There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This article reviews the physics of high-temperature superconductors from the point of view of the doping of a Mott insulator. The basic electronic structure of cuprates is reviewed, emphasizing the physics of strong correlation and establishing the model of a doped Mott insulator as a starting point. A variety of experiments are discussed, focusing on the region of the phase diagram close to the Mott insulator (the underdoped region) where the behavior is most anomalous. The normal state in this region exhibits pseudogap phenomenon. In contrast, the quasiparticles in the superconducting state are well defined and behave according to theory. This review introduces Anderson's idea of the resonating valence bond and argues that it gives a qualitative account of the data. The importance of phase fluctuations is discussed, leading to a theory of the transition temperature, which is driven by phase fluctuations and the thermal excitation of quasiparticles. However, an argument is made that phase fluctuations can only explain pseudogap phenomenology over a limited temperature range, and some additional physics is needed to explain the onset of singlet formation at very high temperatures. A description of the numerical method of the projected wave function is presented, which turns out to be a very useful technique for implementing the strong correlation constraint and leads to a number of predictions which are in agreement with experiments. The remainder of the paper deals with an analytic treatment of the $t\text{\ensuremath{-}}J$ model, with the goal of putting the resonating valence bond idea on a more formal footing. The slave boson is introduced to enforce the constraint againt double occupation and it is shown that the implementation of this local constraint leads naturally to gauge theories. This review follows the historical order by first examining the U(1) formulation of the gauge theory. Some inadequacies of this formulation for underdoping are discussed, leading to the SU(2) formulation. Here follows a rather thorough discussion of the role of gauge theory in describing the spin-liquid phase of the undoped Mott insulator. The difference between the high-energy gauge group in the formulation of the problem versus the low-energy gauge group, which is an emergent phenomenon, is emphasized. Several possible routes to deconfinement based on different emergent gauge groups are discussed, which leads to the physics of fractionalization and spin-charge separation. Next the extension of the SU(2) formulation to nonzero doping is described with a focus on a part of the mean-field phase diagram called the staggered flux liquid phase. It will be shown that inclusion of the gauge fluctuation provides a reasonable description of the pseudogap phase. It is emphasized that $d$-wave superconductivity can be considered as evolving from a stable U(1) spin liquid. These ideas are applied to the high-${T}_{c}$ cuprates, and their implications for the vortex structure and the phase diagram are discussed. A possible test of the topological structure of the pseudogap phase is described.

/pdf/doping-a-mott-insulator-physics-of-high-temperature-55r49vtp31.pdf

Doping a Mott insulator: Physics of high-temperature superconductivity

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 have discovered a new high-Tc oxide superconductor of the Bi-Sr-Ca-Cu-O system without any rare earth element. The oxide BiSrCaCu2Ox has Tc of about 105 K, higher than that of YBa2Cu3O7 by more than 10 K. In this oxide, the coexistence of Sr and Ca is necessary to obtain high Tc.

https://iopscience.iop.org/article/10.1143/JJAP.27.L209/pdf

A New High-TcOxide Superconductor without a Rare Earth Element

Fully human antibodies against a specific antigen can be prepared by administering the antigen to a transgenic animal which has been modified to produce such antibodies in response to antigenic challenge, but whose endogenous loci have been disabled. Various subsequent manipulations can be performed to obtain either antibodies per se or analogs thereof.

Human antibodies derived from immunized xenomice

The activity and diffusivity of oxygen in a liquid Yb1Ba2Cu3 high temperature superconducting precursor alloy have been measured by modified coulometric titration method in a temperature range from 913 to 957 °C. The standard Gibbs formation energies and the diffusivity of oxygen in liquid Yb1Ba2Cu3 for 1/2O2 (1 atm)→O (1 at. %) are determined to be ΔG=−655.20+0.335T(K) (±1.5) kJ/mol and D=1.8×10−2 exp(−48 100/RT) (cm2/s) where R=8.314 J/deg×mol. Despite very strong bonding of oxygen to the liquid alloys, the diffusion coefficient of oxygen is relatively high in the order of 10−4 cm2/s. The solubility of oxygen in the liquid alloy is low, of about 0.0145 and 0.017 at. % at 913 and 935 °C, respectively.

Activity and diffusivity of oxygen in a liquid Yb1Ba2Cu3 high temperature superconducting precursor alloy

The persistent photoinduced changes in the critical temperature TC and the normal state conductivity of (Y0.5Ca0.5)Ba2Cu3Oδ thin films are studied. Previously such effects have been observed only in underdoped YBa2Cu3Oδ or YSrxBa2−xCu3Oδ, which always lead to the enhancement of both TC and conductivity. The current system can be doped from the underdoped regime to the overdoped regime by increasing its oxygen content. The photoinduced TC reduction in the overdoped films is observed. The simultaneous enhancement of conductivity is consistent with the interpretation that photoillumination always increases hole concentration in the “123” systems.

Photoinduced hole-doping effect in (Y0.5Ca0.5)Ba2Cu3Oδ films

A stable and reproducible superconductivity transition between 80 and 93 K has been unambiguously observed both resistively and magnetically in a new Y-Ba-Cu-O compound system at ambient pressure. An estimated upper critical field H c2(0) between 80 and 180 T was obtained.

Superconductivity at 93 K in a New Mixed-Phase Y-Ba-Cu-O Compound System at Ambient Pressure

Synthesis of YBa2Cu3O7 and YBa2Cu4O8 superconductors via carbonate coprecipitation

We have studied the Raman spectra of superconducting FeSe and non-superconducting Cu-doped FeSe crystals at different temperatures. The spectral range covers the phonon modes at low frequency regime to electronic Raman scattering at high frequency regime, up to 2000 cm−1. A hardening in frequency of B1g mode, which is related to the spin-phonon coupling is observed. At high frequency region, our results on superconducting FeSe crystal show that the dzx and dyz orbitals of Fe split at ∼130 K and then become closer to achieve balance as temperature decreases. This result indicates that a modification of d-orbital electron state of iron happens at temperature much higher than the structural transition, implicating a precursor order in iron-based superconductor. In comparison with non-superconducting Cu0.03Fe0.97Se crystal, our observations suggest that the orbital modification could be an important clue for understanding the mechanism of superconductivity in iron-based superconductors.

Maw-Kuen Wu

Papers

Activity and diffusivity of oxygen in a liquid Yb1Ba2Cu3 high temperature superconducting precursor alloy

Photoinduced hole-doping effect in (Y0.5Ca0.5)Ba2Cu3Oδ films

Superconductivity at 93 K in a New Mixed-Phase Y-Ba-Cu-O Compound System at Ambient Pressure

Synthesis of YBa2Cu3O7 and YBa2Cu4O8 superconductors via carbonate coprecipitation

Observation of iron d-orbitals modifications in superconducting FeSe by Raman spectra study