The transport properties of disordered solids have been the subject of much work since at least the 1950s, but with a new burst of activity during the 1980s which has survived up to the present day. There have been numerous reviews of a more or less specialized nature. The present review aims to fill the niche for a non-specialized review of this very active area of research. The basic concepts behind the theory are introduced with more detailed sections covering experimental results, one-dimensional localization, scaling theory, weak localization, magnetic field effects and fluctuations.

https://iopscience.iop.org/article/10.1088/0034-4885/56/12/001/pdf

Localization: theory and experiment

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

Spectacular advances in superconductors have taken place in the past two years. The upper temperature for superconductivity has risen from 23 K to 122 K, and there is reason to believe that the ascent is still ongoing. The materials causing this excitement are oxides. Those oxides that superconduct at the highest temperatures contain copper-oxygen sheets; however, other elements such as bismuth and thallium play a key role in this new class of superconductors. These superconductors are attracting attention because of the possibility of a wide range of applications and because the science is fascinating. A material that passes an electrical current with virtually no loss is more remarkable when this occurs at 120 K instead of 20 K.

https://science.sciencemag.org/content/sci/242/4885/1519.full.pdf

Chemistry of High-Temperature Superconductors

The mechanical resonant response of a solid depends on its shape, density, elastic moduli and dissipation. We describe here instrumentation and computational methods for acquiring and analyzing the resonant ultrasound spectrum of very small (0.001 cm3) samples as a function of temperature, and provide examples to demonstrate the power of the technique. The information acquired is in some cases comparable to that obtained from other more conventional ultrasonic measurement techniques, but one unique feature of resonant ultrasound spectroscopy (RUS) is that all moduli are determined simultaneously to very high accuracy. Thus in circumstances where high relative or absolute accuracy is required for very small crystalline or other anisotropic samples RUS can provide unique information. RUS is also sensitive to the fundamental symmetry of the object under test so that certain symmetry breaking effects are uniquely observable, and because transducers require neither couplant nor a flat surface, broken fragments of a material can be quickly screened for phase transitions and other temperature-dependent responses.

/pdf/resonant-ultrasound-spectroscopic-techniques-for-measurement-wt0fciyopd.pdf

Resonant ultrasound spectroscopic techniques for measurement of the elastic moduli of solids

This article gives an overview of both theoretical and experimental developments concerning states with lattice symmetry breaking in the cuprate high-temperature superconductors. Recent experiments have provided evidence for states with broken rotation as well as translation symmetry, and will be discussed in terms of nematic and stripe physics. Of particular importance here are results obtained using the techniques of neutron and X-ray scattering and scanning tunnelling spectroscopy. Ideas on the origin of lattice-symmetry-broken states will be reviewed, and effective models accounting for various experimentally observed phenomena will be summarized. These include both weak-coupling and strong-coupling approaches, with a discussion of their distinctions and connections. The collected experimental data indicate that the tendency toward uni-directional stripe-like ordering is common to underdoped cuprates, but becomes weaker with increasing number of adjacent CuO2 layers.

/pdf/lattice-symmetry-breaking-in-cuprate-superconductors-stripes-2s61zlujn7.pdf

Lattice symmetry breaking in cuprate superconductors: stripes, nematics, and superconductivity

Measurements are reported of the conductivity and dielectric constant at frequencies up to 10 MHz for a single crystal of La{sub 2}CuO{sub 4+{ital y}} with {ital y}{similar to}0.001 to 0.01. The reported behavior is typical of conventional doped semiconductors, with dielectric constant (at {ital y}=0) and effective mass that are not exceptionally large. The dielectric constant grows as the insulator-to-metal transition is approached, but only for the electric field in the CuO{sub 2} layers, indicating that the transition is two dimensional. The crossover to weak localization occurs close to the antiferromagnetic phase boundary.

Frequency dependence of the conductivity and dielectric constant of La2CuO4+y near the insulator-metal transition.

Phase diagram and single crystal growth of pure and Sr doped La2CuO4

Thermal properties of single-crystal La2CuO4- Delta.

Raman spectra are presented of pristine and doped (Li,Sr) single crystals of ${\mathrm{La}}_{2}\mathrm{Cu}{\mathrm{O}}_{4\ensuremath{-}y}$. Based on polarization measurements, we assign the 424-${\mathrm{cm}}^{\ensuremath{-}1}$ line to the symmetric ${A}_{1g}$ vibration of the out-of-plane oxygen atoms along the tetragonal axis. The line at 231 ${\mathrm{cm}}^{\ensuremath{-}1}$ is identified as the ${A}_{1g}$ vibration of the La atoms along the tetragonal axis and the line at 238 ${\mathrm{cm}}^{\ensuremath{-}1}$ as the ${E}_{g}$ vibration of the out-of-plane oxygen atoms parallel to the Cu-O layers. A symmetry-forbidden Raman line is observed at 680 ${\mathrm{cm}}^{\ensuremath{-}1}$ which, by comparison with infrared measurements, can be tentatively assigned to an in-plane oxygen vibration. The dependence of the Raman spectra upon Li and Sr doping is presented and discussed. Especially noteworthy are two strong and sharp Raman lines (at 757 and 773 ${\mathrm{cm}}^{\ensuremath{-}1}$ at room temperature) in the Sr-doped crystals, because of their higher frequencies, polarization sensitivities, and unusual temperature dependences.

P. J. Picone

Papers

Frequency dependence of the conductivity and dielectric constant of La2CuO4+y near the insulator-metal transition.

Phase diagram and single crystal growth of pure and Sr doped La2CuO4

Top seeded solution growth of La4CuO4

Thermal properties of single-crystal La2CuO4- Delta.

Raman study of pure and doped (Li,Sr) single crystals of La2CuO4-y.