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

http://sces.phys.utk.edu/mostcited/mc1_1114.pdf

Colossal Magnetoresistant Materials: The Key Role of Phase Separation

IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is appreciable only near the boundaries of Brillouin zones, and particularly strong near the corners of these. This leads to the criterion that the metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.

On the theory of superconductivity

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

Nanocomposites of Ferroelectric Polymers with TiO2 Nanoparticles Exhibiting Significantly Enhanced Electrical Energy Density

In conventional superconductors, lattice vibrations (phonons) mediate the attraction between electrons that is responsible for superconductivity1. The high transition temperatures (high-Tc) of the copper oxide superconductors has led to collective spin excitations being proposed as the mediating excitations in these materials2. The mediating excitations must be strongly coupled to the conduction electrons, have energy greater than the pairing energy, and be present at Tc. The most obvious feature in the magnetic excitations of high-Tc superconductors such as YBa2Cu3O6+x is the so-called ‘resonance’3,4,5,6. Although the resonance may be strongly coupled to the superconductivity3,4,5,6,7,8, it is unlikely to be the main cause, because it has not been found in the La2-x(Ba,Sr)xCuO4 family and is not universally present in Bi2Sr2CaCu2O8+δ (ref. 9). Here we use inelastic neutron scattering to characterize possible mediating excitations at higher energies in YBa2Cu3O6.6. We observe a square-shaped continuum of excitations peaked at incommensurate positions. These excitations have energies greater than the superconducting pairing energy, are present at Tc, and have spectral weight far exceeding that of the ‘resonance’. The discovery of similar excitations in La2–xBaxCuO4 (ref. 10) suggests that they are a general property of the copper oxides, and a candidate for mediating the electron pairing.

The structure of the high-energy spin excitations in a high-transition-temperature superconductor

Inelastic neutron scattering was used to study the wave vector– and frequency-dependent magnetic fluctuations in single crystals of superconducting YBa2Cu3O6+x. The spectra contain several important features, including a gap in the superconducting state, a pseudogap in the normal state, and the much-discussed resonance peak. The appearance of the pseudogap determined from transport and nuclear resonance coincides with formation of the resonance in the magnetic excitations. The exchange energy associated with the resonance has the temperature and doping dependences as well as the magnitude to describe approximately the electronic specific heat near the superconducting transition temperature (Tc).

https://science.sciencemag.org/content/sci/284/5418/1344.full.pdf

The magnetic excitation spectrum and thermodynamics of high-Tc superconductors

Polarized and unpolarized neutron triple-axis spectrometry was used to study the dynamical magnetic susceptibility chi"(q,omega) as a function of energy ((h) over bar omega) and wave vector (q) in a wide temperature range for the bilayer superconductor YBa(2)Cu(3)O(6+x) with oxygen concentrations, x, of 0.45, 0.5, 0.6, 0.7, 0.8, 0.93, and 0.95, The most prominent features in the magnetic spectra include a spin gap in the superconducting state, a pseudogap in the normal state, the much-discussed resonance, and incommensurate spin fluctuations below the resonance. We establish the doping dependence of the spin gap in the superconducting state, the resonance energy, and the incommensurability of the spin fluctuations. The magnitude of the spin gap (E(sg)) up to the optimal doping is proportional to the superconducting transition temperature T(c) with E(sg)/k(B)T(c)=3.8. The resonance, which exists exclusively below T(c) for highly doped YBa(2)Cu(3)O(6+x) with x = 0.93 and 0.95, appears above T(c) for underdoped compounds with x less than or equal to0.8. The resonance energy (E(r)) also scales with k(B)T(c), but saturates at E(r)approximate to 40 meV for x close to 0.93. The incommensurate spin fluctuations at energies below the resonance have structures similar to that of the single-layer superconducting La(2-x)Sr(x)CuO(4). However, there are also important differences. While the incommensurability (delta) of the spin fluctuations in La(2-x)Sr(x)CuO(4) is proportional to T(c) for the entire hole-doping range up to the optimal value, the incommensurability in YBa(2)Cu(3)O(6+x) increases with T(c) for low-oxygen doping and saturates to delta =0.1 for x greater than or equal to0.6. In addition, the incommensurability decreases with increasing energy close to the resonance. Finally, the incommensurate spin fluctuations appear above T(c) in underdoped compounds with x less than or equal to0.6 but for highly doped materials they are only observed below T(c). We discuss in detail the procedure used for separating the magnetic scattering from phonon and other spurious effects. In the comparison of our experimental results with various microscopic theoretical models, particular emphasis was made to address the similarities and differences in the spin fluctuations of the two most studied superconductors. Finally, we briefly mention recent magnetic-field-dependent studies of the spin fluctuations and discuss their relevance in understanding the microscopic origin of the resonance.

Evolution of the resonance and incommensurate spin fluctuations in superconducting YBa(2)Cu(3)O(6+x)

We report inelastic neutron scattering measurements at excitation energies $\ensuremath{\Elzxh}\ensuremath{\omega}\ensuremath{\sim}41$ meV in YB${\mathrm{a}}_{2}$C${\mathrm{u}}_{3}$${\mathrm{O}}_{7}$. We separate magnetic and phonon contributions to the scattering cross section by a detailed analysis of the momentum dependence of the scattered intensity. The previously reported broad peak around $\mathbf{q}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(\ensuremath{\pi}/a,\ensuremath{\pi}/a)$ in the normal state can be entirely accounted for by a phonon which primarily involves vibrations of the in-plane oxygen. Magnetic scattering centered around 41 meV and $\mathbf{q}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(\ensuremath{\pi}/a,\ensuremath{\pi}/a)$ appears in the superconducting state only. Theoretical implications of these findings are discussed.

/pdf/phonon-and-magnetic-neutron-scattering-at-41-mev-in-4oqvkz3dhm.pdf

Fatih Dogan

Papers

Nanocomposites of Ferroelectric Polymers with TiO2 Nanoparticles Exhibiting Significantly Enhanced Electrical Energy Density

The structure of the high-energy spin excitations in a high-transition-temperature superconductor

The magnetic excitation spectrum and thermodynamics of high-Tc superconductors

Evolution of the resonance and incommensurate spin fluctuations in superconducting YBa(2)Cu(3)O(6+x)

Phonon and magnetic neutron scattering at 41 meV in YBa2Cu3O7.