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

IT is well known that BCS mean-field theory is remarkably successful in describing conventional superconductors. A central concept of BCS theory is the energy gap in the electronic excitation spectrum below the superconducting transition temperature, Tc. The gap also serves as the order parameter: quite generally, long-range phase coherence and a non-zero gap go hand-in-hand1. But in underdoped high-Tc superconductors there is considerable evidence that a pseudogap (a suppression of spectral weight) is already formed in the normal state above Tc—first, from studies of the spin excitation spectrum2–5,24, which measure a 'spin gap', and later from a variety of other probes6–10. Here we present a study of underdoped Bi2Sr2CaCu2O8+δ (Bi2212) using angle-resolved photoemission spectroscopy (ARPES), which directly measures the momentum-resolved electron excitation spectrum of the CuO2 planes. We find that a pseudogap with d-wave symmetry opens up in the normal state below a temperature T* > Tc, and develops into the d-wave superconducting gap once phase coherence is established below Tc.

Spectroscopic evidence for a pseudogap in the normal state of underdoped high- T c superconductors

Recent studies on high-Tc superconductors have aroused new interest in tunnelling effects in unconventional superconductors. Unlike in conventional s-wave superconductors, the d-wave pairing state in these materials has an internal phase of the pair potential. The internal phase as a function of the wavevector of the Cooper pairs has a large influence on the electric properties of tunnelling junctions. Important effects of the internal phase on the Josephson current were first predicted theoretically. The idea has been established through several experiments using high-Tc Josephson junctions, which detect ?-phase shift between the a- and b-axis directions and fractional flux quanta. These results give convincing evidence for d-wave symmetry in high-Tc superconductors. In addition, the existence of new interference effects in the quasiparticle states near surfaces and boundaries has been suggested through theoretical predictions. Experimentally, a large number of tunnelling spectroscopy data showed zero-bias conductance peaks (ZBCPs), the origin of which cannot be explained in terms of the classical concept that a tunnelling conductance spectrum is a phase-insensitive probe of the electronic states. It is clarified theoretically that the observed ZBCPs reflect the formation of zero-energy states on the surface due to the ?-phase shift of internal phase in the d-wave pairing symmetry. The formulation developed for tunnelling spectroscopy suggests that tunnelling spectroscopy is essentially phase sensitive. In addition, the formation of the bound states has been shown to have a serious influence on the electrical properties of Josephson junctions. Several anomalous properties including strong enhancement of the Josephson current in the low-temperature region have been predicted theoretically. In this report, recent developments in tunnelling effects on surface bound states in unconventional superconductors are reviewed.

https://iopscience.iop.org/article/10.1088/0034-4885/63/10/202/pdf

Tunnelling effects on surface bound states in unconventional superconductors

A wide range of materials, like d-wave superconductors, graphene, and topological insulators, share a fundamental similarity: their low-energy fermionic excitations behave as massless Dirac particles rather than fermions obeying the usual Schrodinger Hamiltonian This emergent behavior of Dirac fermions in condensed matter systems defines the unifying framework for a class of materials we call "Dirac materials'' In order to establish this class of materials, we illustrate how Dirac fermions emerge in multiple entirely different condensed matter systems and we discuss how Dirac fermions have been identified experimentally using electron spectroscopy techniques (angle-resolved photoemission spectroscopy and scanning tunneling spectroscopy) As a consequence of their common low-energy excitations, this diverse set of materials shares a significant number of universal properties in the low-energy (infrared) limit We review these common properties including nodal points in the excitation spectrum, density of states, specific heat, transport, thermodynamic properties, impurity resonances, and magnetic field responses, as well as discuss many-body interaction effects We further review how the emergence of Dirac excitations is controlled by specific symmetries of the material, such as time-reversal, gauge, and spin-orbit symmetries, and how by breaking these symmetries a finite Dirac mass is generated We give examples of how the interaction of Dirac fermions with their distinct real material background leads to rich novel physics with common fingerprints such as the suppression of back scattering and impurity-induced resonant states

Dirac materials

The case for dx2 − y2 pairing in the cuprate superconductors

Superconducting gap anisotropy at least an order of magnitude larger than that of the conventional superconductors has been observed in the a-b plane of ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8+\mathrm{\ensuremath{\delta}}}$ in angle-resolved photoemission spectroscopy. For samples with ${\mathit{T}}_{\mathit{c}}$ of 88 K, the gap size reaches a maximum of approximately 20 meV along the Cu-O bond direction, and a minimum of much smaller or vanishing magnitude 45\ifmmode^\circ\else\textdegree\fi{} away. The experimental data are discussed within the context of various theoretical models. In particular, a detailed comparison with what is expected from a superconductor with a ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$ order parameter is carried out, yielding a consistent picture.

A. J. Arko

Papers

Anomalously large gap anisotropy in the a - b plane of Bi 2 Sr 2 CaCu 2 O 8 + δ