We present an experimental review of the nature of the pseudogap in the cuprate superconductors. Evidence from various experimental techniques points to a common phenomenology. The pseudogap is seen in all high-temperature superconductors and there is general agreement on the temperature and doping range where it exists. It is also becoming clear that the superconducting gap emerges from the normal state pseudogap. The d-wave nature of the order parameter holds for both the superconducting gap and the pseudogap. Although an extensive body of evidence is reviewed, a consensus on the origin of the pseudogap is as lacking as it is for the mechanism underlying high-temperature superconductivity.

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The pseudogap in high-temperature superconductors: an experimental survey

Powdered samples of the type Ce1−xRExO2−y, where RE=La, Pr, Nd, Eu, Gd, and Tb, are synthesized over the range 0≤x≤0.5 starting from nitrate solutions of the rare earths. X‐ray diffraction and Raman scattering are used to analyze the samples. These compounds, at least in the low doping regime and for strictly trivalent dopants, form solid solutions that maintain the fluorite structure of CeO2 with a change in lattice constant that is approximately proportional to the dopant ionic radius. The single allowed Raman mode, which occurs at 465 cm−1 in pure CeO2, is observed to shift to lower frequency with increasing doping level for all the rare earths. However, after correcting for the Gruneisen shift from the lattice expansion, the frequency shift is actually positive for all the strictly trivalent ions. In addition, the Raman line broadens and becomes asymmetric with a low frequency tail, and a new broad feature appears in the spectrum at ∼570 cm−1. These changes in the Raman spectrum are attributed to O va...

Raman and x‐ray studies of Ce1−xRExO2−y, where RE=La, Pr, Nd, Eu, Gd, and Tb

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

Magnetic flux can penetrate a type-II superconductor in the form of Abrikosov vortices (also called flux lines, flux tubes, or fluxons) each carrying a quantum of magnetic flux phi 0=h/2e. These tiny vortices of supercurrent tend to arrange themselves in a triangular flux-line lattice (FLL), which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-Tc superconductors (HTSCs) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSCs the FLL is very soft mainly because of the large magnetic penetration depth lambda . The shear modulus of the FLL is c66~1/ lambda 2, and the tilt modulus c44(k)~(1+k2 lambda 2)-1 is dispersive and becomes very small for short distortion wavelengths 2 pi /k<< lambda . This softness is enhanced further by the pronounced anisotropy and layered structure of HTSCs, which strongly increases the penetration depth for currents along the c axis of these (nearly uniaxial) crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may `melt` the FLL and cause thermally activated depinning of the flux lines or ofthe two-dimensional `pancake vortices` in the layers. Various phase transitions are predicted for the FLL in layered HTSCs. Although large pinning forces and high critical currents have been achieved, the small depinning energy so far prevents the application of HTSCs as conductors at high temperatures except in cases when the applied current and the surrounding magnetic field are small.

https://iopscience.iop.org/article/10.1088/0034-4885/58/11/003/pdf

The flux-line lattice in superconductors

Magnetic flux can penetrate a type-II superconductor in form of Abrikosov vortices. These tend to arrange in a triangular flux-line lattice (FLL) which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-$T_c$ supercon- ductors (HTSC's) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSC's the FLL is very soft mainly because of the large magnetic penetration depth: The shear modulus of the FLL is thus small and the tilt modulus is dispersive and becomes very small for short distortion wavelength. This softness of the FLL is enhanced further by the pronounced anisotropy and layered structure of HTSC's, which strongly increases the penetration depth for currents along the c-axis of these uniaxial crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may melt the FLL and cause thermally activated depinning of the flux lines or of the 2D pancake vortices in the layers. Various phase transitions are predicted for the FLL in layered HTSC's. The linear and nonlinear magnetic response of HTSC's gives rise to interesting effects which strongly depend on the geometry of the experiment.

The Flux-Line Lattice in Superconductors

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

Analyse magnetothermique d'un systeme a forte frustration (Sr−Cr−Ga−O). Mise en evidence d'une transition magnetique a 3,3 K, bien que la temperature de Curie soit elevee (515 K). Le systeme presente d'autres caracteristiques inhabituelles telles une chaleur specifique basse et une relation inverse entre la temperature de transition magnetique et la concentration en ions magnetiques

Strong frustration and dilution-enhanced order in a quasi-2D spin glass.

A solution to the long-standing problem of the companion ${A}_{1}$ Raman line [symmetric breathing mode of Ge${(\mathrm{S},\mathrm{S}\mathrm{e})}_{4}$ tetrahedra] in Ge${(\mathrm{S},\mathrm{S}\mathrm{e})}_{2}$ glasses is proposed based on the observation of a similar doublet in the crystal. The proposed model assumes that $g$-Ge${(\mathrm{S},\mathrm{S}\mathrm{e})}_{2}$ consists of units with a layered structure, in sharp contradistinction to $g$-Si${\mathrm{O}}_{2}$, which consists of a random, fully three-dimensional network.

Microscopic origin of the companion A 1 Raman line in glassy Ge ( S , S e ) 2

The dissipation observed at the superconducting transition of the high-${T}_{c}$ superconductor ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$Ca${\mathrm{Cu}}_{2}$${\mathrm{O}}_{8}$ is explained quantitatively by the Kosterlitz-Thouless theory of vortex-antivortex pair excitations within the Cu${\mathrm{O}}_{2}$ planes. This conclusion is drawn from the observation of an exponential square-root singularity in the resistivity and a power-law dependence of the resistivity on magnetic field. The Kosterlitz-Thouless phase transition (${T}_{c}=84.7$ K) is at the $\ensuremath{\rho}=0$ point, and the mean-field Ginzburg-Landau transition (${T}_{c0}=86.8$ K) at \ensuremath{\sim}25% of the normal-state resistivity.

Vortex-pair excitation near the superconducting transition of Bi2Sr2CaCu2O8 crystals.

The crystal structure of ${\mathrm{CeO}}_{2}$ has been investigated to 70 GPa using energy dispersive x-ray diffraction in a diamond-anvil cell. At 31.5\ifmmode\pm\else\textpm\fi{}1.0 GPa the fluorite phase transforms, on loading, to an orthorhombic \ensuremath{\alpha}-${\mathrm{PbCl}}_{2}$-like structure of space group Pnam, with a 7.5%\ifmmode\pm\else\textpm\fi{}0.7% increase in density. The cubic fluorite phase has a bulk modulus ${B}_{0}$=230\ifmmode\pm\else\textpm\fi{}10 GPa with an assumed pressure derivative of ${B}_{0}^{\mathcal{'}}$=4.00. The \ensuremath{\alpha}-${\mathrm{PbCl}}_{2}$-type structure seems to be the stable high-pressure phase in the case of the group-IVB, lanthanide, and actinide fluorite-type dioxides, independent of metal-ion size, at reduced volumes less than 0.89\ifmmode\pm\else\textpm\fi{}0.01.

G. P. Espinosa

Papers

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

Strong frustration and dilution-enhanced order in a quasi-2D spin glass.

Microscopic origin of the companion A 1 Raman line in glassy Ge ( S , S e ) 2

Vortex-pair excitation near the superconducting transition of Bi2Sr2CaCu2O8 crystals.

High-pressure x-ray diffraction study of CeO 2 to 70 GPa and pressure-induced phase transformation from the fluorite structure