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

The discovery of high-temperature superconductivity in the copper oxides in 1986 triggered a huge amount of innovative scientific inquiry. In the almost three decades since, much has been learned about the novel forms of quantum matter that are exhibited in these strongly correlated electron systems. A qualitative understanding of the nature of the superconducting state itself has been achieved. However, unresolved issues include the astonishing complexity of the phase diagram, the unprecedented prominence of various forms of collective fluctuations, and the simplicity and insensitivity to material details of the 'normal' state at elevated temperatures.

/pdf/from-quantum-matter-to-high-temperature-superconductivity-in-3vq16xcye2.pdf

From quantum matter to high-temperature superconductivity in copper oxides

A superconductor is a material that can conduct electricity without resistance below a superconducting transition temperature, Tc. The highest Tc that has been achieved to date is in the copper oxide system: 133 kelvin at ambient pressure and 164 kelvin at high pressures. As the nature of superconductivity in these materials is still not fully understood (they are not conventional superconductors), the prospects for achieving still higher transition temperatures by this route are not clear. In contrast, the Bardeen-Cooper-Schrieffer theory of conventional superconductivity gives a guide for achieving high Tc with no theoretical upper bound--all that is needed is a favourable combination of high-frequency phonons, strong electron-phonon coupling, and a high density of states. These conditions can in principle be fulfilled for metallic hydrogen and covalent compounds dominated by hydrogen, as hydrogen atoms provide the necessary high-frequency phonon modes as well as the strong electron-phonon coupling. Numerous calculations support this idea and have predicted transition temperatures in the range 50-235 kelvin for many hydrides, but only a moderate Tc of 17 kelvin has been observed experimentally. Here we investigate sulfur hydride, where a Tc of 80 kelvin has been predicted. We find that this system transforms to a metal at a pressure of approximately 90 gigapascals. On cooling, we see signatures of superconductivity: a sharp drop of the resistivity to zero and a decrease of the transition temperature with magnetic field, with magnetic susceptibility measurements confirming a Tc of 203 kelvin. Moreover, a pronounced isotope shift of Tc in sulfur deuteride is suggestive of an electron-phonon mechanism of superconductivity that is consistent with the Bardeen-Cooper-Schrieffer scenario. We argue that the phase responsible for high-Tc superconductivity in this system is likely to be H3S, formed from H2S by decomposition under pressure. These findings raise hope for the prospects for achieving room-temperature superconductivity in other hydrogen-based materials.

Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride system

A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States

The recently discovered layered rare-earth metal oxypnictides have reinvigorated research into high-temperature superconductivity. The first of these, found only a few months ago, had a transition temperature of 26 K. A recent paper in Nature reported an iron–arsenic-based material superconducting at 43 K with the application of pressure. Previously only copper oxides superconductors had beaten the 40 K barrier. Now Chen et al. report bulk superconductivity in the samarium–arsenide oxide SmFeAsO1−xFx with a transition temperature of 43 K without this pressure. A report on the discovery of bulk superconductivity in samarium-arsenide oxides SmFeAsO1−xFx with a transition temperature as high as 43 K. Since the discovery of high-transition-temperature (high-Tc) superconductivity in layered copper oxides, extensive effort has been devoted to exploring the origins of this phenomenon. A Tc higher than 40 K (about the theoretical maximum predicted from Bardeen–Cooper–Schrieffer theory1), however, has been obtained only in the copper oxide superconductors. The highest reported value for non-copper-oxide bulk superconductivity is Tc = 39 K in MgB2 (ref. 2). The layered rare-earth metal oxypnictides LnOFeAs (where Ln is La–Nd, Sm and Gd) are now attracting attention following the discovery of superconductivity at 26 K in the iron-based LaO1-xF x FeAs (ref. 3). Here we report the discovery of bulk superconductivity in the related compound SmFeAsO1-xF x , which has a ZrCuSiAs-type structure. Resistivity and magnetization measurements reveal a transition temperature as high as 43 K. This provides a new material base for studying the origin of high-temperature superconductivity.

Superconductivity at 43 K in SmFeAsO1-xFx.

In the light of the tremendous progress that has been made in raising the transition temperature of the copper oxide superconductors (for a review, see ref. 1), it is natural to wonder how high the transition temperature, Tc, can be pushed in other classes of materials. At present, the highest reported values of Tc for non-copper-oxide bulk superconductivity are 33 K in electron-doped CsxRbyC60 (ref. 2), and 30 K in Ba1-xKxBiO3 (ref. 3). (Hole-doped C60 was recently found4 to be superconducting with a Tc as high as 52 K, although the nature of the experiment meant that the supercurrents were confined to the surface of the C60 crystal, rather than probing the bulk.) Here we report the discovery of bulk superconductivity in magnesium diboride, MgB2. Magnetization and resistivity measurements establish a transition temperature of 39 K, which we believe to be the highest yet determined for a non-copper-oxide bulk superconductor.

Superconductivity at 39 K in magnesium diboride

Superconductivity at 39 K in Magnesium Diboride.

We report the results of nuclear spin–lattice relaxation time, T 1 of 11 B in MgB 2 , Al-doped MgB 2 and NbB 2 . A T 1 T =constant behavior was observed in the normal state, indicating the absence of strong magnetic correlation. In the superconducting (SC) state, 1/ T 1 shows a tiny coherence peak just below T c and decreases exponentially, demonstrating an s-wave superconductivity. The magnitude of SC gap is estimated as 2 Δ / k B T c ∼5, which is quite larger than the weak-coupling value in the BCS theory, 2 Δ / k B T c =3.5. This rules out a possibility for the multiple SC gaps that was suggested in many literatures. The anisotropy in the upper critical field was also corroborated by the T 1 measurement on a bulk polycrystalline sample. In NbB 2 with a low value of T c =5 K, the T 1 measurement revealed the distinct coherence peak just below T c , followed by an exponential decrease with a magnitude of SC gap 2 Δ / k B T c =3.1. These data are consistent with the weak-coupling BCS theory. As Al 3+ is substituted for Mg 2+ , 1/ T 1 T , which is proportional to the square of the density of states at the Fermi level N ( E F ), decreases. The variation in T c against the relative changes in N ( E F ) deduced from 1/ T 1 T is well fitted in terms of the McMillan equation by assuming a characteristic phonon frequency ω ∼ 700 K and an electron–phonon coupling constant λ ∼ 0.87. Thus obtained values are in good agreement with the values suggested by the theoretical works. The high- T c superconductivity in MgB 2 is shown to occur through the strong coupling with high frequency phonons.

Evidence for strong-coupling s-wave superconductivity in MgB2: 11B-NMR study of MgB2 and the related materials

We report ${}^{11}\mathrm{B}$ NMR studies that address the underlying two superconducting (SC) gaps model and a possible mechanism for interpreting a high SC transition temperature ${(T}_{c})$ of $\ensuremath{\sim}40 \mathrm{K}$ in a recently discovered ${\mathrm{MgB}}_{2}$ We reported in a previous paper [Phys Rev Lett $87,$ 127001 (2001)] that the results of the nuclear-spin-lattice relaxation rate, ${1/T}_{1}$ in the SC state revealed the existence of a single large SC gap with $2\ensuremath{\Delta}{/k}_{B}{T}_{c}\ensuremath{\sim}5$ This conclusion is corroborated by the calculation that any two-gap models cannot account for the experimental results In Al-doped ${\mathrm{MgB}}_{2},$ the result of ${1/T}_{1}$ in the SC state revealed that a size in the SC gap is not changed by substituting Al for Mg The reduction in ${T}_{c}$ by Al doping is shown to be due to the decrease of the density of states ${N(E}_{F})$ at the Fermi level According to the McMillan equation, an experimental relation between ${T}_{c}$ and the relative change in ${N(E}_{F})$ allowed us to estimate a characteristic phonon frequency $\ensuremath{\omega}\ensuremath{\sim}700 \mathrm{K}$ and an electron-phonon coupling constant $\ensuremath{\lambda}\ensuremath{\sim}087$ These results suggest that the high-${T}_{c}$ superconductivity in ${\mathrm{MgB}}_{2}$ is mediated by the strong electron-phonon coupling with high-frequency phonons

http://arxiv.org/pdf/cond-mat/0201578.pdf

Evidence for high-frequency phonon mediated S -wave superconductivity: 11 B NMR study of Al-doped MgB 2

A novel intermetallic compound superconductor characterized in that it is an intermetallic compound consisting of magnesium (Mg) and boron (B), is represented by the chemical empirical formula Mg1B2, has a hexagonal AlB2 type crystalline structure, and has a superconductivity transition temperature (Tc) of 39K; an alloy superconductor which contains the intermetallic compound, is excellent in malleability and ductility and has a superconductivity transition temperature (Tc) of 39K; and a method for preparing the alloy superconductor which comprises mixing a raw material powder containing Mg and a raw material powder containing B, and subjecting the resultant mixture to, for example, pressure molding with heating The alloy superconductor exhibits a high superconductivity transition temperature and also excellent malleability and ductility The preparation method allows the preparation of the alloy with good reproducibility and at a low production cost

Norimasa Nakagawa

Papers

Superconductivity at 39 K in magnesium diboride

Superconductivity at 39 K in Magnesium Diboride.

Evidence for strong-coupling s-wave superconductivity in MgB2: 11B-NMR study of MgB2 and the related materials

Evidence for high-frequency phonon mediated S -wave superconductivity: 11 B NMR study of Al-doped MgB 2

Intermetallic compound superconductor and alloy superconductor, and method for their preparation