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T. M. Rice

Other affiliations: ETH Zurich
Bio: T. M. Rice is an academic researcher from Bell Labs. The author has contributed to research in topics: Hubbard model & Pairing. The author has an hindex of 30, co-authored 38 publications receiving 7601 citations. Previous affiliations of T. M. Rice include ETH Zurich.

Papers
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Journal ArticleDOI
TL;DR: Although assuming that doping creates holes primarily on oxygen sites, this work derives explicitly a single-band effective Hamiltonian for the high-${T}_{c}$ Cu-oxide superconductors.
Abstract: Although assuming that doping creates holes primarily on oxygen sites, we derive explicitly a single-band effective Hamiltonian for the high-${T}_{c}$ Cu-oxide superconductors. Cu-O hybridization strongly binds a hole on each square of O atoms to the central ${\mathrm{Cu}}^{2+}$ ion to form a local singlet. This moves through the lattice in a similar way as a hole in the single-band effective Hamiltonian of the strongly interacting Hubbard model.

2,350 citations

Journal ArticleDOI
W. F. Brinkman1, T. M. Rice1
TL;DR: In this article, it was shown that the approximate variational calculation of Gutzwiller predicts a metal-insulator transition as the intra-atomic Coulomb interaction is increased for the case of one electron per atom.
Abstract: It is shown that the approximate variational calculation of Gutzwiller predicts a metal-insulator transition as the intra-atomic Coulomb interaction is increased for the case of one electron per atom. The susceptibility and effective mass are calculated in the metallic phase and are found to be enhanced by a common factor which diverges at the critical value of the interaction.

863 citations

Journal ArticleDOI
P. A. Lee1, T. M. Rice1
TL;DR: In this paper, the authors considered the pinning of charge-density waves by impurities in systems that exhibit at least short-range order in three dimensions and classified impurities into strong and weak with quite different pinning properties.
Abstract: The pinning of charge-density waves by impurities is considered in systems that exhibit at least short-range order in three dimensions. Impurities are classified into strong and weak with quite different pinning properties. The pinning of spin-density waves is weak and the phase values at impurity sites are almost random, in agreement with a recent experiment. The electric field required to depin the charge-density wave is estimated. The coupling between a drifting charge-density wave and carriers either from a remnant Fermi surface or thermal excitation is considered. Attention is focused on umklapp scattering of carriers by phasons as a coupling mechanism at finite temperature. The conductivity in the high-electric-field depinned limit can be large. Dislocations in the charge-density-wave lattice are examined with particular emphasis on the piecewise motion of the charge-density wave through the motion of dislocations. We also discuss the generation of dislocations by the analog of Frank-Read sources. The unusual nonlinear conductivity observed in Nb${\mathrm{Se}}_{3}$ is interpreted in terms of depinning of charge-density waves. The possibility of observing similar effects in other systems is briefly examined.

540 citations

Journal ArticleDOI
W. F. Brinkman1, T. M. Rice1
TL;DR: In this paper, the density of states and the mobility of an extra electron or hole are calculated in the atomic limit of the Hubbard model in terms of the number of paths which return to the origin leaving the spin configuration unchanged.
Abstract: In this paper, the density of states and the mobility of an extra electron or hole are calculated in the atomic limit of the Hubbard model. Both the half-filled single-band and multiple-band situations are discussed. The problem is formulated in terms of the number of paths which return to the origin leaving the spin configuration unchanged. The density of states then depends on spin configuration and we have considered the random (R) (high-temperature) and antiferromagnetic (AF) arrangements. Examination of the first five nonzero moments for the simple cubic lattice indicates that the bands are narrowed by a factor of 0.745 (AF) and 0.805 (R). However, the exact bands have tails extending out to the full free-particle width for both spin arrangements. An approximate one-particle Green's function is obtained by summing all graphs with no closed loops. Such paths give a density of states that is independent of spin arrangement and is relatively flat with a sharp square-root edge at $2{(z\ensuremath{-}1)}^{\frac{1}{2}}t$. Here $z$ is the coordination number and $t$ is the nearest-neighbor hopping integral. Within this approximation, we have calculated the mobility of an extra hole and have found typical values to be \ensuremath{\sim}1 ${\mathrm{cm}}^{2}$/V sec so that the mobility is rather small, even though the density of states has a width of order \ensuremath{\sim}1 eV. Intra-atomic exchange is shown to give a further narrowing of the band [a factor of ${(2)}^{\ensuremath{-}1/2}$ in the two-band large-intra-atomic-exchange example]. The effect of finite $\frac{t}{U}$ is considered, where $U$ is the intra-atomic Coulomb interaction, and is shown to have a strong effect on the band tail but relatively weak effects on the bulk of the band. Finally, we make a few remarks comparing our results with the observed mobilities in NiO and the relevance of intra-atomic exchange to the behavior of the dioxide and sesquioxide series.

432 citations

Journal ArticleDOI
TL;DR: In this article, Zhang et al. used the mean field theory of Anderson's RVB to understand high-temperature superconductivity in the cuprates and showed that it is able to explain the existence of the pseudogap, properties of nodal quasiparticles and approximate spin-charge separation.
Abstract: One of the first theoretical proposals for understanding high-temperature superconductivity in the cuprates was Anderson's RVB theory using a Gutzwiller projected BCS wavefunction as an approximate ground state. Recent work by Paramekanti et al has shown that this variational approach gives a semi-quantitative understanding of the doping dependences of a variety of experimental observables in the superconducting state of the cuprates. In this paper we revisit these issues using the 'renormalized mean field theory' of Zhang et al based on the Gutzwiller approximation in which the kinetic and superexchange energies are renormalized by different doping-dependent factors gt and gS respectively. We point out a number of consequences of this early mean field theory for experimental measurements which were not available when it was first explored, and observe that it is able to explain the existence of the pseudogap, properties of nodal quasiparticles and approximate spin–charge separation, the latter leading to large renormalizations of the Drude weight and superfluid density. We use the Lee–Wen theory of the phase transition as caused by thermal excitation of nodal quasiparticles, and also obtain a number of further experimental confirmations. Finally, we remark that superexchange, and not phonons, is responsible for d-wave superconductivity in the cuprates.

426 citations


Cited by
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Journal ArticleDOI
TL;DR: The dynamical mean field theory of strongly correlated electron systems is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition.
Abstract: We review the dynamical mean-field theory of strongly correlated electron systems which is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition. This mapping is exact for models of correlated electrons in the limit of large lattice coordination (or infinite spatial dimensions). It extends the standard mean-field construction from classical statistical mechanics to quantum problems. We discuss the physical ideas underlying this theory and its mathematical derivation. Various analytic and numerical techniques that have been developed recently in order to analyze and solve the dynamical mean-field equations are reviewed and compared to each other. The method can be used for the determination of phase diagrams (by comparing the stability of various types of long-range order), and the calculation of thermodynamic properties, one-particle Green's functions, and response functions. We review in detail the recent progress in understanding the Hubbard model and the Mott metal-insulator transition within this approach, including some comparison to experiments on three-dimensional transition-metal oxides. We present an overview of the rapidly developing field of applications of this method to other systems. The present limitations of the approach, and possible extensions of the formalism are finally discussed. Computer programs for the numerical implementation of this method are also provided with this article.

5,230 citations

Journal ArticleDOI
TL;DR: In this paper, a generalization of the Local Density Approximation (LDA) method for the systems with strong Coulomb correlations is presented which gives a correct description of the Mott insulators.
Abstract: The generalization of the Local Density Approximation (LDA) method for the systems with strong Coulomb correlations is presented which gives a correct description of the Mott insulators. The LDA+U method is based on the model hamiltonian approach and allows to take into account the non-sphericity of the Coulomb and exchange interactions. parameters. Orbital-dependent LDA+U potential gives correct orbital polarization and corresponding Jahn-Teller distortion. To calculate the spectra of the strongly correlated systems the impurity Anderson model should be solved with a many-electron trial wave function. All parameters of the many-electron hamiltonian are taken from LDA+U calculations. The method was applied to NiO and has shown good agreement with experimental photoemission spectra and with the oxygen Kα X-ray emission spectrum.

3,331 citations

Journal ArticleDOI
TL;DR: In this paper, a review of the physics of high-temperature superconductors from the point of view of the doping of a Mott insulator is presented, with the goal of putting the resonating valence bond idea on a more formal footing.
Abstract: 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.

3,246 citations

Journal ArticleDOI
TL;DR: A review of the most recent ARPES results on the cuprate superconductors and their insulating parent and sister compounds is presented in this article, with the purpose of providing an updated summary of the extensive literature.
Abstract: 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.

3,077 citations

Book
01 Jan 1974
TL;DR: In this article, a discussion is given of some aspects of the metal insulator transition and the status of the "minimum metallic conductivity" is discussed, and the concept is valid for liquids and in some, but not all, solid systems.
Abstract: A discussion is given of some aspects of the metal insulator transition. Particular attention is paid to the status of the “minimum metallic conductivity”. The concept is valid for liquids, and in some, but not all, solid systems.

2,109 citations