Coupling of the B1g phonon to the antinodal electronic states of Bi2Sr2Ca0.92Y0.08Cu2O8+delta

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.

Electronic structure and correlations in planar trilayer nickelate Pr4Ni3O8

The discovery of superconductivity in planar nickelates raises the question of how the electronic structure and correlations of Ni¹⁺ compounds compare to those of the Cu²⁺ cuprate superconductors. Here, we present an angle-resolved photoemission spectroscopy (ARPES) study of the trilayer nickelate Pr₄Ni₃O₈, revealing a Fermi surface resembling that of the hole-doped cuprates but with critical differences. Specifically, the main portions of the Fermi surface are extremely similar to that of the bilayer cuprates, with an additional piece that can accommodate additional hole doping. We find that the electronic correlations are about twice as strong in the nickelates and are almost k-independent, indicating that they originate from a local effect, likely the Mott interaction, whereas cuprate interactions are somewhat less local. Nevertheless, the nickelates still demonstrate the strange-metal behavior in the electron scattering rates. Understanding the similarities and differences between these two families of strongly correlated superconductors is an important challenge.

Gapped Collective Charge Excitations and Interlayer Hopping in Cuprate Superconductors

We use resonant inelastic x-ray scattering to probe the propagation of plasmons in the electron-doped cuprate superconductor Sr_{0.9}La_{0.1}CuO_{2}. We detect a plasmon gap of ∼120  meV at the two-dimensional Brillouin zone center, indicating that low-energy plasmons in Sr_{0.9}La_{0.1}CuO_{2} are not strictly acoustic. The plasmon dispersion, including the gap, is accurately captured by layered t-J-V model calculations. A similar analysis performed on recent resonant inelastic x-ray scattering data from other cuprates suggests that the plasmon gap is generic and its size is related to the magnitude of the interlayer hopping t_{z}. Our work signifies the three dimensionality of the charge dynamics in layered cuprates and provides a new method to determine t_{z}.

Multipole polaron in the devil's staircase of CeSb

Rare-earth intermetallic compounds exhibit rich phenomena induced by the interplay between localized f orbitals and conduction electrons. However, since the energy scale of the crystal-electric-field splitting is only a few millielectronvolts, the nature of the mobile electrons accompanied by collective crystal-electric-field excitations has not been unveiled. Here, we examine the low-energy electronic structures of CeSb through the anomalous magnetostructural transitions below the Néel temperature, ~17 K, termed the 'devil's staircase', using laser angle-resolved photoemission, Raman and neutron scattering spectroscopies. We report another type of electron-boson coupling between mobile electrons and quadrupole crystal-electric-field excitations of the 4f orbitals, which renormalizes the Sb 5p band prominently, yielding a kink at a very low energy (~7 meV). This coupling strength is strong and exhibits anomalous step-like enhancement during the devil's staircase transition, unveiling a new type of quasiparticle, named the 'multipole polaron', comprising a mobile electron dressed with a cloud of the quadrupole crystal-electric-field polarization.

Unconventional spectral signature of Tc in a pure d-wave superconductor

In conventional superconductors, the phase transition into a zero-resistance and perfectly diamagnetic state is accompanied by a jump in the specific heat and the opening of a spectral gap¹. In the high-transition-temperature (high-T_c) cuprates, although the transport, magnetic and thermodynamic signatures of T_c have been known since the 1980s², the spectroscopic singularity associated with the transition remains unknown. Here we resolve this long-standing puzzle with a high-precision angle-resolved photoemission spectroscopy (ARPES) study on overdoped (Bi,Pb)₂Sr₂CaCu₂O_8+δ (Bi2212). We first probe the momentum-resolved electronic specific heat via spectroscopy and reproduce the specific heat peak at T_c, completing the missing link for a holistic description of superconductivity. Then, by studying the full momentum, energy and temperature evolution of the spectra, we reveal that this thermodynamic anomaly arises from the singular growth of in-gap spectral intensity across T_c. Furthermore, we observe that the temperature evolution of in-gap intensity is highly anisotropic in the momentum space, and the gap itself obeys both the d-wave functional form and particle-hole symmetry. These findings support the scenario that the superconducting transition is driven by phase fluctuations. They also serve as an anchor point for understanding the Fermi arc and pseudogap phenomena in underdoped 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.

Antiferromagnetism Induced by Bond Su-Schrieffer-Heeger Electron-Phonon Coupling: A Quantum Monte Carlo Study

Antiferromagnetism (AFM) such as Néel ordering is often closely related to Coulomb interactions such as Hubbard repulsion in two-dimensional (2D) systems. Whether Néel AFM ordering in two dimensions can be dominantly induced by electron-phonon couplings (EPC) has not been completely understood. Here, by employing numerically exact sign-problem-free quantum Monte Carlo (QMC) simulations, we show that bond Su-Schrieffer-Heeger (SSH) phonons with frequency ω and EPC constant λ can induce AFM ordering for a wide range of phonon frequency ω>ω_{c}. For ω<ω_{c}, a valence-bond-solid (VBS) order appears and there is a direct quantum phase transition between VBS and AFM phases at ω_{c}. The phonon mechanism of the AFM ordering is related to the fact that SSH phonons directly couple to electron hopping whose second-order process can induce an effective AFM spin exchange. Our results shall shed new light on understanding AFM ordering in correlated quantum materials.

Anomalously strong near-neighbor attraction in doped 1D cuprate chains

[Figure: see text].

Fermi surface and kink structures in [Formula: see text] revealed by synchrotron-based ARPES

The low-energy electronic structure, including the Fermi surface topology, of the itinerant metamagnet [Formula: see text] is investigated for the first time by synchrotron-based angle-resolved photoemission. Well-defined quasiparticle band dispersions with matrix element dependencies on photon energy or photon polarization are presented. Four bands crossing the Fermi-level, giving rise to four Fermi surface sheets are resolved; and their complete topography, effective mass as well as their electron and hole character are determined. These data reveal the presence of kink structures in the near-Fermi-level band dispersion, with energies ranging from 30 to 69 meV. Together with previously reported Raman spectroscopy and lattice dynamic calculation studies, the data suggest that these kinks originate from strong electron-phonon coupling present in [Formula: see text]. Considering that the kink structures of [Formula: see text] are similar to those of the other three members of the Ruddlesden Popper structured ruthenates, the possible universality of strong coupling of electrons to oxygen-related phonons in [Formula: see text] compounds is proposed.

Why the anti-nodal quasiparticle dispersion is so flat in the superconducting cuprates?

The emergence of the coherent quasiparticle peak and the development of the peak-dip-hump structure in the anti-nodal region below T _c is the most prominent non-BCS signature of the under-doped high-T _c cuprates, in which no coherent quasiparticle can be defined in the anti-nodal region above T _c. The peak-dip-hump structure has been commonly interpreted as the result of the coupling of the electron to some Bosonic mode. However, such an electron-Boson coupling picture does not answer the question of why the quasiparticle dispersion is so flat in the anti-nodal region, a behavior totally unexpected for Bogoliubov quasiparticle in a d-wave BCS superconductor. Here we show that the sharp quasiparticle peak in the anti-nodal region should be understood as a new pole in the electron Green's function generated by the strong coupling of the electron to diffusive spin fluctuation around the antiferromagnetic wave vector Q = (π, π), rather than a nearly free Bogoliubov quasiparticle in a d-wave BCS superconductor. More specifically, we find that the normal self-energy of the electron from the scattering with the diffusive spin fluctuation manifests itself mainly as a level repulsion effect and is responsible for the reduction of both the quasiparticle dispersion and the quasiparticle dissipation rate in the anti-nodal region. We argue that the peak-dip separation in the anti-nodal spectrum should not be interpreted as the energy of the pairing glue.

Incoherent strange metal sharply bounded by a critical doping in Bi2212

In normal metals, macroscopic properties are understood using the concept of quasiparticles. In the cuprate high-temperature superconductors, the metallic state above the highest transition temperature is anomalous and is known as the "strange metal." We studied this state using angle-resolved photoemission spectroscopy. With increasing doping across a temperature-independent critical value p _c ~ 0.19, we observed that near the Brillouin zone boundary, the strange metal, characterized by an incoherent spectral function, abruptly reconstructs into a more conventional metal with quasiparticles. Above the temperature of superconducting fluctuations, we found that the pseudogap also discontinuously collapses at the very same value of p _c These observations suggest that the incoherent strange metal is a distinct state and a prerequisite for the pseudogap; such findings are incompatible with existing pseudogap quantum critical point scenarios.

Mode-Selective Coupling of Coherent Phonons to the Bi2212 Electronic Band Structure

Cuprate superconductors host a multitude of low-energy optical phonons. Using time- and angle-resolved photoemission spectroscopy, we study coherent phonons in Bi_{2}Sr_{2}Ca_{0.92}Y_{0.08}Cu_{2}O_{8+δ}. Sub-meV modulations of the electronic band structure are observed at frequencies of 3.94±0.01 and 5.59±0.06  THz. For the dominant mode at 3.94 THz, the amplitude of the band energy oscillation weakly increases as a function of momentum away from the node. Theoretical calculations allow identifying the observed modes as CuO_{2}-derived A_{1g} phonons. The Bi- and Sr-derived A_{1g} modes which dominate Raman spectra in the relevant frequency range are absent in our measurements. This highlights the mode selectivity for phonons coupled to the near-Fermi-level electrons, which originate from CuO_{2} planes and dictate thermodynamic properties.

Coherent organization of electronic correlations as a mechanism to enhance and stabilize high-T C cuprate superconductivity

Strong diffusive or incoherent electronic correlations are the signature of the strange-metal normal state of the cuprate superconductors, with these correlations considered to be undressed or removed in the superconducting state. A critical question is if these correlations are responsible for the high-temperature superconductivity. Here, utilizing a development in the analysis of angle-resolved photoemission data, we show that the strange-metal correlations don't simply disappear in the superconducting state, but are instead converted into a strongly renormalized coherent state, with stronger normal state correlations leading to stronger superconducting state renormalization. This conversion begins well above T C at the onset of superconducting fluctuations and it greatly increases the number of states that can pair. Therefore, there is positive feedback--the superconductive pairing creates the conversion that in turn strengthens the pairing. Although such positive feedback should enhance a conventional pairing mechanism, it could potentially also sustain an electronic pairing mechanism.

Observation of Bogoliubov Band Hybridization in the Optimally Doped Trilayer Bi_{2}Sr_{2}Ca_{2}Cu_{3}O_{10+δ}

Using a laser-excited angle-resolved photoemission spectroscopy capable of bulk sensitive and high-energy resolution measurements, we reveal a new phenomenon of superconductors in the optimally doped trilayer Bi_{2}Sr_{2}Ca_{2}Cu_{3}O_{10+δ}. We observe a hybridization of the Bogoliubov bands derived from the inner and outer CuO_{2} planes with different magnitudes of energy gaps. Our data clearly exhibit the splitting of coherent peaks and the consequent enhancement of spectral gaps. These features are reproduced by model calculations, which indicate that the gap enhancement extends over a wide range of Fermi surface up to the antinode. The significant modulation of electron pairing uncovered here might be a crucial factor to achieve the highest critical temperature in the trilayer cuprates.

A New Landscape of Multiple Dispersion Kinks in a High-T c Cuprate Superconductor

Conventional superconductivity is caused by electron-phonon coupling. The discovery of high-temperature superconductors raised the question of whether such strong electron-phonon coupling is realized in cuprates. Strong coupling with some collective excitation mode has been indicated by a dispersion “kink”. However, there is intensive debate regarding whether the relevant coupling mode is a magnetic resonance mode or an oxygen buckling phonon mode. This ambiguity is a consequence of the energy of the main prominent kink. Here, we show a new landscape of dispersion kinks. We report that heavily overdoping a Bi₂Sr₂CaCu₂O_8+δ superconductor results in a decline of the conventional main kink and a rise of another sharp kink, along with substantial energy shifts of both. Notably, the latter kink can be ascribed only to an oxygen-breathing phonon. Hence, the multiple phonon branches provide a consistent account of our data set on the multiple kinks. Our results suggest that strong electron-phonon coupling and its dramatic change should be incorporated into or reconciled with scenarios for the evolution of high-T_c superconductivity.

Bi-2212/1T-TaS2 Van der Waals junctions: Interplay of proximity induced high-T c superconductivity and CDW order

Understanding the coexistence, competition and/or cooperation between superconductivity and charge density waves (CDWs) in the transition metal dichalcogenides (TMDs) is an elusive goal which, when realized, promises to reveal fundamental information on this important class of materials. Here, we use four-terminal current-voltage measurements to study the Van der Waals interface between freshly exfoliated flakes of the high-T_c superconductor, Bi-2212, and the CDW-dominated TMD layered material, 1T-TaS₂. For highly transparent barriers, there is a pronounced Andreev reflection feature providing evidence for proximity-induced high-T_c superconductivity in 1T-TaS₂ with a surprisingly large energy gap (~20 meV) equal to half that of intrinsic Bi-2212 (~40 meV). Our systematic study using conductance spectroscopy of junctions with different transparencies also reveals the presence of two separate boson modes, each associated with a “dip-hump” structure. We infer that the proximity-induced high-T_c superconductivity in the 1T-TaS₂ is driven by coupling to the metastable metallic phase coexisting within the Mott commensurate CDW (CCDW) phase and associated with a concomitant change of the CCDW order parameter in the interfacial region.

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.

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.

Anomalous doping variation of the nodal low-energy feature of superconducting (Bi,Pb)2(Sr,La)2CuO(6+δ) crystals revealed by laser-based angle-resolved photoemission spectroscopy

The nodal band dispersion in (Bi,Pb)(2)(Sr,La)(2)CuO(6+δ) (Bi2201) is investigated over a wide range of doping by using 7-eV laser-based angle-resolved photoemission spectroscopy. We find that the low-energy band renormalization ("kink"), recently discovered in Bi(2)Sr(2)CaCu(2)O(8+δ) (Bi2212), also occurs in Bi2201, but at a binding energy around half that in Bi2212. Surprisingly, the coupling energy dramatically increases with a decrease of carrier concentration, showing a sharp enhancement across the optimal doping. These properties (material and doping dependence of the coupling energy) demonstrate the significant correlation among the mode coupling, the energy gap close to the node, and the strong electron correlation. Our results suggest forward scattering arising from the interplay between the electrons and in-plane polarized acoustic phonon branch as the origin of the low-energy renormalization.

Suppression of superconductivity in the Hubbard model by buckling and breathing phonons

We study the effect of buckling and breathing phonons, relevant for cuprate superconductors, on the d-wave superconductivity in the two-dimensional Hubbard model by employing dynamical cluster Monte Carlo calculations. The interplay of electronic correlations and the electron-phonon interaction produces two competing effects: an enhancement of the effective d-wave pairing interaction, which favors d-wave superconductivity, and a strong renormalization of the single-particle propagator, which suppresses superconductivity. In the region of the parameter space relevant for cuprate superconductors, we find that the buckling and the breathing phonons suppress the superconductivity.

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.

Observation of phonons with resonant inelastic x-ray scattering

Phonons, the quantum mechanical representation of lattice vibrations, and their coupling to the electronic degrees of freedom are important for understanding thermal and electric properties of materials. For the first time, phonons have been measured using resonant inelastic x-ray scattering (RIXS) across the Cu K-edge in cupric oxide (CuO). Analyzing these spectra using an ultra-short core-hole lifetime approximation and exact diagonalization techniques, we can explain the essential inelastic features. The relative spectral intensities are related to the electron-phonon coupling strengths.

An electron-boson glue function derived from electronic Raman scattering

Raman scattering cross sections depend on photon polarization. In the cuprates, nodal and antinodal directions are weighted more strongly in B(2g) and B(1g) symmetries, respectively. On the other hand, in angle-resolved photoemission spectroscopy (ARPES), electronic properties are measured along well-defined directions in momentum space rather than their weighted averages being taken. In contrast, the optical conductivity involves a momentum average over the entire Brillouin zone. Newly measured Raman response data on high-quality Bi(2)Sr(2)CaCu(2)O(8 + δ) single crystals up to high energies have been inverted using a modified maximum entropy inversion technique to extract from B(1g) and B(2g) Raman data corresponding electron-boson spectral densities (glue), and these are compared to the results obtained with known ARPES and optical inversions. We find that the B(2g) spectrum agrees qualitatively with nodal direction ARPES while the B(1g) results look more like the optical spectrum. A large peak around 30-40 meV in B(1g) and a much less prominent one in B(2g) are taken as support for the importance of (π, π) scattering at this frequency.

Femtosecond response of quasiparticles and phonons in superconducting YBa(2)Cu(3)O(7-δ) studied by wideband terahertz spectroscopy

We measure the anisotropic midinfrared response of electrons and phonons in bulk YBa(2)Cu(3)O(7-δ) after femtosecond photoexcitation. A line shape analysis of specific lattice modes reveals their transient occupation and coupling to the superconducting condensate. The apex oxygen vibration is strongly excited within 150 fs, demonstrating that the lattice absorbs a major portion of the pump energy before the quasiparticles are thermalized. Our results attest to substantial electron-phonon scattering and introduce a powerful concept probing electron-lattice interactions in a variety of complex materials.

Universal non-Landau, self-organized, lattice disordering percolative dopant network sub-T(c) phase transition in ceramic superconductors

Ceramic superconductors (cuprates, pnictides, etc.) exhibit universal features in both T(c)(max) and in their planar lattice disordering measured by EXAFS, as reflected by three phase transitions. The two highest temperature transitions are known to be associated with formation of Jahn-Teller pseudogaps and superconductive gaps, with corresponding Landau order parameters, but no new gap is associated with the third transition below T(c), and its origin is mysterious. It is argued that the third subT(c) transition is a dopant glass transition, which is remarkably similar to topological transitions previously observed in chalcogenide and oxide alloy network glasses (like window glass).

Dependence of band-renormalization effects on the number of copper oxide layers in Tl-based copper oxide superconductors revealed by angle-resolved photoemission spectroscopy

Here we report the first angle-resolved photoemission measurement on nearly optimally doped multilayer Tl-based superconducting cuprates (Tl-2212 and Tl-1223) and a comparison study to single-layer (Tl-2201) compound. A "kink" in the band dispersion is found in all three compounds but exhibits different momentum dependence for the single-layer and multilayer compounds, reminiscent to that of Bi-based cuprates. This layer number dependent renormalization effect strongly implies that the spin-resonance mode is unlikely to be responsible for the dramatic renormalization effect near the antinodal region.

Unusual layer-dependent charge distribution, collective mode coupling, and superconductivity in multilayer cuprate Ba2Ca3Cu4O8F2

Low energy ultrahigh momentum resolution angle resolved photoemission spectroscopy study on four-layer self-doped high Tc superconductor Ba2Ca3Cu4O8F2 (F0234) revealed fine structure in the band dispersion, identifying the unconventional association of hole and electron doping with the inner and outer CuO2 layers, respectively. For the states originating from two inequivalent CuO2 layers, different energy scales are observed in dispersion kinks associated with the collective mode coupling, with the larger energy scale found in the electron (n-) doped state which also has stronger coupling strength. Given the earlier finding that the superconducting gap is substantially larger along the n-type Fermi surface, our observations connect the mode coupling energy and strength with magnitude of the pairing gap.

Optical spectroscopy of superconducting Ba0.55K0.45Fe2As2: evidence for strong coupling to low-energy bosons

Normal state optical spectroscopy on single crystals of the new iron arsenide superconductor Ba0.55K0.45Fe2As2 shows that the infrared spectrum consists of two major components: a strong metallic Drude band and a well-separated midinfrared absorption centered at 0.7 eV. It is difficult to separate the two components unambiguously but several fits using Lorentzian peaks suggest a model with a Drude peak having a plasma frequency of 1.6 to 2.1 eV and a midinfrared peak with a plasma frequency of 2.5 eV. Detailed analysis of the frequency dependent scattering rate shows that the charge carriers interact with a broad bosonic spectrum extending beyond 100 meV with a very large coupling constant lambda=3.4 at low temperature. As the temperature increases this coupling weakens to lambda=0.78 at ambient temperature. This suggests a bosonic spectrum that is similar to what is seen in the lower Tc cuprates.

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.

Isotopic fingerprint of electron-phonon coupling in high-Tc cuprates

Angle-resolved photoemission spectroscopy with low-energy tunable photons along the nodal direction of oxygen isotope substituted Bi(2)Sr(2)CaCu(2)O(8+delta) reveals a distinct oxygen isotope shift near the electron-boson coupling "kink" in the electronic dispersion. The magnitude (a few meV) and direction of the kink shift are as expected due to the measured isotopic shift of phonon frequency, and are also in agreement with theoretical expectations. This demonstrates the participation of the phonons as dominant players, as well as pinpointing the most relevant of the phonon branches.

Angle-resolved photoemission spectroscopy of electron-doped cuprate superconductors: isotropic electron-phonon coupling

We have performed high resolution angle-resolved photoemission (ARPES) studies on electron-doped cuprate superconductors Sm2-xCexCuO4 (x=0.10, 0.15, 0.18), Nd2-xCexCuO4 (x=0.15), and Eu2-xCexCuO4 (x=0.15). Imaginary parts of the electron removal self energy show steplike features due to an electron-bosonic mode coupling. The steplike feature is seen along both nodal and antinodal directions but at energies of 50 and 70 meV, respectively, independent of the doping and rare earth element. Such energy scales can be understood as being due to preferential coupling to half- and full-breathing mode phonons, revealing the phononic origin of the kink structures. Estimated electron-phonon coupling constant lambda from the self energy is roughly independent of the doping and momentum. The isotropic nature of lambda is discussed in comparison with the hole-doped case where a strong anisotropy exists.

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.

Bond stretching phonon softening and kinks in the angle-resolved photoemission spectra of optimally doped Bi2Sr1.6La0.4Cu2O6+delta superconductors

We report the first measurement of the Cu-O bond stretching phonon dispersion in optimally doped Bi2Sr1.6La0.4Cu2O6+delta using inelastic x-ray scattering. We found a softening of this phonon at q=( approximately 0.25,0,0) from 76 to 60 meV, similar to the one reported in other cuprates. A comparison with angle-resolved photoemission data on the same sample revealed an excellent agreement in terms of energy and momentum between the angle-resolved photoemission nodal kink and the soft part of the bond stretching phonon. Indeed, we find that the momentum space where a 63+/-5 meV kink is observed can be connected with a vector q=(xi,0,0) with xi > or =0.22, corresponding exactly to the soft part of the bond stretching phonon.

Two-mode variational Monte Carlo study of quasiparticle excitations in cuprate superconductors

Recent measurements of quasiparticles in hole-doped cuprates revealed highly unusual features: (i) the doping-independent Fermi velocity, (ii) two energy scales in the quasiparticle spectral function, and (iii) a suppression of the low-energy spectral weight near the zone center. We explain these important facts by a novel two-mode variational Monte Carlo (VMC) study of the t-J model, which resolves a long-standing issue of the sum rule for quasiparticle spectral weights in VMC studies. The electron-doped case is also discussed.

Identification of a new form of electron coupling in the Bi2Sr2CaCu2O8 superconductor by laser-based angle-resolved photoemission spectroscopy

Laser-based angle-resolved photoemission measurements with superhigh resolution have been carried out on an optimally doped Bi(2)Sr(2)CaCu(2)O(8) high temperature superconductor. New high energy features at approximately 115 meV and approximately 150 meV, in addition to the prominent approximately 70 meV one, are found to develop in the nodal electron self-energy in the superconducting state. These high energy features, which cannot be attributed to electron coupling with single phonon or magnetic resonance mode, point to the existence of a new form of electron coupling in high temperature superconductors.

Ultrafast electron relaxation in superconducting Bi(2)Sr(2)CaCu(2)O(8+delta) by time-resolved photoelectron spectroscopy

Time-resolved photoelectron spectroscopy is employed to study the dynamics of photoexcited electrons in optimally doped Bi{2}Sr{2}CaCu{2}O{8+delta} (Bi-2212). Hot electrons thermalize in less than 50 fs and dissipate their energy on two distinct time scales (110 fs and 2 ps). These are attributed to the generation and subsequent decay of nonequilibrium phonons, respectively. We conclude that 20% of the total lattice modes dominate the coupling strength and estimate the second momentum of the Eliashberg coupling function lambdaOmega{0}{2}=360+/-30 meV{2}. For the typical phonon energy of copper-oxygen bonds (Omega{0} approximately 40-70 meV), this results in an average electron-phonon coupling lambda<0.25.

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.

Unified picture of the oxygen isotope effect in cuprate superconductors

High-temperature superconductivity in cuprates was discovered almost exactly 20 years ago, but a satisfactory theoretical explanation for this phenomenon is still lacking. The isotope effect has played an important role in establishing electron-phonon interaction as the dominant interaction in conventional superconductors. Here we present a unified picture of the oxygen isotope effect in cuprate superconductors based on a phonon-mediated d-wave pairing model within the Bardeen-Cooper-Schrieffer theory. We show that this model accounts for the magnitude of the isotope exponent as functions of the doping level as well as the variation between different cuprate superconductors. The isotope effect on the superconducting transition is also found to resemble the effect of pressure on the transition. These results indicate that the role of phonons should not be overlooked for explaining the superconductivity in cuprates.

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.

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.

Interplay of electron–lattice interactions and superconductivity in Bi2Sr2CaCu2O8+δ

Formation of electron pairs is essential to superconductivity. For conventional superconductors, tunnelling spectroscopy has established that pairing is mediated by bosonic modes (phonons); a peak in the second derivative of tunnel current d2I/dV2 corresponds to each phonon mode. For high-transition-temperature (high-T(c)) superconductivity, however, no boson mediating electron pairing has been identified. One explanation could be that electron pair formation and related electron-boson interactions are heterogeneous at the atomic scale and therefore challenging to characterize. However, with the latest advances in d2I/dV2 spectroscopy using scanning tunnelling microscopy, it has become possible to study bosonic modes directly at the atomic scale. Here we report d2I/dV2 imaging studies of the high-T(c) superconductor Bi2Sr2CaCu2O8+delta. We find intense disorder of electron-boson interaction energies at the nanometre scale, along with the expected modulations in d2I/dV2 (refs 9, 10). Changing the density of holes has minimal effects on both the average mode energies and the modulations, indicating that the bosonic modes are unrelated to electronic or magnetic structure. Instead, the modes appear to be local lattice vibrations, as substitution of 18O for 16O throughout the material reduces the average mode energy by approximately 6 per cent--the expected effect of this isotope substitution on lattice vibration frequencies. Significantly, the mode energies are always spatially anticorrelated with the superconducting pairing-gap energies, suggesting an interplay between these lattice vibration modes and the superconductivity.

Doping dependence of the coupling of electrons to bosonic modes in the single-layer high-temperature Bi2Sr2CuO6 superconductor

A recent highlight in the study of high-T(c) superconductors is the observation of band renormalization or self-energy effects on the quasiparticles. This is seen in the form of kinks in the quasiparticle dispersions as measured by photoemission and interpreted as signatures of collective bosonic modes coupling to the electrons. Here we compare for the first time the self-energies in an optimally doped and strongly overdoped, nonsuperconducting single-layer Bi-cuprate (Bi2Sr2CuO6). In addition to the appearance of a strong overall weakening, we also find that the weight of the self-energy in the overdoped system shifts to higher energies. We present evidence that this is related to a change in the coupling to c-axis phonons due to the rapid change of the c-axis screening in this doping range.

Parity of the pairing bosons in a high-temperature Pb-Bi2Sr2CaCu2O8 bilayer superconductor by angle-resolved photoemission spectroscopy

We report the observation of a novel effect in the bilayer Pb-Bi2Sr2CaCu2O8 (Pb-Bi2212) high-T(c) superconductor by means of angle-resolved photoemission with circularly polarized excitation. Different scattering rates, determined as a function of energy separately for the bonding and antibonding copper-oxygen bands, strongly imply that the dominating scattering channel is odd with respect to layer exchange within a bilayer. This is inconsistent with a phonon-mediated scattering and favors the participation of the odd collective spin excitations in the scattering mechanism in near-nodal regions of the k space, suggesting a magnetic nature of the pairing mediator.

Effect of Zn and Ni impurities on the quasiparticle renormalization of superconducting Bi-2212

The Cu substitution by Zn and Ni impurities and its influence on the mass renormalization effects in angle-resolved photoelectron spectra (ARPES) of Bi2Sr2CaCu2O8-delta is addressed. We show that the nonmagnetic Zn atoms have a much stronger effect in both the nodal and antinodal parts of the Brillouin zone than magnetic Ni. The observed changes are consistent with the behavior of the spin resonance mode as seen by inelastic neutron scattering in YBCO. This strongly suggests that the "peak-dip-hump" and the kink in ARPES on the one side and neutron resonance on the other are closely related features.

Persistence of strong electron coupling to a narrow boson spectrum in overdoped Bi2Sr2CaCu2O(8+delta) tunneling data

A d-wave, Eliashberg analysis of break-junction and STM tunneling spectra on Bi2Sr2CaCu2O(8+delta) (Bi2212) reveals that the spectral dip feature is directly linked to strong electronic coupling to a narrow boson spectrum, evidenced by a large peak in alpha2F(omega). The tunneling dip feature remains robust in the overdoped regime of Bi2212 with bulk T(c) values of 56 K-62 K. This is contrary to recent optical conductivity measurements of the self-energy that suggest the narrow boson spectrum disappears in overdoped Bi2212 and therefore cannot be essential for the pairing mechanism. The discrepancy is resolved by considering the way each technique probes the electron self-energy, in particular, the unique sensitivity of tunneling to the off-diagonal or pairing part of the self-energy.