Physics. Is there glue in cuprate superconductors?

Evolution of the Magnetic Excitations in Electron-Doped La_{2-x}Ce_{x}CuO_{4}

We investigated the high energy spin excitations in electron-doped La_{2-x}Ce_{x}CuO_{4}, a cuprate superconductor, by resonant inelastic x-ray scattering (RIXS) measurements. Efforts were paid to disentangle the paramagnon signal from non-spin-flip spectral weight mixing in the RIXS spectrum at Q_{∥}=(0.6π,0) and (0.9π,0) along the (1 0) direction. Our results show that, for doping level x from 0.07 to 0.185, the variation of the paramagnon excitation energy is marginal. We discuss the implication of our results in connection with the evolution of the electron correlation strength in this system.

Ubiquitous coexisting electron-mode couplings in high-temperature cuprate superconductors

In conventional superconductors, electron-phonon coupling plays a dominant role in generating superconductivity. In high-temperature cuprate superconductors, the existence of electron coupling with phonons and other boson modes and its role in producing high-temperature superconductivity remain unclear. The evidence of electron-boson coupling mainly comes from angle-resolved photoemission (ARPES) observations of [Formula: see text]70-meV nodal dispersion kink and [Formula: see text]40-meV antinodal kink. However, the reported results are sporadic and the nature of the involved bosons is still under debate. Here we report findings of ubiquitous two coexisting electron-mode couplings in cuprate superconductors. By taking ultrahigh-resolution laser-based ARPES measurements, we found that the electrons are coupled simultaneously with two sharp modes at [Formula: see text]70meV and [Formula: see text]40meV in different superconductors with different dopings, over the entire momentum space and at different temperatures above and below the superconducting transition temperature. These observations favor phonons as the origin of the modes coupled with electrons and the observed electron-mode couplings are unusual because the associated energy scales do not exhibit an obvious energy shift across the superconducting transition. We further find that the well-known "peak-dip-hump" structure, which has long been considered a hallmark of superconductivity, is also omnipresent and consists of "peak-double dip-double hump" finer structures that originate from electron coupling with two sharp modes. These results provide a unified picture for the [Formula: see text]70-meV and [Formula: see text]40-meV energy scales and their evolutions with momentum, doping and temperature. They provide key information to understand the origin of these energy scales and their role in generating anomalous normal state and high-temperature superconductivity.

Anomalous Ferromagnetism of quasiparticle doped holes in cuprate heterostructures revealed using resonant soft X-ray magnetic scattering

We report strong ferromagnetism of quasiparticle doped holes both within the ab-plane and along the c-axis of Cu-O planes in low-dimensional Au/d-La_1.8Ba_0.2CuO₄/LaAlO₃(001) heterostructures (d = 4, 8 and 12 unit-cells) using resonant soft X-ray and magnetic scattering together with X-ray magnetic circular dichroism. Interestingly, ferromagnetism is stronger at a hole doped peak and at an upper Hubbard band of O with spin-polarization degree as high as 40%, revealing strong ferromagnetism of Mottness. For in-ab-plane spin-polarizations, the spin of doped holes in O2p-Cu3d-O2p is a triplet state yielding strong ferromagnetism. For out-of-ab-plane spin-polarization, while the spins of doped holes in both O2p-O2p and Cu3d-Cu3d are triplet states, the spin of doped holes in Cu3d-O2p is a singlet state yielding ferrimagnetism. A ferromagnetic-(002) Bragg-peak of the doped holes is observed and enhanced as a function of d revealing strong ferromagnetism coupling between Cu-O layers along the c-axis.

High-T c Cuprates: a Story of Two Electronic Subsystems

A review of the phenomenology and microscopy of cuprate superconductors is presented, with particular attention to universal conductance features, which reveal the existence of two electronic subsystems. The overall electronic system consists of 1 + p charges, where p is the doping. At low dopings, exactly one hole is localized per planar copper-oxygen unit, while upon increasing doping and temperature, the hole is gradually delocalized and becomes itinerant. Remarkably, the itinerant holes exhibit identical Fermi liquid character across the cuprate phase diagram. This universality enables a simple count of carrier density and yields comprehensive understanding of the key features in the normal and superconducting state. A possible superconducting mechanism is presented, compatible with the key experimental facts. The base of this mechanism is the interaction of fast Fermi liquid carriers with localized holes. A change in the microscopic nature of chemical bonding in the copper oxide planes, from ionic to covalent, is invoked to explain the phase diagram of these fascinating compounds.

Fermi blockade of the strong electron-phonon interaction in modelled optimally doped high temperature superconductors

We study how manifestations of strong electron-phonon interaction depend on the carrier concentration by solving the two-dimensional Holstein model for the spin-polarized fermions using an approximation free bold-line diagrammatic Monte Carlo method. We show that the strong electron-phonon interaction, obviously present at very small Fermion concentration, is masked by the Fermi blockade effects and Migdal's theorem to the extent that it manifests itself as moderate one at large carriers densities. Suppression of strong electron-phonon interaction fingerprints is in agreement with experimental observations in doped high temperature superconductors.

Critical Nature of the Ni Spin State in Doped NdNiO_{2}

Superconductivity with T_{c}≈15  K was recently found in doped NdNiO_{2}. The Ni^{1+}O_{2} layers are expected to be Mott insulators, so hole doping should produce Ni^{2+} with S=1, incompatible with robust superconductivity. We show that the NiO_{2} layers fall inside a critical region where the large pd hybridization favors a singlet ^{1}A_{1} hole-doped state like in CuO_{2}. However, we find that the superexchange is about one order smaller than in cuprates, thus a magnon "glue" is very unlikely and another mechanism needs to be found.

Experimental Determination of Momentum-Resolved Electron-Phonon Coupling

We provide a novel experimental method to quantitatively estimate the electron-phonon coupling and its momentum dependence from resonant inelastic x-ray scattering (RIXS) spectra based on the detuning of the incident photon energy away from an absorption resonance. We apply it to the cuprate parent compound NdBa_{2}Cu_{3}O_{6} and find that the electronic coupling to the oxygen half-breathing phonon branch is strongest at the Brillouin zone boundary, where it amounts to ∼0.17  eV, in agreement with previous studies. In principle, this method is applicable to any absorption resonance suitable for RIXS measurements and will help to define the contribution of lattice vibrations to the peculiar properties of quantum materials.

Emergence of superconductivity from fully incoherent normal state in an iron-based superconductor (Ba0.6K0.4)Fe2As2

In unconventional superconductors, it is generally believed that understanding the physical properties of the normal state is a pre-requisite for understanding the superconductivity mechanism. In conventional superconductors like niobium or lead, the normal state is a Fermi liquid with a well-defined Fermi surface and well-defined quasipartcles along the Fermi surface. Superconductivity is realized in this case by the Fermi surface instability in the superconducting state and the formation and condensation of the electron pairs (Cooper pairing). The high temperature cuprate superconductors, on the other hand, represent another extreme case that superconductivity can be realized in the underdoped region where there is neither well-defined Fermi surface due to the pseudogap formation nor quasiparticles near the antinodal regions in the normal state. Here we report a novel scenario that superconductivity is realized in a system with well-defined Fermi surface but without quasiparticles along the Fermi surface in the normal state. High resolution laser-based angle-resolved photoemission measurements have been performed on an optimally-doped iron-based superconductor (Ba_0.6K_0.4)Fe₂As₂. We find that, while sharp superconducting coherence peaks emerge in the superconducting state on the hole-like Fermi surface sheets, no quasiparticle peak is present in the normal state. Its electronic behaviours deviate strongly from a Fermi liquid system. The superconducting gap of such a system exhibits an unusual temperature dependence that it is nearly a constant in the superconducting state and abruptly closes at T_c. These observations have provided a new platform to study unconventional superconductivity in a non-Fermi liquid system.

Fully gapped d-wave superconductivity in CeCu2Si2

Identifying the gap structure of superconductors is vital for understanding the underlying pairing mechanism of the Cooper pairs. The first heavy fermion superconductor to be discovered, CeCu₂Si₂, was thought to be a d-wave superconductor with gap nodes, until recent specific heat measurements provided evidence that the gap is fully open across the Fermi surface. We propose a resolution to this puzzle from measurements of the London penetration depth, which give further evidence for fully gapped superconductivity. We analyze the data using a d-wave band-mixing pairing model, which leads to a fully open superconducting gap. Our model accounts well for the penetration depth and specific heat data, while reconciling the nodeless and sign-changing nature of the gap function.

The nature of the pairing symmetry of the first heavy fermion superconductor CeCu₂Si₂ has recently become the subject of controversy. While CeCu₂Si₂ was generally believed to be a d-wave superconductor, recent low-temperature specific heat measurements showed evidence for fully gapped superconductivity, contrary to the nodal behavior inferred from earlier results. Here, we report London penetration depth measurements, which also reveal fully gapped behavior at very low temperatures. To explain these seemingly conflicting results, we propose a fully gapped d+d band-mixing pairing state for CeCu₂Si₂, which yields very good fits to both the superfluid density and specific heat, as well as accounting for a sign change of the superconducting order parameter, as previously concluded from inelastic neutron scattering results.

Entropic Origin of Pseudogap Physics and a Mott-Slater Transition in Cuprates

We propose a new approach to understand the origin of the pseudogap in the cuprates, in terms of bosonic entropy. The near-simultaneous softening of a large number of different q-bosons yields an extended range of short-range order, wherein the growth of magnetic correlations with decreasing temperature T is anomalously slow. These entropic effects cause the spectral weight associated with the Van Hove singularity (VHS) to shift rapidly and nearly linearly toward half filling at higher T, consistent with a picture of the VHS driving the pseudogap transition at a temperature ~T*. As a byproduct, we develop an order-parameter classification scheme that predicts supertransitions between families of order parameters. As one example, we find that by tuning the hopping parameters, it is possible to drive the cuprates across a transition between Mott and Slater physics, where a spin-frustrated state emerges at the crossover.

Glue function of optimally and overdoped cuprates from inversion of the Raman spectra

We address the issue of identifying the mediators of effective interactions in cuprates superconductors. Specifically, we use inversion theory to analyze Raman spectra of optimally and over-doped La2-x Sr x CuO4 samples. This allows us to extract the so-called glue function without making any a priori assumption based on any specific model. We use instead two different techniques, namely the singular value decomposition and a multi-rectangle decomposition. With both techniques we find consistent results showing that: (i) two distinct excitations are responsible for the glue function, which have completely different doping dependence. One excitation becomes weak above optimal doping, where on the contrary the other keeps (or even slightly increases) its strength; (ii) there is a marked temperature dependence on the weight and spectral distribution of these excitations, which therefore must have a somewhat critical character. It is quite natural to identify and characterize these two distinct excitations as damped antiferromagnetic spin waves and damped charge density waves, respectively. This sets the stage for a scenario in which superconductivity is concomitant and competing with a charge ordering instability.

Electron pairing in designer materials: a novel strategy for a negative effective Hubbard U

We propose a set of design rules with a model Hamiltonian that allows electrons to form attracting pairs through the exploitation of a new combination of resonant band alignment and Coulombic repulsion. The pair bands and single particle bands in various lattices are calculated and compared in energy, and regions of net attraction are identified. This work provides guidelines for the construction of molecular systems, nanocrystals, and nanoparticle arrays with the potential for superconductivity.

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.

Nature of strong hole pairing in doped Mott antiferromagnets

Cooper pairing instability in a Fermi liquid is well understood by the BCS theory, but pairing mechanism for doped Mott insulators still remains elusive. Previously it has been shown by density matrix renormalization group (DMRG) method that a single doped hole is always self-localized due to the quantum destructive interference of the phase string signs hidden in the t-J ladders. Here we report a DMRG investigation of hole binding in the same model, where a novel pairing-glue scheme beyond the BCS realm is discovered. Specifically, we show that, in addition to spin pairing due to superexchange interaction, the strong frustration of the phase string signs on the kinetic energy gets effectively removed by pairing the charges, which results in strong binding of two holes. By contrast, if the phase string signs are "switched off" artificially, the pairing strength diminishes significantly even if the superexchange coupling remains the same. In the latter, unpaired holes behave like coherent quasiparticles with pairing drastically weakened, whose sole origin may be attributed to the resonating-valence-bond (RVB) pairing of spins. Such non-BCS pairing mechanism is therefore beyond the RVB picture and may shed important light on the high-T(c) cuprate superconductors.

Superconductivity at the border of electron localization and itinerancy

The superconducting state of iron pnictides and chalcogenides exists at the border of anti-ferromagnetic order. Consequently, these materials could provide clues about the relationship between magnetism and unconventional superconductivity. One explanation, motivated by the so-called bad metal behaviour of these materials proposes that magnetism and superconductivity develop out of quasi-localized magnetic moments that are generated by strong electron-electron correlations. Another suggests that these phenomena are the result of weakly interacting electron states that lie on nested Fermi surfaces. Here we address the issue by comparing the newly discovered alkaline iron selenide superconductors, which exhibit no Fermi-surface nesting, to their iron pnictide counterparts. We show that the strong-coupling approach leads to similar pairing amplitudes in these materials, despite their different Fermi surfaces. We also find that the pairing amplitudes are largest at the boundary between electronic localization and itinerancy, suggesting that new superconductors might be found in materials with similar characteristics.

Kinks in the σ band of graphene induced by electron-phonon coupling

Angle-resolved photoemission spectroscopy reveals pronounced kinks in the dispersion of the σ band of graphene. Such kinks are usually caused by the combination of a strong electron-boson interaction and the cutoff in the Fermi-Dirac distribution. They are therefore not expected for the σ band of graphene that has a binding energy of more than ≈3.5 eV. We argue that the observed kinks are indeed caused by the electron-phonon interaction, but the role of the Fermi-Dirac distribution cutoff is assumed by a cutoff in the density of σ states. The existence of the effect suggests a very weak coupling of holes in the σ band not only to the π electrons of graphene but also to the substrate electronic states. This is confirmed by the presence of such kinks for graphene on several different substrates that all show a strong coupling constant of λ≈1.

Angle and frequency dependence of self-energy from spin fluctuation mediated d-wave pairing for high temperature superconductors

We investigated the characteristics of spin fluctuation mediated superconductivity employing the Eliashberg formalism. The effective interaction between electrons was modeled in terms of the spin susceptibility measured by inelastic neutron scattering experiments on single crystal La(2-x)Sr(x)CuO4 superconductors. The diagonal self-energy and off-diagonal self-energy were calculated by solving the coupled Eliashberg equation self-consistently for the chosen spin susceptibility and tight-binding dispersion of electrons. The full momentum and frequency dependence of the self-energy is presented for optimally doped, overdoped, and underdoped LSCO cuprates in a superconductive state. These results may be compared with the experimentally deduced self-energy from ARPES experiments.

Coexistence of two sharp-mode couplings and their unusual momentum dependence in the superconducting state of Bi2Sr2CaCu2O(8+δ) revealed by laser-based angle-resolved photoemission

High-resolution laser-based angle-resolved photoemission measurements have been carried out on Bi2Sr2CaCu2O(8+δ) (Bi2212) superconductors to investigate momentum dependence of electron coupling with collective excitations (modes). Two coexisting energy scales are clearly revealed over a large momentum space for the first time in the superconducting state of the overdoped Bi2212 superconductor. These two energy scales exhibit distinct momentum dependence: one keeps its energy near 78 meV over a large momentum space while the other changes its energy from ∼40  meV near the antinodal region to ∼70  meV near the nodal region. These observations provide a new picture on momentum evolution of electron-boson coupling in Bi2212 that electrons are coupled with two sharp modes simultaneously over a large momentum space in the superconducting states. Their unusual momentum dependence poses a challenge to our current understanding of electron-mode-coupling and its role for high-temperature superconductivity in cuprate superconductors.

Coupling of a high-energy excitation to superconducting quasiparticles in a cuprate from coherent charge fluctuation spectroscopy

Dynamical information on spin degrees of freedom of proteins or solids can be obtained by NMR and electron spin resonance. A technique with similar versatility for charge degrees of freedom and their ultrafast correlations could move the understanding of systems like unconventional superconductors forward. By perturbing the superconducting state in a high-T c cuprate, using a femtosecond laser pulse, we generate coherent oscillations of the Cooper pair condensate that can be described by an NMR/electron spin resonance formalism. The oscillations are detected by transient broad-band reflectivity and are found to resonate at the typical scale of Mott physics (2.6 eV), suggesting the existence of a nonretarded contribution to the pairing interaction, as in unconventional (non-Migdal–Eliashberg) theories.

Mechanism for explaining differences in the order parameters of FeAs-based and FeP-based pnictide superconductors

We put forward a scenario that explains the difference between the order-parameter character in arsenide (As) and phosphorous (P) iron-based superconductors. Using functional renormalization group to analyze it in detail, we find that nodal superconductivity on the electron pockets (hole pocket gaps are always nodeless) can naturally appear when the hole pocket at (π,π) in the unfolded Brillouin zone is absent, as is the case in LaOFeP. There, electron-electron interactions render the gap on the electron pockets softly nodal (of s(±) form). When the pocket of d(xy) orbital character is present, intraorbital interactions with the d(xy) part of the electron Fermi surface drives the superconductivity nodeless.

Eliashberg analysis of tunneling experiments: support for the pairing glue hypothesis in cuprate superconductors

Evidence for the validity of the pairing glue interpretation of high temperature superconductivity is presented using a modified Eliashberg analysis of experimental superconductor-insulator-superconductor (SIS) tunneling data in B2Sr2CaCu2O8 (Bi2212) over a wide range of doping. This is accomplished by extracting detailed information on the diagonal and anomalous contributions to the quasiparticle self-energy. In particular, a comparison of the imaginary part of the anomalous self-energy ImΦ(ω) and the pairing glue spectral function α2F(ω) used in the model is consistent with Hubbard model simulations in the literature. In addition, the real part of the diagonal self-energy for optimal doped Bi2212 bears a strong resemblance to that obtained from photoemission experiments.

Magnetism and pairing of two-dimensional trapped fermions

The emergence of local phases in a trapped two-component Fermi gas in an optical lattice is studied using quantum Monte Carlo simulations. We treat temperatures that are comparable to or lower than those presently achievable in experiments and large enough systems that both magnetic and paired phases can be detected by inspection of the behavior of suitable short-range correlations. We use the latter to suggest the interaction strength and temperature range at which experimental observation of incipient magnetism and d-wave pairing are more likely and evaluate the relation between entropy and temperature in two-dimensional confined fermionic systems.

First-principles prediction of doped graphane as a high-temperature electron-phonon superconductor

We predict by first-principles calculations that p-doped graphane is an electron-phonon superconductor with a critical temperature above the boiling point of liquid nitrogen. The unique strength of the chemical bonds between carbon atoms and the large density of electronic states at the Fermi energy arising from the reduced dimensionality give rise to a giant Kohn anomaly in the optical phonon dispersions and push the superconducting critical temperature above 90 K. As evidence of graphane was recently reported, and doping of related materials such as graphene, diamond, and carbon nanostructures is well established, superconducting graphane may be feasible.

Evolution of the dynamical pairing across the phase diagram of a strongly correlated high-temperature superconductor

We study the dynamics of the Cooper pairing across the T = 0 phase diagram of the two-dimensional Hubbard model, relevant for high-temperature superconductors, using a cluster extension of dynamical mean-field theory. We find that the superconducting pairing function evolves from an unconventional form in the overdoped region into a more conventional boson-mediated retarded form in the underdoped region of the phase diagram. The boson, however, promotes the rise of a pseudogap in the electron density of states rather than a superconducting gap as in the standard theory of superconductivity. We discuss our results in terms of Mott-related phenomena, and we show that they can be observed in tunneling experiments.

Exchange boson dynamics in cuprates: optical conductivity of HgBa_2CuO_4+delta

The electron-boson spectral density function I;{2}chi(Omega) responsible for carrier scattering of the high temperature superconductor HgBa_{2}CuO_{4+delta} (T_{c}=90 K) is calculated from new data on the optical scattering rate. A maximum entropy technique is used. Published data on HgBa_{2}Ca_{2}Cu_{3}O_{8+delta} (T_{c}=130 K) are also inverted and these new results are put in the context of other known cases. All spectra (with two notable exceptions) show a peak at an energy (Omega_{r}) proportional to the superconducting transition temperature Omega_{r} approximately 6.3k_{B}T_{c}. This charge channel relationship follows closely the magnetic resonance seen by polarized neutron scattering, Omega_{r};{neutron} approximately 5.4k_{B}T_{c}. The amplitudes of both peaks decrease strongly with increasing temperature. In some cases, the peak at Omega_{r} is weak and the spectrum can have additional maxima and a background extending up to several hundred meV.

Direct role of structural dynamics in electron-lattice coupling of superconducting cuprates

The mechanism of electron pairing in high-temperature superconductors is still the subject of intense debate. Here, we provide direct evidence of the role of structural dynamics, with selective atomic motions (buckling of copper-oxygen planes), in the anisotropic electron-lattice coupling. The transient structures were determined using time-resolved electron diffraction, following carrier excitation with polarized femtosecond heating pulses, and examined for different dopings and temperatures. The deformation amplitude reaches 0.5% of the c axis value of 30 A when the light polarization is in the direction of the copper-oxygen bond, but its decay slows down at 45 degrees. These findings suggest a selective dynamical lattice involvement with the anisotropic electron-phonon coupling being on a time scale (1-3.5 ps depending on direction) of the same order of magnitude as that of the spin exchange of electron pairing in the high-temperature superconducting phase.

Dynamics of the pairing interaction in the hubbard and t-J models of high-temperature superconductors

The question of whether one should speak of a "pairing glue" in the Hubbard and t-J models is basically a question about the dynamics of the pairing interaction. If the dynamics of the pairing interaction arises from virtual states, whose energies correspond to the Mott gap, and give rise to the exchange coupling J, the interaction is instantaneous on the relative time scales of interest. In this case, while one might speak of an "instantaneous glue," this interaction differs from the traditional picture of a retarded pairing interaction. However, as we will show, the dominant contribution to the pairing interaction for both of these models arises from energies reflecting the spectrum seen in the dynamic spin susceptibility. In this case, the basic interaction is retarded, and one speaks of a spin-fluctuation glue which mediates the d-wave pairing.