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.

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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

This article reviews the effort to understand the physics of high temperature superconductors from the point of view of doping a Mott insulator. The basic electronic structure of the 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. We introduce Anderson's idea of the resonating valence bond (RVB) and argue that it gives a qualitative account of the data. The importance of phase fluctuation is discussed, leading to a theory of the transition temperature which is driven by phase fluctuation and thermal excitation of quasiparticles. We then describe the numerical method of projected wavefunction which turns out to be a very useful technique to implement 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-J model, with the goal of putting the RVB idea on a more formal footing. The slave-boson is introduced to enforce the constraint of no double occupation. The implementation of the local constraint leads naturally to gauge theories. We give a rather thorough discussion of the role of gauge theory in describing the spin liquid phase of the undoped Mott insulator. We next describe the extension of the SU(2) formulation to nonzero doping. We show that inclusion of gauge fluctuation provides a reasonable description of the pseudogap phase.

Doping a Mott Insulator: Physics of High Temperature Superconductivity

Coupling between electrons and phonons (lattice vibrations) drives the formation of the electron pairs responsible for conventional superconductivity. The lack of direct evidence for electron-phonon coupling in the electron dynamics of the high-transition-temperature superconductors has driven an intensive search for an alternative mechanism. A coupling of an electron with a phonon would result in an abrupt change of its velocity and scattering rate near the phonon energy. Here we use angle-resolved photoemission spectroscopy to probe electron dynamics-velocity and scattering rate-for three different families of copper oxide superconductors. We see in all of these materials an abrupt change of electron velocity at 50-80 meV, which we cannot explain by any known process other than to invoke coupling with the phonons associated with the movement of the oxygen atoms. This suggests that electron-phonon coupling strongly influences the electron dynamics in the high-temperature superconductors, and must therefore be included in any microscopic theory of superconductivity.

Evidence for ubiquitous strong electron-phonon coupling in high-temperature superconductors.

We review recent developments in our understanding of how impurities influence the electronic states in the bulk of superconductors. Our focus is on the quasi-localized states in the vicinity of impurity sites in conventional and unconventional superconductors and our goal is to provide a unified framework for their description. The non-magnetic impurity resonances in unconventional superconductors are directly related to the Yu-Shiba-Rusinov states around magnetic impurities in conventional s-wave systems. We review the physics behind these states, including quantum phase transition between screened and unscreened impurity, and emphasize recent work on d-wave superconductors. The bound states are most spectacularly seen in scanning tunneling spectroscopy measurements on high-$T_c$ cuprates, which we describe in detail. We also discuss very recent progress on the states coupled to impurity sites which have their own dynamics, and impurity resonances in the presence of an order competing with superconductivity. Last part of the review is devoted to influence of local deviations of the impurity concentration from its average value on the density of states in s-wave superconductors. We review how these fluctuations affect the density of states and show that s-wave superconductors are, strictly speaking, gapless in the presence of an arbitrarily small concentration of magnetic impurities.

Impurity-induced states in conventional and unconventional superconductors

The photoemission line shape near (pi, 0) in Bi(2)Sr(2)CaCu(2)O(8+delta) below T(c) is characterized by a sharp peak, followed at higher energy by a dip and hump. We study the evolution of this line shape as a function of momentum, temperature, and doping. We find the hump scales with the peak and persists above T(c) in the pseudogap state. We present strong evidence that the peak-dip-hump structure arises from the interaction of electrons with a collective mode of wave vector (pi, pi). The inferred mode energy and its doping dependence agree well with a magnetic resonance observed by neutron scattering.

/pdf/electronic-spectra-and-their-relation-to-the-p-p-collective-8hdh4narqz.pdf

Electronic Spectra and Their Relation to the ( π,π) Collective Mode in High- Tc Superconductors

Preparation by dc single target sputtering and characterization of superconducting BiSrCaCuO films

Angular dependence of the magneto resistance and of the critical current up to 20 tesla in the bismuth 2212 phase shows remarkable anisotropic behavior. Samples are highly c-axis oriented thin films. The field dependence of the critical current is shown to be essentially dominated by the component of the magnetic field perpendicular to the CuO 2 layers.

Anisotropy of superconducting properties of Bi-Sr-Ca-Cu-O thin films

The scaling behavior of the hysteretic magnetization (or associated with it the critical current density) of high-quality epitaxial Bi 2 Sr 2 CaCu 2 O 8 thin films was studied in the temperature range 5–45 K and over three decades of the magnetic field H (50 G− 50 kG). Above T 0 ≈ 25K the magnetic-field dependence of the critical current density can be scaled in the form j c ( T , H ) = j c ( T ) g ( H / H * ), while below T 0 and above H 0 ≈ 2kG the current density can be represented as j c ( T , H ) = β( H / H * ), where j c ( T ) is the temperature dependence of the critical current in zero magnetic field, β is a constant, and f ( h )and g ( h ) are some scaling functions of the parameter H * . The latter can be associated with the irreversibility field. Below both T 0 and H 0 the current density only weakly depends on the magnetic field. The results can be largely explained by the influence of the thermal fluctuations.

Scaling behavior of the irreversible magnetization in epitaxial Bi2Sr2CaCu2O8 thin films

We report on the preparation of (Bi- 1−x Pb x )-Sr-Ca-Cu-O thin films with T c up to 108K. Lead doping was used to promote the 110 K phase. The highest T c were obtained for deposits with x~15%–20% after 14h (8000A thick film) or 11h (3000A) annealing at 855 °C–860 °C. X-ray diffraction studies and SEM examinations show that films of the 2223 phase are highly c-axis oriented like films of the 2212 phase.

H. Raffy

Papers

Electronic Spectra and Their Relation to the ( π,π) Collective Mode in High- Tc Superconductors

Preparation by dc single target sputtering and characterization of superconducting BiSrCaCuO films

Anisotropy of superconducting properties of Bi-Sr-Ca-Cu-O thin films

Scaling behavior of the irreversible magnetization in epitaxial Bi2Sr2CaCu2O8 thin films

GROWTH OF THE 110 K SUPERCONDUCTING PHASE AND CHARACTERIZATION OF Pb-doped Bi-Sr-Ca-Cu-O THIN FILMS PREPARED BY SPUTTERING