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

Magnetically engineered magnetic tunnel junctions (MTJs) show promise as non-volatile storage cells in high-performance solid-state magnetic random access memories (MRAM). The performance of these devices is currently limited by the modest (< approximately 70%) room-temperature tunnelling magnetoresistance (TMR) of technologically relevant MTJs. Much higher TMR values have been theoretically predicted for perfectly ordered (100) oriented single-crystalline Fe/MgO/Fe MTJs. Here we show that sputter-deposited polycrystalline MTJs grown on an amorphous underlayer, but with highly oriented (100) MgO tunnel barriers and CoFe electrodes, exhibit TMR values of up to approximately 220% at room temperature and approximately 300% at low temperatures. Consistent with these high TMR values, superconducting tunnelling spectroscopy experiments indicate that the tunnelling current has a very high spin polarization of approximately 85%, which rivals that previously observed only using half-metallic ferromagnets. Such high values of spin polarization and TMR in readily manufactureable and highly thermally stable devices (up to 400 degrees C) will accelerate the development of new families of spintronic devices.

Giant tunnelling magnetoresistance at room temperature with MgO (100) tunnel barriers

In this chapter, we will restrict our attention to the ferrites and a few other closely related materials. The great interest in ferrites stems from their unique combination of a spontaneous magnetization and a high electrical resistivity. The observed magnetization results from the difference in the magnetizations of two non-equivalent sub-lattices of the magnetic ions in the crystal structure. Materials of this type should strictly be designated as “ferrimagnetic” and in some respects are more closely related to anti-ferromagnetic substances than they are to ferromagnetics in which the magnetization results from the parallel alignment of all the magnetic moments present. We shall not adhere to this special nomenclature except to emphasize effects, which are due to the existence of the sub-lattices.

Ferromagnetic materials

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

We report that the doping and temperature dependence of photoemission spectra near the Brillouin zone boundary of Bi2Sr2CaCu2O8+δexhibit unexpected sensitivity to the superfluid density. In the superconducting state, the photoemission peak intensity as a function of doping scales with the superfluid density and the condensation energy. As a function of temperature, the peak intensity shows an abrupt behavior near the superconducting phase transition temperature where phase coherence sets in, rather than near the temperature where the gap opens. This anomalous manifestation of collective effects in single-particle spectroscopy raises important questions concerning the mechanism of high-temperature superconductivity.

https://science.sciencemag.org/content/sci/289/5477/277.full.pdf

Signature of Superfluid Density in the Single-Particle Excitation Spectrum of Bi2Sr2CaCu2O8+δ

We report the results of magnetization measurements on pseudomorphic (fully strained) c-axis oriented colossal magnetoresistance manganite thin films grown by molecular beam epitaxy. We observe uniaxial magnetic anisotropy (hard axis/easy plane) with the easy plane being the film plane. Within the plane a weaker biaxial anisotropy is observed with [100] (Mn–O bond direction) easy axes. The magnetization dependence of the uniaxial anisotropy constant follows the predicted magnetization dependence of the magnetostriction constants within single-ion models indicating that the anisotropy energy is dominated by strain-induced anisotropy from the lattice constant mismatch with the SrTiO3 substrate. These results indicate a magnetostriction constant λ100≈+7×10−5, and an induced orbital moment of at least 0.02μb/Mn ion. We predict that by appropriate substrate selection an equilibrium out-of-plane magnetization can be produced.

Magnetoelastic coupling and magnetic anisotropy in La0.67Ca0.33MnO3 films

Using molecular-beam-epitaxy growth techniques, we have synthesized ferromagnet/insulator/ferromagnet trilayer heterostructures with the “colossal” magnetoresistance material La1−xSrxMnO3 as the ferromagnet. These trilayer films were fabricated into magnetic tunnel junctions which exhibit magnetoresistance ΔR/R(H) of as much as 450% in 200 Oe applied field at 14 K, and which persists up to ∼250 K. In situ reflection high-energy electron diffraction (RHEED) allows us to correlate the quality of the epitaxial growth with the magnetoresistive properties. Samples which showed signs of disorder in RHEED also exhibit disorder effects in low-temperature transport and have smaller magnetoresistance which vanishes at lower temperatures.

Colossal magnetoresistance magnetic tunnel junctions grown by molecular-beam epitaxy

We have fabricated thin films of La1−xCaxMnOδ with tetragonal symmetry. For low temperatures and magnetic fields the measured magnetoresistance is anisotropic: initially positive for applied magnetic field perpendicular to the film plane and negative for field applied parallel to the film plane. At high temperatures the magnetoresistance is negative for all fields and field orientations. We also observe an in‐plane magnetoresistance anisotropy with an angular dependence corresponding to that observed in transition metal ferromagnets. We suggest an interpretation requiring a substantial spin‐orbit interaction in the material.

Anisotropic magnetoresistance in tetragonal La1−xCaxMnOδ thin films

We present a detailed analysis of magnetoresistance in tetragonal thin films of ferromagnetic La{sub 0.7}Ca{sub 0.3}MnO{sub {delta}} grown by atomic layer-by-layer molecular-beam epitaxy. The field and temperature dependence of the resistivity {rho} show an explicit dependence only on the fractional magnetization {ital M}/{ital M}{sub sat} and are consistent with a single approximate form {rho}{approx_equal}{rho}(0)exp[{minus}{ital C}({ital M}/{ital M}{sub sat}){sup 2}] for small and intermediate magnetization both above and below the Curie temperature ({ital T}{sub {ital C}}). The microscopic magnetization and susceptibility ({chi}) have been inferred from the low-field magnetoresistance above {ital T}{sub {ital C}} with {chi} following a Curie-Weiss form. We observe a sharp transition in the low-field ({ital H}) dependence of {rho} from quadratic ({proportional_to}{ital H}{sup 2}) above {ital T}{sub {ital C}} to linear ({proportional_to}{ital H}) below, consistent with a temperature-independent {rho}({ital M}). Finally we show that within a simple model this temperature-independent form for {rho} reproduces the behavior of the measured low-field sensitivity below {ital T}{sub {ital C}}. {copyright} {ital 1996 The American Physical Society.}

J. O'Donnell

Papers

Signature of Superfluid Density in the Single-Particle Excitation Spectrum of Bi2Sr2CaCu2O8+δ

Magnetoelastic coupling and magnetic anisotropy in La0.67Ca0.33MnO3 films

Colossal magnetoresistance magnetic tunnel junctions grown by molecular-beam epitaxy

Anisotropic magnetoresistance in tetragonal La1−xCaxMnOδ thin films

Magnetoresistance scaling in MBE-grown La0.7Ca0.3MnO3 thin films.