Hidden order in the cuprates
TL;DR: In this paper, the enigmatic pseudogap phase of cuprate superconductors is characterized by a hidden broken symmetry of ${d}_{{x}^{2}\ensuremath{-}{y}^{ 2}}$-type.
Abstract: We propose that the enigmatic pseudogap phase of cuprate superconductors is characterized by a hidden broken symmetry of ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-type. The transition to this state is rounded by disorder, but in the limit that the disorder is made sufficiently small, the pseudogap crossover should reveal itself to be such a transition. The ordered state breaks time-reversal, translational, and rotational symmetries, but it is invariant under the combination of any two. We discuss these ideas in the context of ten specific experimental properties of the cuprates, and make several predictions, including the existence of an as-yet undetected metal-metal transition under the superconducting dome.
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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
Cites background from "Hidden order in the cuprates"
...12See, for example, Chakravarty et al. (1989, 2001); Varma et al. (1989); Littlewood and Varma (1991); Sachdev and Ye (1992); Emery and Kivelson (1993b); Sokol and Pines (1993); Castellani et al. (1995); Varma (1997)....
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...15See, for example, Affleck and Marston (1988); Kotliar and Liu (1988); Maekawa et al. (1988); Suzumura et al. (1988); Wen and Lee (1996); Chakravarty et al. (2001)....
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...…case the physics, together 13See, for example, Affleck and Marston (1988); Kotliar and Liu (1988); Maekawa et al. (1988); Suzumura et al. (1988); Wen and Lee (1996); Chakravarty et al. (2001). with the superposition of domains, conspires to give the appearance of a large LDA-like Fermi surface)....
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...In this context, possible microscopic descriptions for the pseudogap phase include the circulating-current phase (Varma, 1997, 1999), the charge-density wave (Castellani et al., 1995), and the d-density-wave short-range fluctuations (Chakravarty et al., 2001)....
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TL;DR: The discovery of high-temperature superconductivity in the copper oxides in 1986 triggered a huge amount of innovative scientific inquiry but unresolved issues include the astonishing complexity of the phase diagram, the unprecedented prominence of various forms of collective fluctuations, and the simplicity and insensitivity to material details of the ‘normal’ state at elevated temperatures.
Abstract: The discovery of high-temperature superconductivity in the copper oxides in 1986 triggered a huge amount of innovative scientific inquiry. In the almost three decades since, much has been learned about the novel forms of quantum matter that are exhibited in these strongly correlated electron systems. A qualitative understanding of the nature of the superconducting state itself has been achieved. However, unresolved issues include the astonishing complexity of the phase diagram, the unprecedented prominence of various forms of collective fluctuations, and the simplicity and insensitivity to material details of the 'normal' state at elevated temperatures.
1,859 citations
TL;DR: In this paper, the authors 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, where the magnetism is associated with well defined localized spins, and stripes are viewed as a form of micro phase separation.
Abstract: 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.
1,081 citations
TL;DR: In this article, the authors provide a unified framework for describing quasi-localized states in the vicinity of impurity sites in conventional and unconventional superconductors and show that these fluctuations affect the density of states and are, strictly speaking, gapless in the presence of an arbitrarily small concentration of magnetic impurities.
Abstract: We review recent developments in our understanding of how impurities influence the electronic states in the bulk of superconductors. Our focus is on the quasi-localized states in the vicinity of impurity sites in conventional and unconventional superconductors and our goal is to provide a unified framework for their description. The non-magnetic impurity resonances in unconventional superconductors are directly related to the Yu-Shiba-Rusinov states around magnetic impurities in conventional s-wave systems. We review the physics behind these states, including quantum phase transition between screened and unscreened impurity, and emphasize recent work on d-wave superconductors. The bound states are most spectacularly seen in scanning tunneling spectroscopy measurements on high-$T_c$ cuprates, which we describe in detail. We also discuss very recent progress on the states coupled to impurity sites which have their own dynamics, and impurity resonances in the presence of an order competing with superconductivity. Last part of the review is devoted to influence of local deviations of the impurity concentration from its average value on the density of states in s-wave superconductors. We review how these fluctuations affect the density of states and show that s-wave superconductors are, strictly speaking, gapless in the presence of an arbitrarily small concentration of magnetic impurities.
968 citations
Cites background from "Hidden order in the cuprates"
...The typical competing scenarios for this anomalous phenomenon, including mainly the pre-formed pair with phase-fluctuation model (Emery and Kivelson, 1995), the Bose-Einstein condensation of Cooper pairs (Chen et al., 1998), the 20 time-reversal-symmetry-breaking circulating current model (Varma, 1999), and the d-density-wave model (DDW) (Chakravarty et al., 2001), which is typical kind of staggered flux state (Affleck and Marston, 1988; Hsu et al., 1991; Marston and Affleck, 1989)....
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...In the case of fully non-superconducting PG (e.g., the DDW state), there should be no observable counterpart state....
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...(8.17) In the presence of a single non-magnetic impurity in the DDW state, the T -matrix analysis just shows again that the resonance state is determined by the poles of T (iωn → ω + i0+), i.e., the following equation G(0)(0, 0;ω + i0+) = 1 U0 ....
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...The model Hamiltonian for a clean DDW system is written as: H0 = ∑ ij,σ [−tij + (−1)iiWij ]c†iσcjσ − µ ∑ i,σ c†iσciσ ....
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...The quasiparticle states in the DDW state with a finite concentration of non-magnetic impurities was investigated by Ghosal and Kee (Ghosal and Kee, 2004)....
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TL;DR: The observation of quantum oscillations in the electrical resistance of the oxygen-ordered copper oxide YBa2Cu3O6.5 establishes the existence of a well-defined Fermi surface in the ground state of underdoped copper oxides, once superconductivity is suppressed by a magnetic field.
Abstract: Two papers in this issue report notable contributions towards an understanding of high-temperature superconductivity, still an elusive goal after more than 20 years of intensive research. Doiron-Leyraud et al. report the observation of a Fermi surface in a high-temperature superconductor, a phenomenon regarded as the classic signature of a metal. Gomes et al. tackled the long-standing question of whether the gap in the electronic energy spectrum at temperatures above the critical temperature of a high-temperature superconductor is associated with electron pairing. They find that it is. With these two elegant experimental papers adding some solid new data to the mix, it is the turn of the theorists to work out the implications for superconductivity mechanisms. The observation of quantum oscillations in the electrical resistance of YBa2Cu3O6.5, is reported, establishing the existence of a well-defined Fermi surface in the ground state of underdoped copper oxides (once superconductivity is suppressed by a magnetic field). The low oscillation frequency reveals a Fermi surface made of small pockets, in contrast to the large cylinder characteristic of the overdoped regime. Despite twenty years of research, the phase diagram of high-transition-temperature superconductors remains enigmatic1,2. A central issue is the origin of the differences in the physical properties of these copper oxides doped to opposite sides of the superconducting region. In the overdoped regime, the material behaves as a reasonably conventional metal, with a large Fermi surface3,4. The underdoped regime, however, is highly anomalous and appears to have no coherent Fermi surface, but only disconnected ‘Fermi arcs’5,6. The fundamental question, then, is whether underdoped copper oxides have a Fermi surface, and if so, whether it is topologically different from that seen in the overdoped regime. Here we report the observation of quantum oscillations in the electrical resistance of the oxygen-ordered copper oxide YBa2Cu3O6.5, establishing the existence of a well-defined Fermi surface in the ground state of underdoped copper oxides, once superconductivity is suppressed by a magnetic field. The low oscillation frequency reveals a Fermi surface made of small pockets, in contrast to the large cylinder characteristic of the overdoped regime. Two possible interpretations are discussed: either a small pocket is part of the band structure specific to YBa2Cu3O6.5 or small pockets arise from a topological change at a critical point in the phase diagram. Our understanding of high-transition-temperature (high-Tc) superconductors will depend critically on which of these two interpretations proves to be correct.
813 citations