological materials. This Colloquium discusses the underpinnings of the topological band theory and its materials applications.

Colloquium : Topological band theory

Since the discovery of superconductivity above 30 K by Bednorz and M\"uller in the La copper oxide system, the critical temperature has been raised to 90 K in Y${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ and to 110 and 125 K in Bi-based and Tl-based copper oxides, respectively. In the two years since this Nobel-prize-winning discovery, a large number of electronic structure calculations have been carried out as a first step in understanding the electronic properties of these materials. In this paper these calculations (mostly of the density-functional type) are gathered and reviewed, and their results are compared with the relevant experimental data. The picture that emerges is one in which the important electronic states are dominated by the copper $d$ and oxygen $p$ orbitals, with strong hybridization between them. Photon, electron, and positron spectroscopies provide important information about the electronic states, and comparison with electronic structure calculations indicates that, while many features can be interpreted in terms of existing calculations, self-energy corrections ("correlations") are important for a more detailed understanding. The antiferromagnetism that occurs in some regions of the phase diagram poses a particularly challenging problem for any detailed theory. The study of structural stability, lattice dynamics, and electron-phonon coupling in the copper oxides is also discussed. Finally, a brief review is given of the attempts so far to identify interaction constants appropriate for a model Hamiltonian treatment of many-body interactions in these materials.

Electronic structure of the high-temperature oxide superconductors

We report the characterization of series of oxygen deficient Ba2YCu3Ox samples for 7 ≥ x ≥ 6 prepared by Zr gettered annealing at 440°C. Measurements include complete crystal structure analysis at 5 K by powder neutron diffraction, electron microscopy study of the oxygen ordering, and magnetic measurements of the superconducting transitions, with particular attention to the transition widths. The results show for the first time that the 90 K and 60 K plateaus in Tc as a function of oxygen stoichiometry are associated with plateaus in the effective valence of the plane coppers. We also correlate the disappearance of superconductivity for x

Structural anomalies, oxygen ordering and superconductivity in oxygen deficient Ba2YCu3Ox

It is well known that the breakthrough of Bednorz and Muller1 in discovering superconductivity in (La, Ba)2CuO4 was inspired in part by their knowledge of the superconducting properties of Ba(Pb, Bi)O3 (ref. 2). With a transition temperature, Tc, of ∼12 K, that compound was not generally considered anomalous despite the fact that its Tcis 3–5 times higher than that of traditional superconductors with comparable density of states3–5. The increases in Tc for copper-oxide-based materials continue to generate worldwide excitement, but from both a chemical and theoretical point of view it would also be exciting if high-Tcsuperconductivity were observed in another class of materials. Here we report the results of experiments leading us to the single-phase perovskite Ba0.6K0.4BiO3, which has a magnetically determined onset temperature of 29.8 K—a Tc considerably higher than that of conventional superconductors and surpassed only by copper-containing compounds. Superconductivity in this compound occurs within the framework of a three dimensionally connected bismuth-oxygen array. These results suggest that further research toward exploring the limiting Tcs for bismuth-oxide-based, high-temperature superconductors might be fruitful.

Superconductivity near 30 K without copper: the Ba 0.6 K 0.4 BiO 3 perovskite

Increased understanding of fundamental properties of the new cuprate superconductors depends on advances in the preparation of quality materials for study. Early work focused on the study of sintered polycrystalline samples. In some cases, grain growth during sintering yielded individual grains large enough (˜80 μm) for single crystal X-ray determination1. Larger single crystals allow measurements of physical properties including measurements of anisotropic behaviour. The anisotropy of upper critical fields in YBa2Cu3O7 single crystals has been reported by lye et al.2 who found critical fields characteristic of a quasi-two-dimensional superconductor, which are highest when the field is orientated perpendicular to the c-axis. Dinger et al.3 have measured critical fields and critical currents of single crystals and find anisotropies of 10 and greater3. These studies contain little detail on the crystal growth of YBa2Cu3O7. Here we report the growth of single crystals as large as 4 mm of YBa2Cu3O7 and DyBa2Cu3O7 and confirm superconductivity in them by magnetic and electrical measurements. Single crystals of other rare earth barium cuprates are also obtained although we have yet to optimize growth conditions for these phases.

Superconductivity in YBa2Cu3O7 single crystals

Ambient temperature measurements of the crystallographic cell parameters for oxygen deficient Ba 2 YCu 3 O 7−δ prepared by gettered annealing indicate the presence of microscopic differences in the oxygen configuration at fixed δ dependent on annealing temperature. The loss of superconductivity with increasing oxygen deficiency is shown to be due to a step-like increase in length of the plane copper-apical oxygen bond, and not to the orthorhombic to tetragonal transition. The crystal structure of the 84K superconductor Bi 2 Sr 2 CaCu 2 O 8+δ is described, as is the stabilization of 110K superconductivity via partial Pb/Bi substitution with long time annealing.

Studies of oxygen-deficient Ba2YCu3O7−δ and superconductivity Bi(Pb)SrCaCuO

STARTING with the pioneering work of Bednorz and Muller1, many copper-oxide-based superconductors with high transition temperatures (Tc) have been discovered. All contain layers of copper-oxygen squares, pyramids or octahedra as their electronically active structural components2,3. One structure type, first reported for La2SrCu2O6 and La2CaCu2O6 (ref. 4), has stood as an enigma since the beginning of high-Tc research. This crystal structure4-7 (Fig. 1) is the least complex of all the structures with the double layers of copper oxide pyramids common to the compounds with highest Tc, yet despite considerable effort, both published8,9 and unpublished, it has not until now been made superconducting. Here we report the successful synthesis and preliminary physical characterization of superconducting (La, Sr)2CaCu2O6. The highest transition temperature observed is 60 K at the composition La1.6Sr0.4CaCu2O6. This is a uniquely simple double-layer superconductor, which, like its single-layer analogue (La, Sr)2CuO4, becomes superconducting through the introduction of carriers in an unambiguous manner—by straightforward atomic substitution without the intervention of charge reservoir layers with flexible valence states.

L. W. Rupp

Papers

Superconductivity near 30 K without copper: the Ba 0.6 K 0.4 BiO 3 perovskite

Structural anomalies, oxygen ordering and superconductivity in oxygen deficient Ba2YCu3Ox

Superconductivity in YBa2Cu3O7 single crystals

Studies of oxygen-deficient Ba2YCu3O7−δ and superconductivity Bi(Pb)SrCaCuO

Superconductivity at 60 K in La2-xSrxCaCu2O6: the simplest double-layer cuprate