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 study the electronic states of graphite ribbons with edges of two typical shapes, armchair and zigzag, by performing tight binding band calculations, and find that the graphite ribbons show striking contrast in the electronic states depending on the edge shape. In particular, a zigzag ribbon shows a remarkably sharp peak of density of states at the Fermi level, which does not originate from infinite graphite. We find that the singular electronic states arise from the partly flat bands at the Fermi level, whose wave functions are mainly localized on the zigzag edge. We reveal the puzzle for the emergence of the peculiar edge state by deriving the analytic form in the case of semi-infinite graphite with a zigzag edge. Applying the Hubbard model within the mean-field approximation, we discuss the possible magnetic structure in nanometer-scale micrographite.

Peculiar Localized State at Zigzag Graphite Edge

http://nano-bio.ehu.es/files/articles/Gonze_CPC_2009_590.pdf

ABINIT: First-principles approach to material and nanosystem properties

Recent progress in processing and properties of ZnO

To make the transition from the quasi-long-range order in a chain of antiferromagnetically coupled S = 1/2 spins to the true long-range order that occurs in a plane, one can assemble chains to make ladders of increasing width. Surprisingly, this crossover between one and two dimensions is not at all smooth. Ladders with an even number of legs have purely short-range magnetic order and a finite energy gap to all magnetic excitations. Predictions of this ground state have now been verified experimentally. Holes doped into these ladders are predicted to pair and possibly superconduct.

https://science.sciencemag.org/content/sci/271/5249/618.full.pdf

Surprises on the Way from One- to Two-Dimensional Quantum Magnets: The Ladder Materials

A homologous series of cuprates, Srn -1 Cun + 1 O2n, formed by introducing a parallel array of planar defects into the infinite-layer cuprate, SrCuO2, have been reported by Takano et al. In each CuO2 plane line defects consisting of CuO double chains result. An analysis of the electronic properties of such planes demonstrates that the stoichiometric compounds with n = 3, 7, 11,... will be frustrated quantum antiferromagnets and spin liquids. When lightly doped with holes the spin gap will remain and singlet superconductivity should occur on a separate but high temperature scale. This prediction may shed new light on the origin of the separate energy scales for the spin gap and superconductivity in other lightly doped cuprates.

https://iopscience.iop.org/article/10.1209/0295-5075/23/6/011/pdf

Superconductivity, Spin Gaps and Luttinger Liquids in a Class of Cuprates

We investigate the magnetic properties of the Cu-O planes in stoichiometric ${\mathrm{Sr}}_{\mathit{n}\mathrm{\ensuremath{-}}1}$${\mathrm{Cu}}_{\mathit{n}+1}$${\mathrm{O}}_{2\mathit{n}}$ (n=3,5,7, . . .) which consist of CuO double chains periodically intergrown within the ${\mathrm{CuO}}_{2}$ planes. The double chains break up the two-dimensional antiferromagnetic planes into Heisenberg spin ladders with ${\mathit{n}}_{\mathit{r}}$=1/2(n-1) rungs and ${\mathit{n}}_{\mathit{l}}$=1/2(n+1) legs and described by the usual antiferromagnetic coupling J inside each ladder and a weak and frustrated interladder coupling J'. The resulting lattice is a new two-dimensional trellis lattice. We first examine the spin excitation spectra of isolated quasi-one-dimensional Heisenberg ladders which exhibit a gapless spectrum when ${\mathit{n}}_{\mathit{r}}$ is even and ${\mathit{n}}_{\mathit{l}}$ is odd (corresponding to n=5,9, . . .) and a gapped spectrum when ${\mathit{n}}_{\mathit{r}}$ is odd and ${\mathit{n}}_{\mathit{l}}$ is even (corresponding to n=3,7, . . .). We use the bond operator representation of quantum S=1/2 spins in a mean-field treatment with self-energy corrections and obtain a spin gap of \ensuremath{\approxeq}1/2J for the simplest single-rung ladder (n=3), in agreement with numerical estimates. We also present results of the dynamical structure factor S(q,\ensuremath{\omega}). The spin gap decreases considerably on increasing the width of the ladders. For a double ladder with four legs and three rungs (n=7) we obtain a spin gap of only 0.1J. However, a frustrated coupling, such as that of a trellis lattice, introduced between the double ladders leads to an enhancement of the gap. Thus stoichiometric ${\mathrm{Sr}}_{\mathit{n}\mathrm{\ensuremath{-}}1}$${\mathrm{Cu}}_{\mathit{n}+1}$${\mathrm{O}}_{2\mathit{n}}$ compounds with n=3,7,11, . . ., will be frustrated quantum antiferromagnets with a quantum-disordered or spin-liquid ground state.

Spin ladders with spin gaps: A description of a class of cuprates.

The ‘‘rigid‐pseudoion’’ model is applied to intervalley scattering processes in GaAs The intervalley deformation potentials (IDPs) that we obtain at high‐symmetry points are in good agreement with previous calculations We find that the IDPs show a strong dependence on the wave vector of the intervalley phonon, therefore a numerical integration over the Brillouin zone (eg, with the tetrahedron method) is necessary to obtain realistic scattering rates that can be compared with those obtained from experiments We calculate the lifetimes of electrons at the L and X valleys as a function of temperature (L: 22±05 ps; X: 130±20 fs at room temperature) and discuss our results in comparison with recent ultrafast laser experiments and Monte Carlo simulations Finally, the IDPs show an anisotropy that might be important when simulating electrical transport in hot‐electron devices

Microscopic theory of intervalley scattering in GaAs : K dependence of deformation potentials and scattering rates

We calculate the isotope and temperature shifts of the indirect and direct band gaps in natural silicon (M\ifmmode\bar\else\textasciimacron\fi{}=28.09 u), in natural diamond $^{12}\mathrm{C}$ and its isotope $^{13}\mathrm{C}$, in natural germanium (M\ifmmode\bar\else\textasciimacron\fi{}=72.59 u), and the isotope $^{70}\mathrm{Ge}$, and in the isotope mixture $^{75.7}\mathrm{Ge}$, due to the deformation-potential-type electron-phonon interaction (within the pseudopotential-bond-charge-model framework). We compare these results to existing experimental information and to data obtained by us with spectroscopic ellipsometry. We find that there are small, but noticeable shifts of the band gaps between different isotopes (about 13 meV for diamond, 1 meV for germanium). The isotopic influence on the broadenings of the ${\mathit{E}}_{1}$ transition in Ge is also observed.

Isotope and temperature shifts of direct and indirect band gaps in diamond-type semiconductors.

We have performed LDA calculations of structure, phonon frequencies, and the electron-phonon interaction. We find good agreement with available data and estimate: λ=1. Saddlepoints 20 meV below the Fermi level are important.

Sudha Gopalan

Papers

Superconductivity, Spin Gaps and Luttinger Liquids in a Class of Cuprates

Spin ladders with spin gaps: A description of a class of cuprates.

Microscopic theory of intervalley scattering in GaAs : K dependence of deformation potentials and scattering rates

Isotope and temperature shifts of direct and indirect band gaps in diamond-type semiconductors.

Electrons, phonons, and their interaction in YBa2Cu3O7