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

This article discusses fluctuating order in a quantum disordered phase proximate to a quantum critical point, with particular emphasis on fluctuating stripe order. Optimal strategies are derived for extracting information concerning such local order from experiments, with emphasis on neutron scattering and scanning tunneling microscopy. These ideas are tested by application to two model systems---an exactly solvable one-dimensional (1D) electron gas with an impurity, and a weakly interacting 2D electron gas. Experiments on the cuprate high-temperature superconductors which can be analyzed using these strategies are extensively reviewed. The authors adduce evidence that stripe correlations are widespread in the cuprates. They compare and contrast the advantages of two limiting perspectives on the high-temperature superconductor: weak coupling, in which correlation effects are treated as a perturbation on an underlying metallic (although renormalized) Fermi-liquid state, and strong coupling, in which the magnetism is associated with well-defined localized spins, and stripes are viewed as a form of micro phase separation. The authors present quantitative indicators that the latter view better accounts for the observed stripe phenomena in the cuprates.

How to detect fluctuating stripes in the high-temperature superconductors

Angle-resolved photoemission experiments reveal evidence of an energy gap in the normal state excitation spectrum of the cuprate superconductor Bi2Sr2CaCu2O8+delta. This gap exists only in underdoped samples and closes around the doping level at which the superconducting transition temperature Tc is a maximum. The momentum dependence and magnitude of the gap closely resemble those of the dx2-y2 gap observed in the superconducting state. This observation is consistent with results from several other experimental techniques, which also indicate the presence of a gap in the normal state. Some possible theoretical explanations for this effect are reviewed.

https://science.sciencemag.org/content/sci/273/5273/325.full.pdf

Excitation Gap in the Normal State of Underdoped Bi2Sr2CaCu2O8+δ

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

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

Inelastic neutron scattering experiments have been carried out on YBa2Cu3O6+x single crystals to investigate the spin dynamics in the pure AF-state (x = 0.15, TN = 410 K), in the doped AF-state (x = 0.37, TN = 180 K), in the metallic weakly doped superconducting state (x = 0.45, Tc = 37 K; x = 0.51, Tc = 47 K) and in the Tc = 60 K superconducting phase (x = 0.69, Tc = 59 K). The main results are summarized: the two dimensional character of the spin-wave spectrum in the AF-state, strong renormalization of low-energy excitations and overdamping of in-plane spin fluctuations in the doped AF-state, dynamical AF correlations in the superconducting state, evidence for a pseudo-gap induced by superconductivity and existence of superconducting correlations above Tc.

Investigation of the spin dynamics in YBa2Cu3O6+x by inelastic neutron scattering

Neutron diffraction experiments, performed on a powder sample, have shown that the reduced compound YBa 2 Cu 3 O 6 orders with an antiferromagnetic structure at a temperature as high as 500 K. Magnetic moments of about 0.48±0.05 μ B are aligned along the tetragonal c -axis and exhibit an antiferromagnetic coupling both in the basal plane ( k 0 =[ 1 2 1 2 0] ) and in between the two CuO 2 layers of the unit cell. A discussion of the results is presented.

Evidence for high temperature antiferromagnetic ordering in YBa2Cu3O6

Hall effect and thermoelectric power of an YBa2Cu3O6.8 single crystal

The specific heat of a single crystal of YBa2Cu3O7 was measured by adiabatic calorimetry between 40 and 150 K. The typical scatter of the data is well below 0.1%. Fields up to 20 T were applied either parallel or perpendicular to the c-axis. The shape of the anomaly at Tc changes with the magnetic field in the same manner for both directions, within a scale factor that determines the bulk anisotropy ratio, 5.5 ± 0.5, for (dHc2/dT)Tc. The superconducting transition is still observable in 20 T. A growing mixed-state Maki term is present. The characteristic non-classical behavior of YBa2Cu3O7 in a field, featuring a considerable smearing of the transition and an apparently field-independent onset, may be qualitatively understood as a phenomenological consequence of the small and anisotropic value of the coherence length ξ alone, using the relevant models of field-induced critical 1D fluctuations on the one hand, and a London-like regime for the mean-field part of the transition on the other hand.

Specific heat of an YBa2Cu3O7 single crystal in fields up to 20 T

Inelastic neutron scattering experiments have been carried out on YBa 2 Cu 3 O 6+ξ single crystals in order to perform a systematic investigation of the spin dynamics in the various typical regimes: the pure and doped AF-states (ξ = 0.15, 0.37), the weakly doped (χ = 0.45, 0.51), the heavily doped (χ = 0.69, 0.92) and the overdoped (χ = 1) metallic states. In the insulating state, the hole doping strongly affects the AF-order and yields a strong renormalization of the spin wave velocity. In the metallic state, dynamical AF-correlations remain, but the in-plane correlation length becomes very short (ξ/a ≌ 0.8) as the doping increases. However, the AF-coupling between the two CuO 2 -layers is not affected, except in the overdoped regime. At low temperatures the spin excitation spectrum exhibits an energy gap in any superconducting samples. Its value, E G / kT c ≌ 3.5, becomes much weaker close to the I-M transition. Moreover, a pseudo-gap persists above T c in the heavily doped regime.

J.Y. Henry

Papers

Investigation of the spin dynamics in YBa2Cu3O6+x by inelastic neutron scattering

Evidence for high temperature antiferromagnetic ordering in YBa2Cu3O6

Hall effect and thermoelectric power of an YBa2Cu3O6.8 single crystal

Specific heat of an YBa2Cu3O7 single crystal in fields up to 20 T

Inelastic neutron scattering study of the spin dynamics in the YBa2Cu3O6+χ system