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 review studies of the electromagnetic response of various classes of correlated electron materials including transition metal oxides, organic and molecular conductors, intermetallic compounds with $d$- and $f$-electrons as well as magnetic semiconductors. Optical inquiry into correlations in all these diverse systems is enabled by experimental access to the fundamental characteristics of an ensemble of electrons including their self-energy and kinetic energy. Steady-state spectroscopy carried out over a broad range of frequencies from microwaves to UV light and fast optics time-resolved techniques provide complimentary prospectives on correlations. Because the theoretical understanding of strong correlations is still evolving, the review is focused on the analysis of the universal trends that are emerging out of a large body of experimental data augmented where possible with insights from numerical studies.

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Electrodynamics of correlated electron materials

4.3. Manganese Oxide-Based Compounds 1291 4.3.1. MnO2-Type Compounds 1291 4.3.2. Ternary Lithiated LixMnOy Compounds 1293 4.4. Vanadium Pentoxide V2O5 1298 4.4.1. V2O5 Structure 1298 4.4.2. LixV2O5 Bulk Phases 1300 4.4.3. LixV2O5 Crystallized Thin Films 1303 4.5. Titanium Oxide-Based Compounds 1305 4.5.1. Lithium Titanate Li4Ti5O12 1306 4.5.2. TiO2 Anatase 1308 5. Phospho-olivine LiFePO4 Compound 1312 6. General Conclusion 1314 7. Acknowledgments 1315 8. References 1315

Raman Microspectrometry Applied to the Study of Electrode Materials for Lithium Batteries

Inelastic light scattering is an intensively used tool in the study of electronic properties of solids. Triggered by the discovery of high-temperature superconductivity in the cuprates and by new developments in instrumentation, light scattering in both the visible (Raman effect) and x-ray part of the electromagnetic spectrum has become a method complementary to optical (infrared) spectroscopy while providing additional and relevant information. The main purpose of the review is to position Raman scattering with regard to single-particle methods like angle-resolved photoemission spectroscopy, and other transport and thermodynamic measurements in correlated materials. Particular focus will be placed on photon polarizations and the role of symmetry to elucidate the dynamics of electrons in different regions of the Brillouin zone. This advantage over conventional transport (usually measuring averaged properties) provides new insights into anisotropic and complex many-body behavior of electrons in various systems. Recent developments in the theory of electronic Raman scattering in correlated systems and experimental results in paradigmatic materials such as the A15 superconductors, magnetic and paramagnetic insulators, compounds with competing orders, as well as the cuprates with high superconducting transition temperatures are reviewed. An overview of the manifestations of complexity in the Raman response due to the impact of correlations and developing competing orders is presented. In a variety of materials, observations which may be understood and a summary of important open questions that pave the way to a detailed understanding of correlated electron systems, are discussed.

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Inelastic light scattering from correlated electrons

Although the vast majority of high-$T_c$ cuprate superconductors are hole-doped, a small family of electron-doped compounds exists. Under investigated until recently, there has been tremendous recent progress in their characterization. A consistent view is being reached on a number of formerly contentious issues, such as their order parameter symmetry, phase diagram, and normal state electronic structure. Many other aspects have been revealed exhibiting both their similarities and differences with the hole-doped compounds. This review summarizes the current experimental status of these materials, with a goal to providing a snapshot of our current understanding of electron-doped cuprates. When possible we put our results in the context of the hole-doped compounds. We attempt to synthesize this information into a consistent view on a number of topics important to both this material class as well as the overall cuprate phenomenology including the phase diagram, the superconducting order parameter symmetry, phase separation, pseudogap effects, the role of competing orders, the spin-density wave mean-field description of the normal state, and electron-phonon coupling.

Progress and perspectives on electron-doped cuprates

Topological Dirac semimetals (TDSs) represent a new state of quantum matter recently discovered that offers a platform for realizing many exotic physical phenomena. A TDS is characterized by the linear touching of bulk (conduction and valance) bands at discrete points in the momentum space [i.e., three-dimensional (3D) Dirac points], such as in $\mathrm{N}{\mathrm{a}}_{3}\mathrm{Bi}$ and $\mathrm{C}{\mathrm{d}}_{3}\mathrm{A}{\mathrm{s}}_{2}$. More recently, new types of Dirac semimetals with robust Dirac line nodes (with nontrivial topology or near the critical point between topological phase transitions) have been proposed that extend the bulk linear touching from discrete points to one-dimensional (1D) lines. In this paper, using angle-resolved photoemission spectroscopy (ARPES), we explored the electronic structure of the nonsymmorphic crystals $M\text{SiS}$ $(M=\mathrm{Hf}$, Zr). Remarkably, by mapping out the band structure in the full 3D Brillouin zone (BZ), we observed two sets of Dirac line-nodes in parallel with the ${k}_{z}$ axis and their dispersions. Interestingly, along directions other than the line nodes in the 3D BZ, the bulk degeneracy is lifted by spin-orbit coupling (SOC) in both compounds with larger magnitude in HfSiS. Our paper not only experimentally confirms a new Dirac line-node semimetal family protected by nonsymmorphic symmetry but also helps understanding and further exploring the exotic properties, as well as practical applications of the $M\text{SiS}$ family of compounds.

Dirac line nodes and effect of spin-orbit coupling in the nonsymmorphic critical semimetals MSiS (M = Hf, Zr)

We present an analysis of the measured excess conductivity which results from the fluctuation of the superconducting order parameter of a Bi 2 Sr 2 CaCu 2 O 8+y single crystal and found it was fit best by the two-dimensional Aslamazov-Larkin theory. The magnetoconductivity and magnetization studies are in good agreement with the two-dimensional (2D) scaling behavior in the fremework of Lawrence-Doniach model revealing the 2D nature of the fluctuation near the mean-field transition temperature in the presence of a field.

Fluctuation phenomena in excess conductivity and magnetization of single-crystal Bi 2 Sr 2 CaCu 2 O 8+y

We have measured Raman spectra of polycrystalline samples of the Li1+xTi2−xO4 superconducting system (0⩽x⩽13) at room temperature. For LiTi2O4 (x=0), which is a superconductor (Tc=13K), the frequencies of the detected phonon modes are 200, 339, 429, 494 and 628 cm−1, corresponding to the expected five zone-centre Raman active modes for the spinel-type structure. For Li[Li13Ti53]O4(x=13), which is an insulator, we observe five phonon peaks centred on 239, 274, 367, 427 and 675 cm−1. However for intermediate values of x, the scattering peaks broaden; in the range of 0.1 < x < 0.2, the Raman spectra can barely be resolved, consistent with chemical inhomogeneity of Li1+xTi2−xO4 due to a spinodal decomposition.

Changkang Chen

Papers

Dirac line nodes and effect of spin-orbit coupling in the nonsymmorphic critical semimetals MSiS (M = Hf, Zr)

Fluctuation phenomena in excess conductivity and magnetization of single-crystal Bi 2 Sr 2 CaCu 2 O 8+y

Raman scattering of the Li1+xTi2−xO4 superconducting system

Phase diagram and single crystal growth of (La, Sr)2CuO4 from CuO solution

Crystal field Raman scattering in Nd2CuO4