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

Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

A new approach to correlated Fermi systems such as the Hubbard model, the periodic Anderson model etc. is discussed, which makes use of the limit of high spatial dimensions. This limit — which is wellknown in the case of classical as well as localized quantum spin models — is found to be very helpful also in the case of quantum mechanical models with itinerant degrees of freedom. Many investigations, which are prohibitively difficult in lower dimensions, become tractable in this limit. In particular, essential features of systems in d = 3, and even lower dimensions, are very well described by the results in d = ∞ or expansions around this limit. A brief review of the state-of-the-art is presented.

Correlated lattice fermions in d=∞ dimensions

This review presents a summary and evaluation of the experimental properties of unconventional superconductivity in ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ as they were known in the spring of 2002. At the same time, the paper is intended to be useful as an introduction to the physics of spin-triplet superconductivity. First, the authors show how the normal-state properties of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ are quantitatively described in terms of a quasi-two-dimensional Fermi liquid. Then they summarize its phenomenological superconducting parameters in the framework of the Ginzburg-Landau model, and discuss the existing evidence for spin-triplet pairing. After a brief introduction to the vector order parameter, they examine the most likely symmetry of the triplet state. The structure of the superconducting energy gap is discussed, as is the effect of symmetry-breaking magnetic fields on the phase diagram. The article concludes with a discussion of some outstanding issues and desirable future work. Appendixes on additional details of the normal state, difficulty in observing the bulk Fermi surface by angle-resolved photoemission, and the enhancement of superconducting transition temperature in a two-phase ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}\ensuremath{-}\mathrm{Ru}$ system are included.

The superconductivity of Sr 2 RuO 4 and the physics of spin-triplet pairing

T-linear term of specific heat and magnetic susceptibility at zero temperature are derived for the heavy eleCtron systems, and relations among these quantities are discussed on the basis of the Fermi liquid theory. Further, a rigorous expression of the T2-term of resistivity at low temperatures is also obtained on the basis of Kubo formula. It is shown that the coefficient of the T2-term arising from the electron interaction is strongly enhanced though it vanishes because of the momentum conservation for a free electron system possessing no crystal lattice.

/pdf/fermi-liquid-theory-on-the-basis-of-the-periodic-anderson-2e79ff7ilg.pdf

Fermi Liquid Theory on the Basis of the Periodic Anderson Hamiltonian

Neutron-scattering experiments have been performed on lightly-doped La(2-x)Sr(x)CuO4 single crystals in both the insulating (x=0.03,0.04,0.05) and superconducting (x=0.06) regions. Elastic magnetic peaks are observed at low temperatures in all samples with the maximum peak linewidth occuring at the critical concentration x_c=0.05. New incommensurate peaks are observed only at x=0.05, the positions of which are rotated by 45 degrees in reciprocal space about (pi,pi) from those observed for x>=0.06 in the superconducting phase.

http://arxiv.org/pdf/cond-mat/9902201.pdf

Observation of New Incommensurate Magnetic Correlations at the Lower Critical Concentration for Superconductivity (x=0.05) in La(2-x)Sr(x)CuO4

On discute du comportement de Kondo dense observe dans Ce, sur alliages et composes en tenant compte du couplage spin-orbite et du deplacement du champ cristallin. En utilisant une expression pour la temperature de Kondo sous champ cristallin on eclaircit la raison pour laquelle l'effet Kondo predomine dans l'interaction RKKY

/pdf/comments-on-the-dense-kondo-state-32fq0bp1od.pdf

Comments on the Dense Kondo State

We discuss the possibility of spin-triplet superconductivity within the third order perturbation theory with respect to on-site Coulomb repulsion U . Critical temperature T c for spin-triplet pairing state is calculated in a single-band two-dimensional Hubbard model and relatively high T c is obtained for moderately large U . The present situation considered here is particularly intended for the main branch γ in Sr 2 RuO 4 . According to the calculation, third order vertex correction terms, which are not direct contribution from spin fluctuation, are important, while the bare susceptibility χ 0 ( q ) need not always have a prominent peak at q =0 for the spin-triplet pairing state. The picture that strong ferromagnetic spin fluctuations mainly induce the spin-triplet superconductivity in Sr 2 RuO 4 may not be appropriate, and such momentum dependence of renormalized effective interaction between quasi-particles as is not sufficiently taken into account in spin fluctuation mediated interaction is essential ...

Perturbation Theory of Spin-Triplet Superconductivity for Sr2RuO4.

We present the highly anisotropic p -wave superconducting gap structure of Sr 2 RuO 4 , which was determined microscopically by solving the linearized Eliashberg equation on the basis of the perturbation theory with respect to the Coulomb energy at Ru sites. We trace the evolution of the gap function below T c , following the elementary BCS theory, and calculate specific heat for the superconducting state with the symmetry represented by $\mbi{d}(\mbi{k}) \sim (k_{x}+ \text{i} k_{y})\hat{\mbi{z}}$. The strong momentum dependences of the gap structure provide a line-node-like power-law behavior of the specific heat even at extremely low temperature. As a result, the calculation results of specific heat agree with the experimental results well for moderately strong inter-orbit couplings.

Kosaku Yamada

Papers

Fermi Liquid Theory on the Basis of the Periodic Anderson Hamiltonian

Observation of New Incommensurate Magnetic Correlations at the Lower Critical Concentration for Superconductivity (x=0.05) in La(2-x)Sr(x)CuO4

Comments on the Dense Kondo State

Perturbation Theory of Spin-Triplet Superconductivity for Sr2RuO4.

Detailed Investigation of Gap Structure and Specific Heat in the p-wave Superconductor Sr2RuO4.