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.

/pdf/the-pseudogap-in-high-temperature-superconductors-an-22i3tjkdfn.pdf

The pseudogap in high-temperature superconductors: an experimental survey

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

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.

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.

/pdf/electrodynamics-of-correlated-electron-materials-2qg1x9aaaz.pdf

Electrodynamics of correlated electron materials

There is a strong tendency for dilute holes in an antiferromagnet to phase separate. (This is a generic feature of doping into a commensurate correlated insulating state.) We review the general and model-specific theoretical arguments that support this conclusion for neutral holes. In the presence of long-range Coulomb interactions, there is frustrated phase separation leading to large-amplitude, low-energy fluctuations in the hole density at intermediate length scales, provided the dielectric constant is sufficiently large. We describe extensive experimental evidence showing that such “clumping” of the holes is an important feature of the cuprate superconductors. We also summarize theoretical results which suggest that frustrated phase separation may account for the anomalous properties of the normal state and give rise to high-temperature superconductivity.

Frustrated electronic phase separation and high-temperature superconductors

The structure of the 80 K superconductor YBa 2 Cu 4 O 8 has been measured as a function of temperature and pressure between 5 K and 165 K by high resolution neutron powder diffraction. The oxygen bridging CuO planes to double CuO chains moves away from the chains, toward the planes as T c increases with increasing pressure, indicating charge transfer to the planes. A similar effect occurs when YBa 2 Cu 3 O 6+ x is oxidised to YBa 2 Cu 3 O 7 , again increasing T c . The a - and c -axes of YBa 2 Cu 4 O 8 increase smoothly with temperature, but the b -axis, parallel to the direction of the CuO chains, appears to have a minimum near T c . This results in a slight inflexion in the orthorhombic distortion near T c , similar to that observed in YBa 2 Cu 4 O 7 . The oxygens within these chains appear disordered even at low temperature, again as in YBa 2 Cu 4 O 7 . However, in YBa 2 Cu 4 O 8 oxygens from the CuO-planes also have relatively large out-of-plane amplitudes. High resolution electron microscopy and diffraction show that YBa 2 Cu 4 O 8 , unlike YBa 2 Cu 3 O 7 , does not have planar structural defects; there are no twins or superstructures.

Low temperature anomalies and pressure effects on the structure and Tc of the superconductor YBa2Cu4O8 (Tc=80 K)

Muon-spin-rotation (\ensuremath{\mu}SR) experiments on a high-quality sintered ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{\mathit{x}}$ sample [x=6.970(1)] were performed, in order to obtain an accurate knowledge of the magnitude and the temperature dependence of the magnetic penetration depth in this copper oxide superconductor. Special attention was given to the data analysis. In particular, the systematic errors introduced by different types of analyses were estimated. Our results show that the temperature dependence of the effective penetration depth ${\ensuremath{\lambda}}_{\mathrm{eff}}$ into the sintered sample is well described by the two-fluid model, with ${\ensuremath{\lambda}}_{\mathrm{eff}}$(0)=155(10) nm. This behavior of ${\ensuremath{\lambda}}_{\mathrm{eff}}$(T) is consistent with conventional s-wave pairing. With the anisotropy ratio \ensuremath{\gamma}=${\ensuremath{\lambda}}_{\mathit{c}}$/${\ensuremath{\lambda}}_{\mathit{a}\mathit{b}}$=5(1) measured in a previous \ensuremath{\mu}SR experiment, the penetration depths ${\ensuremath{\lambda}}_{\mathit{a}\mathit{b}}$(0)=130(10) nm and ${\ensuremath{\lambda}}_{\mathit{c}}$(0)=500--800 nm (parallel and perpendicular to the ${\mathrm{CuO}}_{2}$ planes, respectively) were extracted. Our results are compared with those obtained by other experimental techniques and theoretical predictions.

Muon-spin-rotation measurements of the London penetration depths in YBa2Cu3O6.97.

High pressure preparation and neutron-diffraction study of the high Tc superconductor YBa2Cu4O8″^X

In this paper we present a study of the thermodynamic, structural and physical properties of Y2Ba4Cu7O15±x, the new high-Tc superconductor we have discovered recently. The nonstoichiometry of Y2Ba4Cu7O15±x has been varied between -0.70 T c , 1 2 =26.5 K ) indicating that possibly a coupling over long distance (11.5 A) takes place.

The nonstoichiometry of the high-Tc superconductor Y2Ba4Cu7O15±x (14 K⩽Tc⩽68 K)

We present Raman spectra of high-temperature superconducting single crystals of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{4}$${\mathrm{O}}_{8}$ and ${\mathrm{Y}}_{2}$${\mathrm{Ba}}_{4}$${\mathrm{Cu}}_{7}$${\mathrm{O}}_{15\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$, differing from the well-known ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ by having double CuO chains By performing polarization-dependent measurements, we were able to identify the symmetry of the observed phonons In both materials, we detected four out of six Raman-allowed modes of the double Cu(1)-O(1) chains and assign the peaks to Cu(1) ${\mathit{A}}_{\mathit{g}}$ (250 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$), O(1) ${\mathit{A}}_{\mathit{g}}$ (605 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$), Cu(1) ${\mathit{B}}_{3\mathit{g}}$ (314 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$), and O(1) ${\mathit{B}}_{2\mathit{g}}$ (228 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$) in addition to the 5 ${\mathit{A}}_{\mathit{g}}$ phonons (in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{4}$${\mathrm{O}}_{8}$ near 104, 153, 341, 438, and 500 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$), which are also present in the well-known ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ Contrary to previous reports of Raman scattering on double-${\mathrm{CuO}}_{2}$-plane superconductors, ${\mathit{B}}_{2\mathit{g}}$ and ${\mathit{B}}_{3\mathit{g}}$ phonons can unambiguously be observedThey are, in fact, stronger than some of the ${\mathit{A}}_{\mathit{g}}$ phonons The peaks at 605, 314, 250, and 228 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ are more than twice as large in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{4}$${\mathrm{O}}_{8}$ than in ${\mathrm{Y}}_{2}$${\mathrm{Ba}}_{4}$${\mathrm{Cu}}_{7}$${\mathrm{O}}_{15\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$, thus confirming that they are chain related The Raman intensities of the ${\mathit{A}}_{\mathit{g}}$ modes at 250, 500, and 605 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ are much larger in yy (along the chains) than in xx polarization, proving that the crystals are untwinned and stressing the importance of the chains for the Raman activity of these modes When lowering the temperature below ${\mathit{T}}_{\mathit{c}}$=74 K the ${\mathit{B}}_{1\mathit{g}}$-like O(2)-O(3) phonon near 104 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ as well as the Ba ${\mathit{A}}_{\mathit{g}}$ phonon at 341 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ exhibit a rather sharp softening The Ba mode shows a pronounced Fano line asymmetry, while that of the O(2)-O(3) line is rather weak

Optical phonons in YBa2Cu4O8 and Y2Ba4Cu7O15- delta.

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