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

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

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.

A set of highly sensitive cavity perturbation techniques, quite different from the ones most commonly used to measure thin films, has been developed for measuring the surface impedance of small crystals of high-${\mathit{T}}_{\mathit{c}}$ superconductors. Since the results of these studies differ markedly from most surface-impedance measurements of thin films of high-${\mathit{T}}_{\mathit{c}}$ superconductors, we describe the techniques in detail, including recent improvements. Measurements of the surface resistance and penetration depth of a twin-free crystal of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{6.95}$ indicate two striking differences from the surface impedance of conventional superconductors. Both quantities exhibit linear temperature dependence at low temperatures rather than the exponentially activated behavior of an s-wave BCS superconductor. Also, a broad peak in the temperature dependence of the surface resistance indicates that the large transport scattering rate in the normal state collapses below ${\mathit{T}}_{\mathit{c}}$ as the holes condense into the superconducting condensate. Systematic studies of the influence of Zn and Ni impurities on the surface impedance indicate that these properties are very sensitive to defects and this sensitivity provides further insight into the pairing state. Although both types of impurities provide strong elastic scattering that limits the collapse of the scattering rate and suppresses the peak in the surface resistance, only Zn has a strong pair-breaking effect. As little as 0.31% Zn substitution makes ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{6.95}$ gapless, but Ni, which is a magnetic impurity has no such pair-breaking effect up to 0.75% substitution. This difference is the opposite of that expected for an s-wave BCS superconductor.

Comparison of the influence of Ni and Zn impurities on the electromagnetic properties of YBa2Cu3O6.95.

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.

/pdf/microwave-determination-of-the-quasiparticle-scattering-time-21k85xjoi3.pdf

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

The temperature dependence of the surface resistance ${R}_{s}$, and the penetration depth $\ensuremath{\lambda}$ has been measured in both $a$ and $b$ directions in ${\mathrm{Yba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{6.95}$. The overall temperature dependences are similar and show a linear behavior at low $T$. This argues against the chains playing a direct role in the unconventional behavior of the surface impedance. The residual ${R}_{s}$ of these twin-free crystals is very small, implying a residual conductivity of the order of the minimum value predicted by Lee Phys. Rev. Lett. 71 1837 1993 for a $d$-wave superconductor.

Kuan Zhang

Papers

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

Comparison of the influence of Ni and Zn impurities on the electromagnetic properties of YBa2Cu3O6.95.

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

Measurement of the ab plane anisotropy of microwave surface impedance of untwinned YBa2Cu3O6.95 single crystals.

The microwave surface impedance of YBa2Cu3O7 − δ