The last decade witnessed significant progress in angle-resolved photoemission spectroscopy (ARPES) and its applications. Today, ARPES experiments with 2-meV energy resolution and $0.2\ifmmode^\circ\else\textdegree\fi{}$ angular resolution are a reality even for photoemission on solids. These technological advances and the improved sample quality have enabled ARPES to emerge as a leading tool in the investigation of the high-${T}_{c}$ superconductors. This paper reviews the most recent ARPES results on the cuprate superconductors and their insulating parent and sister compounds, with the purpose of providing an updated summary of the extensive literature. The low-energy excitations are discussed with emphasis on some of the most relevant issues, such as the Fermi surface and remnant Fermi surface, the superconducting gap, the pseudogap and $d$-wave-like dispersion, evidence of electronic inhomogeneity and nanoscale phase separation, the emergence of coherent quasiparticles through the superconducting transition, and many-body effects in the one-particle spectral function due to the interaction of the charge with magnetic and/or lattice degrees of freedom. Given the dynamic nature of the field, we chose to focus mainly on reviewing the experimental data, as on the experimental side a general consensus has been reached, whereas interpretations and related theoretical models can vary significantly. The first part of the paper introduces photoemission spectroscopy in the context of strongly interacting systems, along with an update on the state-of-the-art instrumentation. The second part provides an overview of the scientific issues relevant to the investigation of the low-energy electronic structure by ARPES. The rest of the paper is devoted to the experimental results from the cuprates, and the discussion is organized along conceptual lines: normal-state electronic structure, interlayer interaction, superconducting gap, coherent superconducting peak, pseudogap, electron self-energy, and collective modes. Within each topic, ARPES data from the various copper oxides are presented.

https://arxiv.org/pdf/cond-mat/0208504.pdf

Angle-resolved photoemission studies of the cuprate 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.

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The pseudogap in high-temperature superconductors: an experimental survey

This review presents a summary and evaluation of the experimental properties of unconventional superconductivity in ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ as they were known in the spring of 2002. At the same time, the paper is intended to be useful as an introduction to the physics of spin-triplet superconductivity. First, the authors show how the normal-state properties of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ are quantitatively described in terms of a quasi-two-dimensional Fermi liquid. Then they summarize its phenomenological superconducting parameters in the framework of the Ginzburg-Landau model, and discuss the existing evidence for spin-triplet pairing. After a brief introduction to the vector order parameter, they examine the most likely symmetry of the triplet state. The structure of the superconducting energy gap is discussed, as is the effect of symmetry-breaking magnetic fields on the phase diagram. The article concludes with a discussion of some outstanding issues and desirable future work. Appendixes on additional details of the normal state, difficulty in observing the bulk Fermi surface by angle-resolved photoemission, and the enhancement of superconducting transition temperature in a two-phase ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}\ensuremath{-}\mathrm{Ru}$ system are included.

The superconductivity of Sr 2 RuO 4 and the physics of spin-triplet pairing

We review recent developments in our understanding of how impurities influence the electronic states in the bulk of superconductors. Our focus is on the quasi-localized states in the vicinity of impurity sites in conventional and unconventional superconductors and our goal is to provide a unified framework for their description. The non-magnetic impurity resonances in unconventional superconductors are directly related to the Yu-Shiba-Rusinov states around magnetic impurities in conventional s-wave systems. We review the physics behind these states, including quantum phase transition between screened and unscreened impurity, and emphasize recent work on d-wave superconductors. The bound states are most spectacularly seen in scanning tunneling spectroscopy measurements on high-$T_c$ cuprates, which we describe in detail. We also discuss very recent progress on the states coupled to impurity sites which have their own dynamics, and impurity resonances in the presence of an order competing with superconductivity. Last part of the review is devoted to influence of local deviations of the impurity concentration from its average value on the density of states in s-wave superconductors. We review how these fluctuations affect the density of states and show that s-wave superconductors are, strictly speaking, gapless in the presence of an arbitrarily small concentration of magnetic impurities.

Impurity-induced states in conventional and unconventional 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

A miniature superconducting resonator operating at 1.3 K and 900 MHz has been used to measure the change in λ(T) from 1.3 K to T c in very high quality single crystals of YBa 2 Cu 3 O 6.95 . The data, which have a resolution of 1-2 A, show a strong linear term extending from approximately 3 to 25 K. We believe the strong linear dependence to be characteristic of the pure system and that its apparent absence in thin films and some crystals is due to the presence of defects

Precision measurements of the temperature dependence of lambda in YBa2Cu3O6.95: Strong evidence for nodes in the gap function.

We report microwave surface resistance (Rs) measurements on two very-high-quality YBa2Cu3O6.95 crystals which exhibit extremely low residual loss at 1.2 K (2-6 μΩ at 2 GHz), a broad, reproducible peak at around 38 K, and a rapid increase in loss, by 4 orders of magnitude, between 80 and 93 K. These data provide one ingredient in the determination of the temperature dependence of the real part of the microwave conductivity, σ1(T), and of the quasiparticle scattering time. The other necessary ingredient is an accurate knowledge of the magnitude and temperature dependence of the London penetration depth, λ(T). This is derived from published data, from microwave data of Anlage, Langley, and co-workers and from, high-quality μSR data. We infer, from a careful analysis of all available data, that λ2(0)/λ2(T) is well approximated by the simple function 1-t2, where t=T/Tc, and that the low-temperature data are incompatible with the existence of an s-wave, BCS-like gap. Combining the Rs and λ(T) data, we find that σ1(T), has a broad peak around 32 K with a value about 20 times that at Tc. Using a generalized two-fluid model, we extract the temperature dependence of the quasiparticle scattering rate which follows an exponential law, exp(T/T0), where T0≊12 K, for T between 15 and 84 K. Such a temperature dependence has previously been observed in measurements of the nuclear spin-lattice relaxation rate. Both the uncertainties in our analysis and the implications for the mechanism of high-temperature superconductivity are discussed.

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Microwave determination of the quasiparticle scattering time in YBa2Cu3O6.95.

There has long been a discrepancy between microwave conductivity measurements in high temperature superconductors and the conductivity spectrum expected in the simplest models for impurity scattering in a d-wave superconductor. Here we present a new type of broadband measurement of microwave surface resistance that finally shows some of the spectral features expected for a d x 2- y 2 pairing state. Cusp-shaped conductivity spectra, consistent with weak impurity scattering of nodal quasiparticles, were obtained in the 0.6-21 GHz frequency range in highly ordered crystals of YBa 2 CU 3 O 6 . 5 0 and YBa 2 Cu 3 O 6 . 9 9 .

http://arxiv.org/pdf/cond-mat/0111353.pdf

Observation of weak-limit quasiparticle scattering via broadband microwave spectroscopy of a d-wave superconductor.

A cavity perturbation technique using split‐ring resonators has been developed for measuring the surface resistance of metals in the frequency range 0.3–5.0 GHz. The system is designed particularly for measurements of films and crystals of high‐Tc oxide superconductors. The small size of split‐ring resonators in this frequency range makes them useful for measuring crystals with areas as small as 0.1 mm2. The measurement geometry is favorable for the study of films because the sample screens its substrate from the microwave fields. The resonator temperature can be kept fixed at 4.2 or 1.2 K for sample temperatures as high as 120 K and this thermal isolation from the sample allows the use of a superconducting split‐ring resonator. An unloaded Q of 1.2×106 has been achieved with a superconducting resonator at 1.78 GHz and this makes it sensitive enough to detect surface resistances of the order of a few μΩ. This resonator has been used to measure the surface resistance (25 μΩ/⧠) of a 1‐mm2 crystal of Bi2Sr2CaCu2O8.

Split-ring resonators for measuring microwave surface resistance of oxide superconductors

A novel low-temperature bolometric method has been devised and implemented for high-precision measurements of the microwave surface resistance of small single-crystal platelet samples having very low absorption, as a continuous function of frequency. The key to the success of this nonresonant method is the in situ use of a normal metal reference sample that calibrates the absolute rf field strength. The sample temperature can be controlled independently of the 1.2 K liquid-helium bath, allowing for measurements of the temperature evolution of the absorption. However, the sensitivity of the instrument decreases at higher temperatures, placing a limit on the useful temperature range. Using this method, the minimum detectable power at 1.3 K is 1.5 pW, corresponding to a surface resistance sensitivity of ≈1 μΩ for a typical 1 mm×1 mm platelet sample.

D. C. Morgan

Papers

Precision measurements of the temperature dependence of lambda in YBa2Cu3O6.95: Strong evidence for nodes in the gap function.

Microwave determination of the quasiparticle scattering time in YBa2Cu3O6.95.

Observation of weak-limit quasiparticle scattering via broadband microwave spectroscopy of a d-wave superconductor.

Split-ring resonators for measuring microwave surface resistance of oxide superconductors

Bolometric technique for high-resolution broadband microwave spectroscopy of ultra-low-loss samples