Signature of superfluid density in the single-particle excitation spectrum of Bi(2)Sr(2)CaCu(2)O(8+delta)

Universal Stripe Symmetry of Short-Range Charge Density Waves in Cuprate Superconductors

The omnipresence of charge density waves (CDWs) across almost all cuprate families underpins a common organizing principle. However, a longstanding debate of whether its spatial symmetry is stripe or checkerboard remains unresolved. While CDWs in lanthanum- and yttrium-based cuprates possess a stripe symmetry, distinguishing these two scenarios is challenging for the short-range CDW in bismuth-based cuprates. Here, high-resolution resonant inelastic x-ray scattering is employed to uncover the spatial symmetry of the CDW in Bi2 Sr2 - x Lax CuO6 + δ . Across a wide range of doping and temperature, anisotropic CDW peaks with elliptical shapes are found in reciprocal space. Based on Fourier transform analysis of real-space models, the results are interpreted as evidence of unidirectional charge stripes, hosted by mutually 90°-rotated anisotropic domains. This work paves the way for a unified symmetry and microscopic description of CDW order in cuprates.

B_{1g}-Phonon Anomaly Driven by Fermi Surface Instability at Intermediate Temperature in YBa_{2}Cu_{3}O_{7-δ}

We performed temperature- and doping-dependent high-resolution Raman spectroscopy experiments on YBa_{2}Cu_{3}O_{7-δ} to study B_{1g} phonons. The temperature dependence of the real part of the phonon self-energy shows a distinct kink at T=T_{B1g} above T_{c} due to softening, in addition to the one due to the onset of the superconductivity. T_{B1g} is clearly different from the pseudogap temperature with a maximum in the underdoped region and resembles charge density wave onset temperature, T_{CDW}. We attribute the B_{1g}-phonon softening to an energy gap on the Fermi surface induced by a charge density wave order, which is consistent with the results of a recent electronic Raman scattering study. Our work demonstrates a way to investigate Fermi surface instabilities above T_{c} via phonon Raman studies.

Bosonic Mode and Impurity-Scattering in Monolayer Fe(Te,Se) High-Temperature Superconductors

The electron pairing mechanism has always been one of the most challenging problems in high-temperature superconductors. Fe(Te,Se), as the superconductor with intrinsic topological property, may host Majorana bound states and has attracted tremendous interest. While in bulk Fe(Te,Se) the pairing mechanism has been experimentally investigated, it remains little understood in its two-dimensional limit counterpart. Here, by in situ scanning tunneling spectroscopy, we show clear evidence of the bosonic mode Ω beyond the superconducting gap Δ in monolayer FeTe_0.5Se_0.5/SrTiO₃(001) high-temperature superconductor. Statistically, Ω shows an obvious anticorrelation with Δ and appears below 2Δ, consistent with the spin-excitation nature. Furthermore, the in-gap bound states induced by two types of magnetically different impurities support the sign-reversing pairing scenario. Our results not only suggest that the spin-excitation-like bosonic mode within a sign-reversing pairing plays an essential role in monolayer FeTe_0.5Se_0.5/SrTiO₃(001) but also offer the crucial information for investigating the high-temperature superconductivity in interfacial iron selenides.

Effect of Structural Supermodulation on Superconductivity in Trilayer Cuprate Bi_{2}Sr_{2}Ca_{2}Cu_{3}O_{10+δ}

We investigate the spatial and doping evolutions of the superconducting properties of trilayer cuprate Bi_{2}Sr_{2}Ca_{2}Cu_{3}O_{10+δ} by using scanning tunneling microscopy and spectroscopy. Both the superconducting coherence peak and gap size exhibit periodic variations with structural supermodulation, but the effect is much more pronounced in the underdoped regime than at optimal doping. Moreover, a new type of tunneling spectrum characterized by two superconducting gaps emerges with increasing doping, and the two-gap features also correlate with the supermodulation. We propose that the interaction between the inequivalent outer and inner CuO_{2} planes is responsible for these novel features that are unique to trilayer cuprates.

Photoemission perspective on pseudogap, superconducting fluctuations, and charge order in cuprates: a review of recent progress

In the course of seeking the microscopic mechanism of superconductivity in cuprate high temperature superconductors, the pseudogap phase- the very abnormal 'normal' state on the hole-doped side- has proven to be as big of a quandary as superconductivity itself. Angle-resolved photoemission spectroscopy (ARPES) is a powerful tool for assessing the momentum-dependent phenomenology of the pseudogap, and recent technological developments have permitted a more detailed understanding. This report reviews recent progress in understanding the relationship between superconductivity and the pseudogap, the Fermi arc phenomena, and the relationship between charge order and pseudogap from the perspective of ARPES measurements.

Collapse of superconductivity in cuprates via ultrafast quenching of phase coherence

The possibility of driving phase transitions in low-density condensates through the loss of phase coherence alone has far-reaching implications for the study of quantum phases of matter. This has inspired the development of tools to control and explore the collective properties of condensate phases via phase fluctuations. Electrically gated oxide interfaces^1,2, ultracold Fermi atoms^3,4 and cuprate superconductors^5,6, which are characterized by an intrinsically small phase stiffness, are paradigmatic examples where these tools are having a dramatic impact. Here we use light pulses shorter than the internal thermalization time to drive and probe the phase fragility of the Bi₂Sr₂CaCu₂O_8+δ cuprate superconductor, completely melting the superconducting condensate without affecting the pairing strength. The resulting ultrafast dynamics of phase fluctuations and charge excitations are captured and disentangled by time-resolved photoemission spectroscopy. This work demonstrates the dominant role of phase coherence in the superconductor-to-normal state phase transition and offers a benchmark for non-equilibrium spectroscopic investigations of the cuprate phase diagram.

Suppression of Superfluid Density and the Pseudogap State in the Cuprates by Impurities

We use scanning tunneling microscopy (STM) to study magnetic Fe impurities intentionally doped into the high-temperature superconductor Bi_{2}Sr_{2}CaCu_{2}O_{8+δ}. Our spectroscopic measurements reveal that Fe impurities introduce low-lying resonances in the density of states at Ω_{1}≈4  meV and Ω_{2}≈15  meV, allowing us to determine that, despite having a large magnetic moment, potential scattering of quasiparticles by Fe impurities dominates magnetic scattering. In addition, using high-resolution spatial characterizations of the local density of states near and away from Fe impurities, we detail the spatial extent of impurity-affected regions as well as provide a local view of impurity-induced effects on the superconducting and pseudogap states. Our studies of Fe impurities, when combined with a reinterpretation of earlier STM work in the context of a two-gap scenario, allow us to present a unified view of the atomic-scale effects of elemental impurities on the pseudogap and superconducting states in hole-doped cuprates; this may help resolve a previously assumed dichotomy between the effects of magnetic and nonmagnetic impurities in these materials.

From quantum matter to high-temperature superconductivity in copper oxides

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.

Direct spectroscopic evidence for phase competition between the pseudogap and superconductivity in Bi2Sr2CaCu2O(8+δ)

In the high-temperature (T(c)) cuprate superconductors, a growing body of evidence suggests that the pseudogap phase, existing below the pseudogap temperature T*, is characterized by some broken electronic symmetries distinct from those associated with superconductivity. In particular, recent scattering experiments have suggested that charge ordering competes with superconductivity. However, no direct link of an interplay between the two phases has been identified from the important low-energy excitations. Here, we report an antagonistic singularity at T(c) in the spectral weight of Bi2Sr2CaCu2O(8+δ) as compelling evidence for phase competition, which persists up to a high hole concentration p ~ 0.22. Comparison with theoretical calculations confirms that the singularity is a signature of competition between the order parameters for the pseudogap and superconductivity. The observation of the spectroscopic singularity at finite temperatures over a wide doping range provides new insights into the nature of the competitive interplay between the two orders and the complex phase diagram near the pseudogap critical point.

Relation between the nodal and antinodal gap and critical temperature in superconducting Bi2212

An energy gap is, in principle, a dominant parameter in superconductivity. However, this view has been challenged for the case of high-T_c cuprates, because anisotropic evolution of a d-wave-like superconducting gap with underdoping has been difficult to formulate along with a critical temperature T_c. Here we show that a nodal-gap energy 2Δ_N closely follows 8.5 k_BT_c with underdoping and is also proportional to the product of an antinodal gap energy Δ^* and a square-root superfluid density √P_s for Bi₂Sr₂CaCu₂O_8+δ, using low-energy synchrotron-radiation angle-resolved photoemission. The quantitative relations imply that the distinction between the nodal and antinodal gaps stems from the separation of the condensation and formation of electron pairs, and that the nodal-gap suppression represents the substantial phase incoherence inherent in a strong-coupling superconducting state. These simple gap-based formulae reasonably describe a crucial part of the unconventional mechanism governing T_c.

In conventional superconductors, the critical temperature is proportional to the superconducting energy gap, but this is not so in unconventional superconductors. Anzai et al. identify an alternative relationship involving nodal and antinodal gaps in an underdoped cuprate superconductor.

New insights into the phase diagram of the copper oxide superconductors from electronic Raman scattering

The mechanism of unconventional superconductivity is still unknown despite over 25 years passing since the discovery of high-T(c) cuprate superconductors by Bednorz and Muller (1986 Z. Phys. B 64 189). Here, we explore the cuprate phase diagram by electronic Raman spectroscopy and shed light on the superconducting state in hole-doped curates, namely, how superconductivity and the critical temperature T(c) are affected by the pseudogap.

Phase competition in trisected superconducting dome

A detailed phenomenology of low energy excitations is a crucial starting point for microscopic understanding of complex materials, such as the cuprate high-temperature superconductors. Because of its unique momentum-space discrimination, angle-resolved photoemission spectroscopy (ARPES) is ideally suited for this task in the cuprates, where emergent phases, particularly superconductivity and the pseudogap, have anisotropic gap structure in momentum space. We present a comprehensive doping- and temperature-dependence ARPES study of spectral gaps in Bi(2)Sr(2)CaCu(2)O(8+δ), covering much of the superconducting portion of the phase diagram. In the ground state, abrupt changes in near-nodal gap phenomenology give spectroscopic evidence for two potential quantum critical points, p = 0.19 for the pseudogap phase and p = 0.076 for another competing phase. Temperature dependence reveals that the pseudogap is not static below T(c) and exists p > 0.19 at higher temperatures. Our data imply a revised phase diagram that reconciles conflicting reports about the endpoint of the pseudogap in the literature, incorporates phase competition between the superconducting gap and pseudogap, and highlights distinct physics at the edge of the superconducting dome.

Insensitivity of the superconducting gap to variations in the critical temperature of Zn-substituted Bi2Sr2CaCu2O(8+δ) superconductors

The phase diagram of the superconducting high-T(c) cuprates is governed by two energy scales: T*, the temperature below which a gap is opened in the excitation spectrum, and T(c), the superconducting transition temperature. The way these two energy scales are reflected in the low-temperature energy gap is being intensively debated. Using Zn substitution and carefully controlled annealing we prepared a set of samples having the same T* but different T(c)'s, and measured their gap using angle-resolved photoemission spectroscopy (ARPES). We show that T(c) is not related to the gap shape or size, but it controls the size of the coherence peak at the gap edge.

The effect of in-plane mass anisotropy on the properties of high temperature superconductors in states of mixed symmetry

Experiments have suggested that the high- T(c) cuprate YBCO shows marked anisotropy in penetration depth and coherence length measurements. In order to take into account the presence of this anisotropy in the system and its corresponding effect on the various properties of the high- T(c) superconducting materials, we have developed an anisotropic two-order parameter Ginzburg-Landau (GL) theory involving a mixed symmetry state of the order parameter components. For this we have generalized a two-order parameter GL theory, recently developed for the isotropic high- T(c) superconductors involving a mixed symmetry state of the order parameter components (Karmakar and Dey 2008 J. Phys. Condens. Matter 20 255218), in which the effect of the presence of in-plane anisotropy has been taken into account by an effective mass approximation, with the anisotropy being characterized by the parameter γ = m(x)/m(y). The work goes beyond the limitations of the earlier studies in this field as it enables us to carry out a detailed study of the various properties of the system over the entire range of applied magnetic field and wide range of temperature for arbitrary values of the GL parameter κ(y) and vortex lattice symmetry. The model successfully explains not only the observed oblique vortex lattice structure in the presence of in-plane anisotropy but also the experimentally observed angle between the primitive axes of the vortex lattice. The generation of two-fold symmetry of the vortices in the presence of in-plane anisotropy, for a very low applied magnetic field can also be analyzed by our model. We have also compared our theoretical results with various other experiments on high- T(c) cuprate YBCO.

Competition between the pseudogap and superconductivity in the high-T(c) copper oxides

In a classical Bardeen-Cooper-Schrieffer superconductor, pairing and coherence of electrons are established simultaneously below the critical transition temperature (T(c)), giving rise to a gap in the electronic energy spectrum. In the high-T(c) copper oxide superconductors, however, a pseudogap extends above T(c). The relationship between the pseudogap and superconductivity is one of the central issues in this field. Spectral gaps arising from pairing precursors are qualitatively similar to those caused by competing electronic states, rendering a standard approach to their analysis inconclusive. The issue can be settled, however, by studying the correlation between the weights associated with the pseudogap and superconductivity spectral features. Here we report a study of two spectral weights using angle-resolved photoemission spectroscopy. The weight of the superconducting coherent peak increases away from the node following the trend of the superconducting gap, but starts to decrease in the antinodal region. This striking non-monotonicity reveals the presence of a competing state. We demonstrate a direct correlation, for different values of momenta and doping, between the loss in the low-energy spectral weight arising from the opening of the pseudogap and a decrease in the spectral weight associated with superconductivity. We therefore conclude that the pseudogap competes with the superconductivity by depleting the spectral weight available for pairing.

Momentum dependence of the superconducting gap in NdFeAsO0.9F0.1 single crystals measured by angle resolved photoemission spectroscopy

We use angle resolved photoemission spectroscopy to study the momentum dependence of the superconducting gap in NdFeAsO0.9F0.1 single crystals. We find that the Gamma hole pocket is fully gapped below the superconducting transition temperature. The value of the superconducting gap is 15+/-1.5 meV and its anisotropy around the hole pocket is smaller than 20% of this value-consistent with an isotropic or anisotropic s-wave symmetry of the order parameter. This is a significant departure from the situation in the cuprates, pointing to the possibility that the superconductivity in the iron arsenic based system arises from a different mechanism.

Superconducting coherence peak in the electronic excitations of a single-layer Bi2Sr1.6La0.4CuO6+delta cuprate superconductor

Angle resolved photoemission spectroscopy study is reported on a high quality optimally doped Bi2Sr1.6La0.4CuO6+delta high-Tc superconductor. In the antinodal region with a maximal d-wave gap, the symbolic superconducting coherence peak, which has been widely observed in multi-CuO2-layer cuprate superconductors, is unambiguously observed in a single-layer system. The associated peak-dip separation is just about 19 meV, which is much smaller than its counterparts in multilayered compounds, but correlates with the energy scales of spin excitations in single-layer cuprates.

Anomalous momentum dependence of the superconducting coherence peak and its relation to the pseudogap of La1.85Sr0.15CuO4

We performed high-resolution angle-resolved photoemission spectroscopy on La1.85Sr0.15CuO4 to study the nature of the single-particle excitation gap. We found that there is a well-defined superconducting coherence peak in the off-nodal region while it is strongly suppressed around the antinode. The momentum dependence of the single-particle excitation gap shows a striking deviation from the dx-y2--wave symmetry with anomalous enhancement around the antinode in both the superconducting and the pseudogap state. The observed close correlation between the superconducting coherence peak and the pseudogap suggests a substantial contribution of the pseudogap to the anomalous behavior of the gap in the superconducting state.

Strong and complex electron-lattice correlation in optimally doped Bi2Sr2CaCu2O8+delta

We discuss the nature of electron-lattice interaction in optimally doped Bi_{2}Sr_{2}CaCu_{2}O_{8+delta} samples, using the isotope effect (IE) in angle resolved photoemission spectroscopy (ARPES) data. The IE in the ARPES linewidth and the IE in the ARPES dispersion are both quite large, implying a strong electron-lattice correlation. The strength of the electron-lattice interaction is "intermediate," i.e., stronger than the Migdal-Eliashberg regime but weaker than the small polaron regime, requiring a more general picture of the ARPES kink than the commonly used Migdal-Eliashberg picture. The two IEs also imply a complex interaction, due to their strong momentum dependence and their differing sign behaviors. In sum, we propose an intermediate-strength coupling of electrons to localized lattice vibrations via charge density fluctuations.

Electronic structure of strongly correlated d-wave superconductors

We study the electronic structure of a strongly correlated d-wave superconducting state. Combining a renormalized mean field theory with direct calculation of matrix elements, we obtain explicit analytical results for the nodal Fermi velocity upsilon(F), the Fermi wave vector k(F), and the momentum distribution n(k) as a function of hole doping in a Gutzwiller projected d-wave superconductor. We calculate the energy dispersion E(k) and spectral weight of the Gutzwiller-Bogoliubov quasiparticles and find that the spectral weight associated with the quasiparticle excitation at the antinodal point shows a nonmonotonic behavior as a function of doping. Results are compared to angle resolved photoemission spectroscopy of the high-temperature superconductors.

Dopant-induced nanoscale electronic inhomogeneities in Ca(2-x)Sr(x)RuO4

Ca(2-x)Sr(x)RuO4 single crystals with 0.1 < or = x < or = 2.0 have been studied systematically using scanning tunneling microscopy (STM) and spectroscopy, low-energy electron diffraction, and angle resolved photoelectron spectroscopy (ARPES). In contrast with the well-ordered lattice structure, the local density of states at the surface clearly shows a strong doping dependent nanoscale electronic inhomogeneity, regardless of the fact of isovalent substitution. Remarkably, the surface electronic roughness measured by STM and the inverse spectral weight of quasiparticle states determined by ARPES are found to vary with x in the same manner as the bulk in-plane residual resistivity, following the Nordheim rule. For the first time, the surface measurements--especially those with STM--are shown to be in good agreement with the bulk transport results, all clearly indicating a doping-induced electronic disorder in the system.

Gap-inhomogeneity-induced electronic states in superconducting Bi2Sr2CaCu2O(8+delta)

In this Letter, we analyze, using scanning tunneling spectroscopy, the density of electronic states in nearly optimally doped Bi2Sr2CaCu2O(8+delta) in zero magnetic field. Focusing on the superconducting gap, we find patches of what appear to be two different phases in a background of some average gap, one with a relatively small gap and sharp large coherence peaks and one characterized by a large gap with broad weak coherence peaks. We compare these spectra with calculations of the local density of states for a simple phenomenological model in which a 2xi0 x 2xi0 patch with an enhanced or suppressed d-wave gap amplitude is embedded in a region with a uniform average d-wave gap.

Effect of disorder outside the CuO2 planes on Tc of copper oxide superconductors

The effect of disorder on the superconducting transition temperature T(c) of cuprate superconductors is examined. Disorder is introduced into the cation sites in the plane adjacent to the CuO2 planes of two single-layer systems, Bi(2.0)Sr(1.6)Ln(0.4)CuO(6+delta) and La(1.85-y)Nd(y)Sr0.15CuO4. Disorder is controlled by changing rare earth (Ln) ions with a different ionic radius in the former, and by varying the Nd content in the latter with the doped carrier density kept constant. We show that this type of disorder works as weak scatterers in contrast to the in-plane disorder produced by Zn, but remarkably reduces T(c), suggesting novel effects of disorder on high-T(c) superconductivity.

Coincidence of checkerboard charge order and antinodal state decoherence in strongly underdoped superconducting Bi2Sr2CaCu2O8 + delta)

The doping dependence of nanoscale electronic structure in superconducting Bi(2)Sr(2)CaCu(2)O(8 + delta) is studied by scanning tunneling microscopy. At all dopings, the low energy density-of-states modulations are analyzed according to a simple model of quasiparticle interference and found to be consistent with Fermi-arc superconductivity. The superconducting coherence peaks, ubiquitous in near-optimal tunneling spectra, are destroyed with strong underdoping and a new spectral type appears. Exclusively in regions exhibiting this new spectrum, we find local "checkerboard" charge ordering of high energy states, with a wave vector of Q = (+/- 2pi/4.5a(0),0); (0, +/- 2pi/4.5a(0)) +/- 15%. Surprisingly, this spatial ordering of high energy states coexists harmoniously with the low energy Bogoliubov quasiparticle states.

Quasiparticle line shape of Sr2RuO4 and its relation to anisotropic transport

The bulk-representative low-energy spectrum of Sr2RuO4 can be directly measured by angle-resolved photoemission. We find that the quasiparticle spectral line shape of Sr2RuO4 is sensitive to both temperature and momentum. Along the (0,0)-(pi,0) direction, both gamma and beta bands develop a sharp quasiparticle peak near k(F) at low temperatures, but as the temperature increases the spectra quickly lose coherent weight and become broad backgrounds above approximately 130 K, which is the metal-nonmetal crossover temperature, T(M), in the c-axis resistivity. However, spectra along the (0,0)-(pi,pi) direction evolve smoothly across T(M). A simple transport model can describe both in-plane and c-axis resistivity in terms of the quasiparticle line shape. Comparisons are also made to the cuprates, with implications for two dimensionality, magnetic fluctuations, and superconductivity.

BCS-like Bogoliubov quasiparticles in high-T(c) superconductors observed by angle-resolved photoemission spectroscopy

We performed high-resolution angle-resolved photoemission spectroscopy on triple-layered high-T(c) cuprate Bi(2)Sr(2)Ca(2)Cu(3)O(10+delta). We have observed the full energy dispersion (electron and hole branches) of Bogoliubov quasiparticles and determined the coherence factors above and below E(F) as a function of momentum from the spectral intensity as well as from the energy dispersion based on BCS theory. The good quantitative agreement between the experiment and the theoretical prediction suggests the basic validity of BCS formalism in describing the superconducting state of cuprates.

Relating atomic-scale electronic phenomena to wave-like quasiparticle states in superconducting Bi2Sr2CaCu2O8+delta

The electronic structure of simple crystalline solids can be completely described in terms either of local quantum states in real space (r-space), or of wave-like states defined in momentum-space (k-space). However, in the copper oxide superconductors, neither of these descriptions alone may be sufficient. Indeed, comparisons between r-space and k-space studies of Bi2Sr2CaCu2O8+delta (Bi-2212) reveal numerous unexplained phenomena and apparent contradictions. Here, to explore these issues, we report Fourier transform studies of atomic-scale spatial modulations in the Bi-2212 density of states. When analysed as arising from quasiparticle interference, the modulations yield elements of the Fermi-surface and energy gap in agreement with photoemission experiments. The consistency of numerous sets of dispersing modulations with the quasiparticle interference model shows that no additional order parameter is required. We also explore the momentum-space structure of the unoccupied states that are inaccessible to photoemission, and find strong similarities to the structure of the occupied states. The copper oxide quasiparticles therefore apparently exhibit particle-hole mixing similar to that of conventional superconductors. Near the energy gap maximum, the modulations become intense, commensurate with the crystal, and bounded by nanometre-scale domains. Scattering of the antinodal quasiparticles is therefore strongly influenced by nanometre-scale disorder.

Imaging quasiparticle interference in Bi2Sr2CaCu2O8+delta

Scanning tunneling spectroscopy of the high-Tc superconductor Bi2Sr2CaCu2O8+delta reveals weak, incommensurate, spatial modulations in the tunneling conductance. Images of these energy-dependent modulations are Fourier analyzed to yield the dispersion of their wavevectors. Comparison of the dispersions with photoemission spectroscopy data indicates that quasiparticle interference, due to elastic scattering between characteristic regions of momentum-space, provides a consistent explanation for the conductance modulations, without appeal to another order parameter. These results refocus attention on quasiparticle scattering processes as potential explanations for other incommensurate phenomena in the cuprates. The momentum-resolved tunneling spectroscopy demonstrated here also provides a new technique with which to study quasiparticles in correlated materials.

Origin of the peak-dip-hump line shape in the superconducting-state (pi,0) photoemission spectra of Bi2Sr2CaCu2O8

From detailed high-resolution measurements of the photon energy dependence of the (pi,0) superconducting-state photoemission spectrum of the bilayer Bi high-temperature superconductors, we show that the famous peak-dip-hump line shape is dominated by a superposition of spectral features originating from different electronic states which reside at different binding energies, but are each describable by essentially identical single-particle spectral functions. The previously identified bilayer-split CuO2 bands are the culprit: with the "superconducting" peak being due to the antibonding band, while the hump is mainly formed by its bonding bilayer-split counterpart.

Is the onset of high-temperature superconductivity associated with a dimensional crossover?

Angle-resolved ultraviolet photoemission spectroscopy (ARUPS) from high-T(c) superconductors shows an effective-mass renormalization and intense quasiparticle peaks close to the Fermi energy E(F), which change dramatically with temperature as T(c) is crossed. They are attributed to many-body effects, but their precise nature has been controversial until now. We find very similar spectral fingerprints, even with a similar temperature dependence albeit with much higher critical temperature, in a quasi-one-dimensional Br/Pt surface compound. The striking parallels support an interpretation based on spin-charge separation and are consistent with a dimensional crossover taking place at T(c).

Low energy excitation and scaling in Bi(2)Sr(2)Ca(n-1)Cu(n)O(2n+4) (n=1-3): angle-resolved photoemission spectroscopy

Angle-resolved photoemission spectroscopy (ARPES) has been performed on the single- to triple-layered Bi-family high-T (c) superconductors (Bi(2)Sr(2)Ca(n-1)Cu(n)O(2n+4), n=1-3). We found a sharp coherent peak as well as a pseudogap at the Fermi level in the triple-layered compound. Comparison among three compounds has revealed a universal rule that the characteristic energies of superconducting and pseudogap behaviors are scaled with the maximum T (c).

Quasiparticle liquid in the highly overdoped Bi(2)Sr(2)CaCu(2)O(8+delta)

Results from the study of a highly overdoped (OD) Bi(2)Sr(2)CaCu(2)O(8+delta) with a T(c) = 51 K using angle-resolved photoemission spectroscopy are presented. We observe a sharp peak in the spectra near ( pi,0) that persists well above T(c), a nodal self-energy which approaches that seen for the Mo(110) surface state, and a more k-independent line shape at the Fermi surface than the lower-doped cuprates. This allows for a realistic comparison of the lifetime values to the experimental resistivity measurements. These observations point to the validity of the quasiparticle picture for the OD even in the normal state.

Superconductivity-induced transfer of in-plane spectral weight in Bi2Sr2CaCu2O8+delta

Optical data are reported on a spectral weight transfer over a broad frequency range of Bi2Sr2CaCu2O8+delta, when this material became superconducting. Using spectroscopic ellipsometry, we observed the removal of a small amount of spectral weight in a broad frequency band from 10(4) cm(-1) to at least 2 x 10(4) cm(-1), due to the onset of superconductivity. We observed a blue shift of the ab-plane plasma frequency when the material became superconducting, indicating that the spectral weight was transferred to the infrared range. Our observations are in agreement with models in which superconductivity is accompanied by an increased charge carrier spectral weight. The measured spectral weight transfer is large enough to account for the condensation energy in these compounds.

Electronic structure of the trilayer cuprate superconductor Bi(2)Sr(2)Ca(2)Cu(3)O(10+delta)

The low-energy electronic structure of the nearly optimally doped trilayer cuprate superconductor Bi(2)Sr(2)Ca(2)Cu(3)O(10+delta) is investigated by angle-resolved photoemission spectroscopy. The normal state quasiparticle dispersion and Fermi surface and the superconducting d-wave gap and coherence peak are observed and compared with those of single- and bilayer systems. We find that both the superconducting gap magnitude and the relative coherence-peak intensity scale linearly with T(c) for various optimally doped materials.

Antiferromagnetism from phase disordering of a d-wave superconductor

The unbinding of vortex defects in the superconducting condensate with d-wave symmetry at T = 0 is shown to lead to the insulator with incommensurate spin-density-wave order. The transition is similar to the spontaneous generation of the chiral mass in the three-dimensional quantum electrodynamics. A possible relation to recent experiments on underdoped cuprates is discussed.

Coherent quasiparticle weight and its connection to high-T(c) superconductivity from angle-resolved photoemission

We study the doping and temperature dependence of the single-particle coherent weight, z(A), for high- T(c) superconductors Bi(2)Sr(2)CaCu(2)O(8+x) using angle-resolved photoemission. We find that at low temperatures the coherent weight z(A) at (pi,0) is proportional to the carrier concentration x and that the temperature dependence of z(A) is similar to that of the c-axis superfluid density. We show that, for a wide range of carrier concentration, the superconducting transition temperature scales with the product of the low-temperature coherent weight and the maximum superconducting gap.

Projected wave functions and high temperature superconductivity

We study the Hubbard model with parameters relevant to cuprates using variational Monte Carlo for projected d-wave states. For doping 0<x approximately less than or equal to 0.35 we obtain a superconductor whose order parameter Phi(x) tracks the observed nonmonotonic T(c)(x). The variational parameter Delta(var)(x) scales with the (pi,0) "hump" and T* seen in photoemission. Projection leads to incoherence in the spectral function and from the singular behavior of its moments we obtain the nodal quasiparticle weight Z approximately x though the Fermi velocity remains finite as x-->0. The Drude weight D(low) and superfluid density are consistent with experiment and D(low) approximately Z.

Nodal quasiparticles in stripe ordered superconductors

We study the properties of a quasi-one-dimensional superconductor which consists of an alternating array of two inequivalent chains. This model is a simple caricature of a striped high temperature superconductor, and is more generally a theoretically controllable system in which the superconducting state emerges from a non-Fermi-liquid normal state. Even in this limit, " d-wave-like" order parameter symmetry is natural, but the superconducting state can either have a complete gap in the quasiparticle spectrum, or gapless "nodal" quasiparticles. We also find circumstances in which antiferromagnetic order (typically incommensurate) coexists with superconductivity.

Microscopic electronic inhomogeneity in the high-Tc superconductor Bi2Sr2CaCu2O8+x

The parent compounds of the copper oxide high-transition-temperature (high-Tc) superconductors are unusual insulators (so-called Mott insulators). Superconductivity arises when they are 'doped' away from stoichiometry. For the compound Bi2Sr2CaCu2O8+x, doping is achieved by adding extra oxygen atoms, which introduce positive charge carriers ('holes') into the CuO2 planes where the superconductivity is believed to originate. Aside from providing the charge carriers, the role of the oxygen dopants is not well understood, nor is it clear how the charge carriers are distributed on the planes. Many models of high-Tc superconductivity accordingly assume that the introduced carriers are distributed uniformly, leading to an electronically homogeneous system as in ordinary metals. Here we report the presence of an electronic inhomogeneity in Bi2Sr2CaCu2O8+x, on the basis of observations using scanning tunnelling microscopy and spectroscopy. The inhomogeneity is manifested as spatial variations in both the local density of states spectrum and the superconducting energy gap. These variations are correlated spatially and vary on the surprisingly short length scale of approximately 14 A. Our analysis suggests that this inhomogeneity is a consequence of proximity to a Mott insulator resulting in poor screening of the charge potentials associated with the oxygen ions left in the BiO plane after doping, and is indicative of the local nature of the superconducting state.

Bilayer splitting in the electronic structure of heavily overdoped Bi(2)Sr(2)CaCu(2)O(8+delta)

The electronic structure of heavily overdoped Bi(2)Sr(2)CaCu(2)O(8+delta) is investigated by angle-resolved photoemission spectroscopy. The long-sought bilayer band splitting in this two-plane system is observed in both normal and superconducting states, which qualitatively agrees with the bilayer Hubbard model calculations. The maximum bilayer energy splitting is about 88 meV for the normal state feature, while it is only about 20 meV for the superconducting peak.

Scanning tunneling spectroscopy of Bi(2)Sr(2)CuO(6+delta): new evidence for the common origin of the pseudogap and superconductivity

Using scanning tunneling spectroscopy, we investigated the temperature dependence of the quasiparticle density of states of overdoped Bi(2)Sr(2)CuO(6+delta) between 275 mK and 82 K. Below T(c) = 10 K, the spectra show a gap with well-defined coherence peaks at +/-Delta(p) approximately 12 meV, which disappear at T(c). Above T(c), the spectra display a clear pseudogap of the same magnitude, gradually filling up and vanishing at T(*) approximately 68 K. The comparison with Bi(2)Sr(2)CaCu(2)O(8+delta) demonstrates that the pseudogap and the superconducting gap scale with each other, providing strong evidence that they have a common origin.

Superconducting gap and strong in-plane anisotropy in untwinned YBa2Cu3O(7-delta)

With significantly improved sample quality and instrumental resolution, we clearly identify in the ( pi,0) photoemission spectra from YBa(2)Cu(3)O(6.993), in the superconducting state, the long-sought "peak-dip-hump" structure. This advance allows us to investigate the large a-b anisotropy of the in-plane electronic structure including, in particular, a 50% difference in the magnitude of the superconducting gap that scales with the energy position of the hump feature. This anisotropy, likely induced by the presence of the CuO chains, raises serious questions about attempts to quantitatively explain the YBa(2)Cu(3)O(7-delta) data from various experiments using models based on a perfectly square lattice.

Evidence of electron fractionalization from photoemission spectra in the high temperature superconductors

In the normal state of the high temperature superconductors Bi(2)Sr(2)CaCu(2)O(8+delta) and La2(-x)Sr(x)CuO4, and in the related "stripe ordered" material, La(1.25)Nd(0.6)Sr(0.15)CuO4, there is sharp structure in the measured single hole spectral function, A<(k-->,omega), considered as a function of k--> at fixed small binding energy omega. At the same time, as a function of omega at fixed k--> on much of the putative Fermi surface, any structure in A<(k-->,omega), other than the Fermi cutoff, is very broad. This is characteristic of the situation in which there are no stable excitations with the quantum numbers of the electron, as is the case in the one-dimensional electron gas.