Phenomenological models for the gap anisotropy of Bi2Sr2CaCu2O8 as measured by angle-resolved photoemission spectroscopy

Bosonic excitation spectra of superconductingBi2Sr2CaCu2O8+δandYBa2Cu3O6+xextracted from scanning tunneling spectra

A detailed interpretation of scanning tunneling spectra obtained on unconventional superconductors enables one to gain information on the pairing boson. Decisive for this approach are inelastic tunneling events. Due to the lack of momentum conservation in tunneling from or to the sharp tip, those are enhanced in the geometry of a scanning tunneling microscope compared to planar tunnel junctions. This work extends the method of obtaining the bosonic excitation spectrum by deconvolution from tunneling spectra to nodald-wave superconductors. In particular, scanning tunneling spectra of slightly underdopedBi2Sr2CaCu2O8+δwith aTcof 82 K and optimally dopedYBa2Cu3O6+xwith aTcof 92 K reveal a resonance mode in their bosonic excitation spectrum atΩres≈63 meVandΩres≈61 meVrespectively. In both cases, the overall shape of the bosonic excitation spectrum is indicative of predominant spin scattering with a resonant mode atΩres<2Δand overdamped spin fluctuations for energies larger than 2Δ. To perform the deconvolution of the experimental data, we implemented an efficient iterative algorithm that significantly enhances the reliability of our analysis.

Unusual Low-Energy Collective Charge Excitations in High-Tc Cuprate Superconductors

Despite decades of intensive experimental and theoretical efforts, the physics of cuprate high-temperature superconductors in general, and, in particular, their normal state, is still under debate. Here, we report our investigation of low-energy charge excitations in the normal state. We find that the peculiarities of the electronic band structure at low energies have a profound impact on the nature of the intraband collective modes. It gives rise to a new kind of mode with huge intensity and non-Lorentzian spectral function in addition to well-known collective excitations like conventional plasmons and spin fluctuation. We predict two such modes with maximal spectral weight in the nodal and antinodal directions. Additionally, we found a long-living quasi-one-dimensional plasmon becoming an intense soft mode over an extended momentum range along the antinodal direction. These modes might explain some of the resonant inelastic X-ray scattering spectroscopy data.

Electronic and vibrational properties of the highTcsuperconductor Bi2Sr2CaCu2O8: anab initiostudy

In this work,ab initiocalculations were performed in order to study the vibrational spectra of the Bi₂Sr₂CaCu₂O₈(Bi2212) compound. A structural modulation correction on some atomic positions, producing a distorted structure with lower symmetry, is used for the calculation. We argue that this correction allows to account for an average effect of the incommensurate superstructure, generating a more accurate representation of the real unit cell observed in this compound. A complete and conclusive vibrational assignment is performed, discussing the correspondences with previous experimental and theoretical reports. A brief analysis of the electronic density of states and band structure comparing the tetragonal and distorted unit cell is also included.

Spin Susceptibility above the Superfluid Onset in Ultracold Fermi Gases

Ultracold atomic Fermi gases can be tuned to interact strongly, which produces a display of spectroscopic signatures above the superfluid transition reminiscent of the pseudogap in cuprates. However, the extent of the analogy can be questioned since many thermodynamic quantities in the low temperature spin-imbalanced normal state can be described successfully using Fermi liquid theory. Here we present spin susceptibility measurements across the interaction strength-temperature phase diagram using a novel radio frequency technique with ultracold ^{6}Li gases. For all significant interaction strengths and at all temperatures we find the spin susceptibility is reduced compared to the equivalent value for a noninteracting Fermi gas. At unitarity, we can use the local density approximation to extract the integrated spin susceptibility for the uniform gas as a function of temperature, which at high temperatures is generally less than theoretically predicted. At low temperatures, our data lie within the range of theoretical predictions, although we can also describe the entire curve using a very simple one-parameter mean field model with monotonically increasing spin susceptibility.

On the Remarkable Superconductivity of FeSe and Its Close Cousins

Emergent electronic phenomena in iron-based superconductors have been at the forefront of condensed matter physics for more than a decade. Much has been learned about the origins and intertwined roles of ordered phases, including nematicity, magnetism, and superconductivity, in this fascinating class of materials. In recent years, focus has been centered on the peculiar and highly unusual properties of FeSe and its close cousins. This family of materials has attracted considerable attention due to the discovery of unexpected superconducting gap structures, a wide range of superconducting critical temperatures, and evidence for nontrivial band topology, including associated spin-helical surface states and vortex-induced Majorana bound states. Here, we review superconductivity in iron chalcogenide superconductors, including bulk FeSe, doped bulk FeSe, FeTe1−xSex, intercalated FeSe materials, and monolayer FeSe and FeTe1−xSex on SrTiO3. We focus on the superconducting properties, including a survey of the relevant experimental studies, and a discussion of the different proposed theoretical pairing scenarios. In the last part of the paper, we review the growing recent evidence for nontrivial topological effects in FeSe-related materials, focusing again on interesting implications for superconductivity.

Phase diagram of Bi2Sr2CaCu2O8+δ revisited

In cuprate superconductors, the doping of carriers into the parent Mott insulator induces superconductivity and various other phases whose characteristic temperatures are typically plotted versus the doping level p. In most materials, p cannot be determined from the chemical composition, but it is derived from the superconducting transition temperature, Tc, using the assumption that the Tc dependence on doping is universal. Here, we present angle-resolved photoemission studies of Bi2Sr2CaCu2O8+δ, cleaved and annealed in vacuum or in ozone to reduce or increase the doping from the initial value corresponding to Tc = 91 K. We show that p can be determined from the underlying Fermi surfaces and that in-situ annealing allows mapping of a wide doping regime, covering the superconducting dome and the non-superconducting phase on the overdoped side. Our results show a surprisingly smooth dependence of the inferred Fermi surface with doping. In the highly overdoped regime, the superconducting gap approaches the value of 2Δ0 = (4 ± 1)kBTc.

Anomalous density fluctuations in a strange metal

A central mystery in high-temperature superconductivity is the origin of the so-called strange metal (i.e., the anomalous conductor from which superconductivity emerges at low temperature). Measuring the dynamic charge response of the copper oxides, [Formula: see text], would directly reveal the collective properties of the strange metal, but it has never been possible to measure this quantity with millielectronvolt resolution. Here, we present a measurement of [Formula: see text] for a cuprate, optimally doped Bi_2.1Sr_1.9CaCu₂O_8+x (T_c = 91 K), using momentum-resolved inelastic electron scattering. In the medium energy range 0.1-2 eV relevant to the strange metal, the spectra are dominated by a featureless, temperature- and momentum-independent continuum persisting to the electronvolt energy scale. This continuum displays a simple power-law form, exhibiting q² behavior at low energy and q²/ω² behavior at high energy. Measurements of an overdoped crystal (T_c = 50 K) showed the emergence of a gap-like feature at low temperature, indicating deviation from power law form outside the strange-metal regime. Our study suggests the strange metal exhibits a new type of charge dynamics in which excitations are local to such a degree that space and time axes are decoupled.

Particle-Hole Asymmetry in the Cuprate Pseudogap Measured with Time-Resolved Spectroscopy

One of the most puzzling features of high-temperature cuprate superconductors is the pseudogap state, which appears above the temperature at which superconductivity is destroyed. There remain fundamental questions regarding its nature and its relation to superconductivity. But to address these questions, we must first determine whether the pseudogap and superconducting states share a common property: particle-hole symmetry. We introduce a new technique to test particle-hole symmetry by using laser pulses to manipulate and measure the chemical potential on picosecond time scales. The results strongly suggest that the asymmetry in the density of states is inverted in the pseudogap state, implying a particle-hole asymmetric gap. Independent of interpretation, these results can test theoretical predictions of the density of states in cuprates.

Classification of charge density waves based on their nature

The concept of a charge density wave (CDW) permeates much of condensed matter physics and chemistry. CDWs have their origin rooted in the instability of a one-dimensional system described by Peierls. The extension of this concept to reduced dimensional systems has led to the concept of Fermi surface nesting (FSN), which dictates the wave vector [Formula: see text] of the CDW and the corresponding lattice distortion. The idea is that segments of the Fermi contours are connected by [Formula: see text], resulting in the effective screening of phonons inducing Kohn anomalies in their dispersion at [Formula: see text], driving a lattice restructuring at low temperatures. There is growing theoretical and experimental evidence that this picture fails in many real systems and in fact it is the momentum dependence of the electron-phonon coupling (EPC) matrix element that determines the characteristic of the CDW phase. Based on the published results for the prototypical CDW system 2H-NbSe2, we show how well the [Formula: see text]-dependent EPC matrix element, but not the FSN, can describe the origin of the CDW. We further demonstrate a procedure of combing electronic band and phonon measurements to extract the EPC matrix element, allowing the electronic states involved in the EPC to be identified. Thus, we show that a large EPC does not necessarily induce the CDW phase, with Bi2Sr2CaCu2O8+δ as the example, and the charge-ordered phenomena observed in various cuprates are not driven by FSN or EPC. To experimentally resolve the microscopic picture of EPC will lead to a fundamental change in the way we think about, write about, and classify charge density waves.

The Origin of Tc Enhancement in Heterostructure Cuprate Superconductors

Recent experiments on heterostructures composed of two or more films of cuprate superconductors of different oxygen doping levels have shown a remarkable Tc enhancement (up to 50%) relative to single compound films. We provide a simple explanation of the enhancement which arises naturally from a collection of experimental works. We show that the enhancement could be caused by a structural change in the lattice, namely an increase in the distance of the apical oxygen from the copper-oxygen plane. This increase modifies the effective off-site interaction in the plane which in turn enhances the d-wave superconductivity order parameter. To illustrate this point we study the extended Hubbard model using the fluctuation exchange approximation.

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.

Direct determination of the electron-phonon coupling matrix element in a correlated system

High-resolution electron energy loss spectroscopy measurements have been carried out on an optimally doped cuprate Bi(2)Sr(2)CaCu(2)O(8+δ). The momentum-dependent energy and linewidth of an A1 optical phonon were obtained. Based on these data as well as detailed knowledge of the electronic structure, we developed a scheme to determine the electron-phonon coupling (EPC) matrix element related to a specific phonon mode. Such an approach is general and applicable to elucidating the full structure of EPC in a system with anisotropic electronic structure.

High-energy scale revival and giant kink in the dispersion of a cuprate superconductor

In the present photoemission study of a cuprate superconductor Bi1.74Pb0.38Sr1.88CuO6+delta, we discovered a large scale dispersion of the lowest band, which unexpectedly follows the band structure calculation very well. Similar behavior observed in blue bronze and the Mott insulator Ca2CuO2Cl2 suggests that the origin of hopping-dominated dispersion in an overdoped cuprate might be quite complicated. A giant kink in the dispersion is observed, and the complete self-energy containing all interaction information is extracted for a doped cuprate. These results recovered significant missing pieces in our current understanding of the electronic structure of cuprates.

Effects of pairing potential scattering on Fourier-transformed inelastic tunneling spectra of high-Tc cuprate superconductors with bosonic modes

Recent scanning tunneling microscopy (STM) experimentally observed strong gap inhomogeneity in Bi2Sr2CaCu2O(8+delta) (BSCCO). We argue that disorder in the pair potential underlies the gap inhomogeneity, and investigate its role in the Fourier-transformed inelastic tunneling spectra as revealed in the STM. We find that the random pair potential induces unique q-space patterns in the local density of states (LDOS) of a d-wave superconductor. We consider the effects of electron coupling to various bosonic modes and find the pattern of LDOS modulation due to coupling to the B(1g) phonon mode to be consistent with the one observed in the inelastic electron tunnneling STM experiment in BSCCO. These results suggest strong electron-lattice coupling as an essential part of the superconducting state in high-Tc materials.

Tunneling spectra of layered strongly correlated d-wave superconductors

Tunneling conductance experiments on cuprate superconductors exhibit a large diversity of spectra that appear in different nanosized regions of inhomogeneous samples. In this Letter, we use a mean-field approach to the tt't''J model in order to address the features in these spectra that deviate from the BCS paradigm, namely, the bias sign asymmetry at high bias, the generic lack of evidence for the van Hove singularity, and the absence of coherence peaks at low dopings. We conclude that these features can be reproduced in homogeneous layered d-wave superconductors solely due to a proximate Mott insulating transition. We also establish the connection between the above tunneling spectral features and the strong renormalization of the electron dispersion around (0, pi) and (pi, 0) and the momentum space anisotropy of electronic states observed in angle-resolved photoemission spectroscopy experiments.

Frequency-dependent thermal response of the charge system and the restricted sum rules of La2-xSrxCuO4

In La2-xSrxCuO4 (LSCO) the spectral weight W=integralOmega0sigma(ab)1(omega,T)domega [where sigma(ab)1(omega,T) is the ab-plane conductivity] obeys the same law W=W0-BOmegaT2 as in a conventional metal such as gold, for any Omega up to the plasma edge. However, in LSCO BOmega points toward correlation effects and, unlike in gold, is related to an energy scale tT<<t0 approximately W0. The Ferrell-Glover-Tinkham sum rule is fulfilled in LSCO superconductors for Omega greater than or approximately equal to 2000 cm(-1).

Local ordering in the pseudogap state of the high-Tc superconductor Bi2Sr2CaCu2O(8+delta)

We report atomic-scale characterization of the pseudogap state in a high-Tc superconductor, Bi2Sr2CaCu2O(8+delta). The electronic states at low energies within the pseudogap exhibit spatial modulations having an energy-independent incommensurate periodicity. These patterns, which are oriented along the copper-oxygen bond directions, appear to be a consequence of an electronic ordering phenomenon, the observation of which correlates with the pseudogap in the density of electronic states. Our results provide a stringent test for various ordering scenarios in the cuprates, which have been central in the debate on the nature of the pseudogap and the complex electronic phase diagram of these compounds.

Dispersion anomalies in bilayer cuprates and the odd symmetry of the magnetic resonance

We demonstrate that recent angle resolved photoemission data in bilayer cuprate superconductors imply that scattering of electrons between bonding and antibonding bands is strong compared to scattering within these bands. As a consequence, the resulting data can be reproduced only by a model which assumes that the electrons are interacting with a bosonic mode that is odd with respect to the layer indices. This odd symmetry is a unique property of the magnetic resonance observed by inelastic neutron scattering.

Density of states in high- T(c) superconductor vortices

We calculated the electronic structure of a vortex in a pseudogapped superconductor within a model featuring strong correlations. With increasing strength of the correlations, the BCS core states are suppressed and the spectra inside and outside the core become similar. If the correlations are short range, we find new core states in agreement with the observations in YBa2Cu3O7-delta and Bi2Sr2CaCu2O8+delta. Our results point to a common phenomenology for these two systems and indicate that normal-state correlations survive below T(c) without taking part in the overall phase coherence.

Neutron resonance: modeling photoemission and tunneling data in the superconducting state of Bi2Sr2CaCu2O8+delta

Motivated by neutron scattering data, we develop a model of electrons interacting with a magnetic resonance and use it to analyze angle resolved photoemission and tunneling data in the superconducting state of Bi(2)Sr(2)CaCu(2)O(8+delta). We not only can explain the peak-dip-hump structure observed near the (pi,0) point, and its particle-hole asymmetry as seen in superconductor-insulator-normal tunneling spectra, but also its evolution throughout the Brillouin zone, including a velocity "kink" near the d-wave node.

Fermi surface of Bi2Sr2CaCu2O8

We study the Fermi surface of Bi2Sr2CaCu2O8 using angle resolved photoemission spectroscopy (ARPES) with a momentum resolution of approximately 0.01 of the Brillouin zone. We show that, contrary to recent suggestions, the ARPES derived Fermi surface is a large hole barrel centered at (pi,pi), independent of the incident photon energy. We caution that the photon energy and k dependence of the matrix elements, if not properly accounted for, can lead to misinterpretation of ARPES intensities.