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

2. GRAVITY 7. MICROSCOPIC PHYSICS 13. TOPOLOGY OF DEFECTS 18. ANOMALOUS NON-CONSERVATION OF FERMIONIC CHARGE 22. EDGE STATES AND FERMION ZERO MODES ON SOLITON 26. LANDAU CRITICAL VELOCITY 29. CASIMIR EFFECT AND VACUUM ENERGY

The Universe in a Helium Droplet

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

Electrochromic tungsten oxide films: Review of progress 1993–1998

This article discusses fluctuating order in a quantum disordered phase proximate to a quantum critical point, with particular emphasis on fluctuating stripe order. Optimal strategies are derived for extracting information concerning such local order from experiments, with emphasis on neutron scattering and scanning tunneling microscopy. These ideas are tested by application to two model systems---an exactly solvable one-dimensional (1D) electron gas with an impurity, and a weakly interacting 2D electron gas. Experiments on the cuprate high-temperature superconductors which can be analyzed using these strategies are extensively reviewed. The authors adduce evidence that stripe correlations are widespread in the cuprates. They compare and contrast the advantages of two limiting perspectives on the high-temperature superconductor: weak coupling, in which correlation effects are treated as a perturbation on an underlying metallic (although renormalized) Fermi-liquid state, and strong coupling, in which the magnetism is associated with well-defined localized spins, and stripes are viewed as a form of micro phase separation. The authors present quantitative indicators that the latter view better accounts for the observed stripe phenomena in the cuprates.

How to detect fluctuating stripes in the high-temperature superconductors

We report microwave surface resistance (Rs) measurements on two very-high-quality YBa2Cu3O6.95 crystals which exhibit extremely low residual loss at 1.2 K (2-6 μΩ at 2 GHz), a broad, reproducible peak at around 38 K, and a rapid increase in loss, by 4 orders of magnitude, between 80 and 93 K. These data provide one ingredient in the determination of the temperature dependence of the real part of the microwave conductivity, σ1(T), and of the quasiparticle scattering time. The other necessary ingredient is an accurate knowledge of the magnitude and temperature dependence of the London penetration depth, λ(T). This is derived from published data, from microwave data of Anlage, Langley, and co-workers and from, high-quality μSR data. We infer, from a careful analysis of all available data, that λ2(0)/λ2(T) is well approximated by the simple function 1-t2, where t=T/Tc, and that the low-temperature data are incompatible with the existence of an s-wave, BCS-like gap. Combining the Rs and λ(T) data, we find that σ1(T), has a broad peak around 32 K with a value about 20 times that at Tc. Using a generalized two-fluid model, we extract the temperature dependence of the quasiparticle scattering rate which follows an exponential law, exp(T/T0), where T0≊12 K, for T between 15 and 84 K. Such a temperature dependence has previously been observed in measurements of the nuclear spin-lattice relaxation rate. Both the uncertainties in our analysis and the implications for the mechanism of high-temperature superconductivity are discussed.

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Microwave determination of the quasiparticle scattering time in YBa2Cu3O6.95.

Possible Neel orderings of antiferromagnetically coupled spins on a kagome lattice are studied using linearspin-wave theory and high-temperature expansions. Spin-wave analysis, applied to q=0 (three spins per magnetic unit cell) and to √3 × √3 (nine spins per cell) Neel orderings yield identical excitation spectra with twofold-degenerate linear modes and a dispersionless zero-energy mode. This dispersionless mode is equivalent to an excitation localized to an arbitrary hexagon of nearest-neighbor spins. Second( J2) and third( J3) neighbor interactions are shown to stabilize the q=0 state for J2>J3 and the √3 × √3 state for J23. A hightemperature expansion of the spin-spin susceptibility χαβ(q) is performed to order 1/T8, for n-component, classical spins with nearest-neighbor interactions only. To order 1/T7 the largest eigenvalue of the susceptibility matrix is found to be independent of wave vector with an eigenvector that corresponds to the dispersionless mode of the ordered phase. This degeneracy is removed at order 1/T8. For n=0, the q=0 mode is favored; for n=1, the band is flat; and, for n>1, the maximum susceptibility is found for a √3 × √3 excitation. Similar results are found for the three-dimensional pyrochlore lattice. The high-temperature expansion is used to interpret experimental data for the uniform susceptibility and powder-neutron-diffraction spectrum for the kagome-lattice system SrCr8−xGa4+xO19.

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Possible Néel orderings of the Kagomé antiferromagnet.

We show that a superconducting vortex in underdoped high T{sub c} superconductors could have an antiferromagnetic core. This type of vortex configuration arises as a topological solution in the recently constructed SO(5) nonlinear {sigma} model and in Landau-Ginzburg theory with competing antiferromagnetic and superconducting order parameters. Experimental detection of this type of vortex by muon spin resonance and neutron scattering is proposed. {copyright} {ital 1997} {ital The American Physical Society}

Superconducting Vortex with Antiferromagnetic Core

The metal atoms in the pyrochlore system of compounds ({ital A}{sub 2}{ital B2}O{sub 7}, where {ital A} and {ital B} are metals) form an infinite three-dimensional network of corner-sharing tetrahedra with cubic symmetry. For antiferromagnetic nearest-neighbor interactions and only {ital B} atoms magnetic, there is a very high degree of frustration, and no long-range order is predicted in the absence of further neighbor interactions. A general form of the mean-field theory is developed for dealing with {ital n}-component classical vector spins on any lattice. Calculations for the pyrochlore problem show that the Fourier modes of the system are completely degenerate for all wave vectors in the first Brillouin zone. In some cases further neighbor interactions will select the {bold q}={bold 0} or incommensurate modes. A comparison is made with long-range order known to exist in the pyrochlore form of FeF{sub 3}. The highly degenerate ordered phases of more complicated systems, where both {ital A} and {ital B} atoms are magnetic, will also be discussed. A comparison is made of the corner-sharing tetrahedral lattice and the more familiar stacked triangular antiferromagnets, with regard to the degree of frustration in both systems. Results for the Kagome lattice and the square lattice withmore » crossings, which are the two-dimensional analogs of the corner-sharing tetrahedral lattice, are also briefly discussed.« less

Mean-field approach to magnetic ordering in highly frustrated pyrochlores.

Antiferromagnetic ordering on a kagome$iaa--- net is frustrated by the geometry of the lattice. The infinite number of classical ground states suggests that the system might not order at zero temperature, even for Heisenberg spins. However, high-temperature series expansions and earlier simulations indicate that this degeneracy is resolved by thermal fluctuations (i.e., order by disorder), suggesting a nine-sublattice coplanar N\'eel-like ordering of the spins. Coplanar nematic, random three-state Potts, and N\'eel orderings for the Heisenberg kagome$aa--- lattice antiferromagnet are investigated with Monte Carlo simulations coupled with state-of-the-art histogram methods for data analysis. We see strong evidence for thermal selection of long-range order with the spin correlations exhibiting algebraic decay, but the low-temperature phases are also seen to posses a chiral domain structure and very short-range chiral correlations. It is argued that the spin correlations are, surprisingly, rather insensitive to this lack of chiral order. Our results are consistent with T=0 being a critical point for this model system.

A. J. Berlinsky

Papers

Microwave determination of the quasiparticle scattering time in YBa2Cu3O6.95.

Possible Néel orderings of the Kagomé antiferromagnet.

Superconducting Vortex with Antiferromagnetic Core

Mean-field approach to magnetic ordering in highly frustrated pyrochlores.

Order by disorder in the classical Heisenberg kagomé antiferromagnet