Electron-phonon interaction in copper oxide superconductors is still enigmatic. Strong coupling for certain optic phonons is now well established experimentally, but theoretical understanding is challenging. Scattering of electrons near the Fermi surface by the longitudinal acoustic (LA) phonons is expected from basic theory because these phonons modulate electron density. We used inelastic neutron scattering on a large single crystal sample of optimally-doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ to show that low-energy LA phonons could couple to electronic density fluctuations only at small phonon wavevectors, which naturally limits any interaction to forward scattering. Such scattering should not be pairbreaking in the case of the d-wave gap. We also found that previously the reported low energy phonon spectral weight half-way to the zone boundary is consistent with conventional lattice dynamics and does not reflect an incipient charge density wave.
There is an ongoing debate about the nature of the bosonic excitations responsible for the quasiparticle self energy in high temperature superconductors -- are they phonons or spin fluctuations? We present a careful analysis of the bosonic excitations as revealed by the `kink' feature at 70 meV in angle resolved photoemission data using Eliashberg theory for a d-wave superconductor. Starting from the assumption that nodal quasiparticles are not coupled to the $(π,π)$ magnetic resonance, the sharp structure at $70 $meV can be assigned to phonons. We find that not only can we account for the shi…
The equilibrium structure, energy bands, phonon dispersions, and s- and d-channel electron-phonon interactions (EPIs) are calculated for the infinite-layer superconductor CaCuO2 doped with 0.24 holes per CuO2. The LDA and the linear-response full-potential LMTO method were used. In the equilibrium structure, oxygen is found to buckle slightly out of the plane and, as a result, the characters of the energy bands near EF are found to be similar to those of other optimally doped HTSCs. For the EPI we find lambda(s)=0.4, in accord with previous LDA calculations for YBa2Cu3O7. This supports the com…
Using ultrafast optical techniques, we detect two types of bosons strongly coupled to electrons in the family of Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$ from the underdoped to overdoped regimes. The different doping dependences of the electron-boson coupling strengths enables us to identify them as phonons and spin fluctuations: electron-phonon coupling ($λ_{e-ph}$) peaks at optimal doping, and electron-spin fluctuation coupling ($λ_{e-sf}$) decreases monotonically with doping. This observation is consistent with two facts: (1) superconductivity is in close proximity with antiferromagnetism at low…
We employ Momentum-Resolved Electron Energy Loss Spectroscopy (M-EELS) on Bi2.1Sr1.9CaCu2O8+x to resolve the issue of the kink feature in the electron dispersion widely observed in the cuprates. To this end, we utilize the GW approximation to relate the density response function measured in in M-EELS to the self-energy, isolating contributions from phonons, electrons, and the momentum dependence of the effective interaction to the decay rates. The phononic contributions, present in the M-EELS spectra due to electron-phonon coupling, lead to kink features in the corresponding single-particle sp…
We report the first observation of soft-x-ray scattering from spin fluctuations in a high-Tc parent compound. An antiferromagnetic charge transfer insulator, CaCuO2, was irradiated by Cu M-edge soft x-rays. Ultra-high resolution measurements of scattered intensity revealed magnon-magnon excitations, due to spin exchange scattering, as low-energy loss features. The process is analogous to optical Raman scattering. The spectra provide the first measurement of the two-magnon excitation energy and the antiferromagnetic exchange parameter in infinite-layer CaCuO2. The results reveal resonant inelas…
We report a persistent low-energy phonon broadening around $q_{B} \sim 0.28$ r.l.u. along the Cu-O bond direction in the high-$T_c$ cuprate Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (Bi-2212). We show that such broadening exists both inside and outside the conventional charge density wave (CDW) phase, via temperature dependent measurements in both underdoped and heavily overdoped samples. Combining inelastic hard x-ray scattering, diffuse scattering, angle-resolved photoemission spectroscopy, and resonant soft x-ray scattering at the Cu $L_3$-edge, we exclude the presence of a CDW in the heavily overdoped…
Using resonant X-ray diffraction and Raman spectroscopy, we study charge correlations and lattice dynamics in two model cuprates, HgBa$_{2}$CuO$_{4+δ}$ and HgBa$_{2}$CaCu$_{2}$O$_{6+δ}$. We observe a maximum of the characteristic charge order temperature around the same hole concentration ($p \approx 0.09$) in both compounds, and concomitant pronounced anomalies in the lattice dynamics that involve the motion of atoms in and/or adjacent to the CuO$_2$ layers. These anomalies are already present at room temperature, and therefore precede the formation of the static charge correlations, and we a…
Pure electronic Raman spectra with no phonon structures superimposed to the electronic continuum, are reported, in optimally doped HgBa_{2}CaCu_{2}O_{6+δ} single crystals (T_{c }=126 K). As a consequence, the spectra in the A_{1g }, B_{1g } and B_{2g } symmetries, including the crucial low energy frequency dependence of the electronic scattering, are directly and reliably measured. The B_{2g } and, most strikingly, the B_{1g } spectra exhibit a strong intrinsic linear term, which suggests that the nodes are shifted from the [110] and [1\bar{1}0] directions, a result inconsistent with a pure d_…
Despite the intensive efforts for determining the mechanism that causes high-temperature superconductivity in copper oxide materials, no consensus on the pairing mechanism has been reached. Recent advances in high resolution angle-resolved photoemission spectroscopies have suggested that a sizeable electron-phonon coupling exists as the principal cause for kinks in the dispersion relations (energy versus wave vector) of the electronic states. Here, we report on a systematic study about the influence of the electron-phonon coupling parameter "$λ$" in the electronic quasiparticle dispersions alo…
We investigate the dispersion and temperature dependence of a number of phonons in the recently discovered superconductor CaC6 utilizing inelastic x-ray scattering. Four [00L] and two ab-plane phonon modes are observed, and measured at temperatures both above and below T_c. In general, our measurements of phonon dispersions are in good agreement with existing theoretical calculations of the phonon dispersion. This is significant in light of several discrepancies between experimental measurements of phonon-derived quantities and theoretical calculations. The present work suggests that the origi…
Using high-resolution angle-resolved photoemission spectroscopy on $Bi_{2}Sr_{2}CaCu_{2}O_{8+δ}$, we have made the first observation of a mass renormalization or "kink" in the E vs. $\vec k$ dispersion relation localized near $(π, 0)$. Compared to the kink observed along the nodal direction, this new effect is clearly stronger, appears at a lower energy near 40 meV, and is only present in the superconducting state. The kink energy scale defines a cutoff below which well-defined quasiparticle excitations occur. This effect is likely due to coupling to a bosonic excitation, with the most plausib…
Cuprates are promising candidates for study in developing higher temperature superconductors. A thorough understanding of a material's phonon modes enables further investigation of its emergent properties, however, no complete reference of the phonon modes exists. Here, using density functional theory, we evaluate the phonon frequencies and atomic displacements for $\text{La}_2\text{CuO}_4$, $\text{Bi}_2\text{Sr}_2\text{CuO}_6$, and $\text{Bi}_2\text{Sr}_2\text{CaCu}_2\text{O}_8$ in their tetragonal structures. The phonon modes for all materials agree with those expected from space group symme…
Inelastic x-ray scattering and $ab$-$initio$ calculation are applied to investigate the lattice dynamics and electron-phonon coupling of the ternary silicide superconductor CaAlSi ($P/bar{6}m2$). A soft c-axis polarized mode is clearly observed along the $/Gamma$-$A$-$L$ symmetry directions. The soft mode is strongly anharmonically broadened at room temperature, but, at 10 K, its linewidth narrows and becomes in good agreement with calculations of linear electron-phonon coupling. This establishes a coherent description of the detailed phonon properties in this system and links them clearly and…
Room-temperature optical constants of crystalline Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ were determined using data extracted from Brillouin light scattering spectra. Optical extinction coefficient-to-refractive index ratios at a wavelength of 532 nm were obtained from bulk phonon peak linewidth and frequency shift measurements and range from $0.19 \leq 2κ/n \leq 0.29$ for directions close to the crystallographic $c$-axis. These ratios, and optical extinction coefficients, absorption coefficients, and imaginary parts of the dielectric function determined from these ratios and known refractive index, ar…
Using ultrafast optical techniques, we probe the hole-doping dependence of the electron-boson coupling constant $λ$ in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$. In the overdoped region, we observe a correlation between ($λ$) and the superconducting transition temperature $T_{c}$. Upon performing the McMillan analysis, however, we find that $λ$ is too small to explain the high $T_{c}$'s, and that the Coulomb pseudopotential $μ^{\ast}$ is negative. Our analysis therefore reveals two components in the mechanism of high-$T_{c}$ superconductivity -- a dominant pre-existing pairing interaction, together …
In the iron pnictides, the strong sensitivity of the iron magnetic moment to the arsenic position suggests a significant relationship between phonons and magnetism. We measured the phonon dispersion of several branches in the high temperature tetragonal phase of CaFe2As2 using inelastic x-ray scattering on single-crystal samples. These measurements were compared to ab initio calculations of the phonons. Spin polarized calculations imposing the antiferromagnetic order present in the low temperature orthorhombic phase dramatically improve agreement between theory and experiment. This is discusse…
Inelastic x-ray scattering is used to investigate charge density wave (CDW) formation and the low-energy lattice dynamics of the underdoped high temperature superconductor ortho-II YBa2Cu3O6.54. We find that, for a temperature ~1/3 of the CDW onset temperature (~155 K), the CDW order is static within the resolution of the experiment, that is the inverse lifetime is less than 0.3 meV. In the same temperature region, low-energy phonons near the ordering wavevector of the CDW show large increases in their linewidths. This contrasts with the usual behavior in CDW systems where the phonon anomalies…
We report measurements of the temperature dependence of phonon densities of states in K0.8Fe1.6Se2 using inelastic neutron scattering technique. While cooling down to 150 K, a phonon peak splitting around 25 meV is observed and a new peak appears at 31 meV. The measurements support the recent Raman and infra-red measurements indicating a lowering of symmetry of K0.8Fe1.6Se2 upon cooling below 250 K. Ab-initio phonon calculations have been carried out for K0.8Fe1.6Se2 and KFe2Se2. The comparison of the phonon spectra as obtained from the magnetic as well as non magnetic calculations show pronou…
In Fe-As based superconductors magnetism and superconductivity show strong sensitivity to the lattice, suggesting a possibility of unconventional electron-phonon coupling. We investigated c-axis polarized phonons in doped and undoped BaFe2As2 by inelastic X-ray scattering. Phonon peak positions and linewidths did not vary significantly as a function of doping either by Co or by K. The linewidth of the Fe vibration shows unusual wavevector-dependence, which may be due to hybridization with in-plane modes. Comparison with the density functional theory shows significant difference for the energy …
The properties of the d-wave superconducting state in the two-dimensional system have been studied. It has been assumed, that the pairing mechanism is based on the electron-phonon and the electron-electron-phonon interactions. The obtained results have shown the energy gap amplitude ($Δ_{tot}$) crossover, from the BCS to non-BCS behavior, as the value of the electron-electron-phonon potential increases. The model has been tested for the ${\rm La_{2-x}Sr_{x}CuO_{4}}$ and ${\rm Bi_{2}Sr_{2}CaCu_{2}O_{8+δ}}$ high-$T_{C}$ superconductors. It has been shown, that the dependence of the $2Δ^{(0)}_{to…
The phonon dispersion was measured at room temperature along (0,0,L) in the tetragonal phase of LaFeAsO using inelastic x-ray scattering. Spin-polarized first-principles calculations imposing various types of antiferromagnetic order are in better agreement with the experimental results than nonmagnetic calculations, although the measurements were made well above the magnetic ordering temperature, T_N. Splitting observed between two A_{1g} phonon modes at 22 and 26 meV is only observed in spin-polarized calculations. Magneto-structural effects similar to those observed in the AFe_2As_2 material…
We present a study of the lattice dynamical properties of superconducting SrPt$_3$P ($T_c = 8.4$ K) via high-resolution inelastic x-ray scattering (IXS) and ab initio calculations. Density functional perturbation theory including spin-orbit coupling (SOC) results in enhanced electron-phonon coupling (EPC) for the optic phonon modes originating from the Pt(I) atoms, with energies $\sim 5$ meV, resulting in a large EPC constant $λ\sim 2$. An overall softening of the IXS powder spectra occurs from room to low temperatures, consistent with the predicted strong EPC and with recent specific-heat exp…
The interplay between superconductivity and charge density waves (CDWs) under hole doping in cuprates is one of the central phenomena in condensed matter physics. Recently, CDWs are also observed in CaCuO$_2$-analogous nickelates RNiO$_2$ (R = La, Nd) but exhibit fundamentally different hole-doping-dependent behaviors compared to that in cuprates, raising a challenging question on its origin. In this article, we propose that electronic instability (EI) and moment-dependent electron-phonon coupling (MEPC), mainly contributed by Ni 3dx2-y2 and R 5dz2, respectively, may be the possible reasons fo…
We investigate the high-energy magnetic excitation spectrum of the high-$T_c$ cuprate superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (Bi-2212) using Cu $L_3$ edge resonant inelastic x-ray scattering (RIXS). Broad, dispersive magnetic excitations are observed, with a zone boundary energy of $\sim$300 meV and a weak dependence on doping. These excitations are strikingly similar to the bosons proposed to explain the high-energy `kink' observed in photoemission. A calculation of the spin-response based on the ARPES-derived electronic structure and YRZ-quasi-particles reproduces the key features of t…
Two-phonon contributions to meV-resolved inelastic x-ray scattering spectra of MgB2 at 300K are identified, in good agreement, in both intensity and energy, with a harmonic calculation using the force constant matrix from ab-inito LDA calculations. This contribution impacts the determination of the linewidth of the E2g phonon mode that is so important for the high Tc of this material. To the best of our knowledge, this is the first observation of peaks in measurements of phonon dispersion (q>0) due to 2-phonon scattering in a non-rare-gas solid.
We report a detailed study of specific heat, electrical resistivity and thermal expansion in combination with inelastic neutron and inelastic X-ray scattering to investigate the origin of superconductivity in the two silicon clathrate superconductors Ba8Si46 and Ba24Si100. Both compounds have a similar structure based on encaged barium atoms in oversized silicon cages. However, the transition temperatures are rather different: 8 K and 1.5 K respectively. By extracting the superconducting properties, phonon density of states, electron-phonon coupling function and phonon anharmonicity from these…
This paper has been withdrawn by the authors, because we had probably observed some spurious intensity with x=0.29 sample (Fig.3(b)). This came out after further studies of the detailed x-dependence of the highest energy LO phonon branch in LSCO.
Phonon spectra of detwinned {SrFe$_2$As$_2$} crystals, as measured by inelastic x-ray scattering, show clear anisotropy accompanying the magneto-structural transition at 200 K. We model the mode splitting using magnetic DFT calculations, including a phenomenological reduction in force-constant anisotropy that can be attributed to magnetic fluctuations. This serves as a starting point for a general model of phonons in this material applicable to both magnetic and non-magnetic phase. Using this model, the measured splitting in the magnetic phase below $\it T_{N}$, and the measured phonon linewid…
We report an inelastic x-ray scattering investigation of phonons in FeSe superconductor. Comparing the experimental phonon dispersion with density functional theory (DFT) calculations in the non-magnetic state, we found a significant disagreement between them. Improved overall agreement was obtained by allowing for spin-polarization in the DFT calculations, despite the absence of magnetic order in the experiment. This calculation gives a realistic approximation, at DFT level, of the disordered paramagnetic state of FeSe, in which strong spin fluctuations are present.
In this work we present the results of an inelastic x-ray scattering experiment detailing the behavior of the transverse acoustic [110] phonon in BaFe2As2 as a function of temperature. When cooling through the structural transition temperature, the transverse acoustic phonon energy is reduced from the value at room temperature, reaching a maximum shift near inelastic momentum transfer q=0.1. This softening of the lattice results in a change of the symmetry from tetragonal to orthorhombic at the same temperature as the transition to long-range antiferromagnetic order. While the lattice distorti…
The phonon dispersions of $\mathrm{Nd_{1.86}Ce_{0.14}CuO_{4+δ}}$ along the $[ξ,0,0]$ direction have been determined by inelastic x-ray scattering. Compared to the undoped parent compound, the two highest longitudinal phonon branches, associated with the Cu-O bond-stretching and out-of-plane oxygen vibration, are shifted to lower energies. Moreover, an anomalous softening of the bond-stretching band is observed around $\mathbf{q}=(0.2,0,0)$. These signatures provide evidence for strong electron-phonon coupling in this electron-doped high-temperature superconductor.
Electron-phonon interaction is of central importance for the electrical and heat transport properties of metals, and is directly responsible for charge-density-waves or (conventional) superconducting instabilities. The direct observation of phonon dispersion anomalies across electronic phase transitions can provide insightful information regarding the mechanisms underlying their formation. Here, we review the current status of phonon dispersion studies in superconductors under hydrostatic and uniaxial pressure. Advances in the instrumentation of high resolution inelastic X-ray scattering beaml…
Lattice Dynamics of LiFeAs studied by Inelastic Neutron Scattering and Density Functional Theory calculations
II. Physikalisches Institut, Universität zu Köln（科隆大学第二物理研究所）；Institut Laue Langevin（朗之万研究所）；Karlsruher Institut für Technologie (KIT)（卡尔斯鲁厄理工学院）；Université Paris-Saclay, CNRS, CEA, Laboratoire Léon Brillouin（巴黎萨克雷大学）；CNRS UMR 7198, Université de Lorraine（洛林大学）；Leibniz-Institut für Festkörper u. Werkstoffforschung (IFW) Dresden（德累斯顿莱布尼茨固体与材料研究所）；Indian Institute of Science Education and Research, Pune（浦那印度科学教育与研究学院）
Motivated by predictions of a substantial contribution of the "buckling" vibration of the CuO2 layers to d-wave superconductivity in the cuprates, we have performed an inelastic neutron scattering study of this phonon in an array of untwinned crystals of YBa2Cu3O7. The data reveal a pronounced softening of the phonon at the in-plane wave vector q = (0, 0.3) upon cooling below ~ 105 K, but no corresponding anomaly at q = (0.3, 0). Based on the observed in-plane anisotropy, we argue that the electron-phonon interaction responsible for this anomaly supports an electronic instability associated wi…
Nonlinear electrical effects in superconducting S-c-S contacts, including the spectroscopy of electron-phonon interactions (EPI) in these systems, and the recovery of the EPI function from experimental data are discussed. The effect of a magnetic field on the current-voltage characteristics(I-V curves) and their derivatives for ErNi_2B_2C point contacts (PC) with $d\ge ξ$ (where $d$ is the diameter of the PC and $ξ$ is the coherence length) is studied. It is found that in zero magnetic fields and in near-critical fields, when the size of the superconducting gap can be neglected, the position o…
Measurements of spin excitations are essential for an understanding of spin-mediated pairing for superconductivity; and resonant inelastic X-ray scattering (RIXS) provides a considerable opportunity to probe high-energy spin excitations. However, whether RIXS correctly measures the collective spin excitations of doped superconducting cuprates remains under debate. Here we demonstrate distinct Raman- and fluorescence-like RIXS excitations of Bi$_{1.5}$Pb$_{0.6}$Sr$_{1.54}$CaCu$_{2}$O$_{8+δ}$ in the mid-infrared energy region. Combining photon-energy and momentum dependent RIXS measurements with…
Fine structures in the tunneling spectra of superconductors have been widely used to identify fingerprints of the interaction responsible for Cooper pairing. Here we show that for scanning tunneling microscopy (STM) of Pb, the inclusion of inelastic tunneling processes is crucial for the proper interpretation of these fine structures. For STM the usual McMillan inversion algorithm of tunneling spectra must therefore be modified to include inelastic tunneling events, an insight that is crucial for the identification of the pairing glue in conventional and unconventional superconductors alike.
The low energy phonons of two different graphite intercalation compounds (GICs) have been measured as a function of temperature using inelastic x-ray scattering (IXS). In the case of the non-superconductor BaC6, the phonons observed are significantly higher (up to 20 %) in energy than those predicted by theory, in contrast to the reasonable agreement found in superconducting CaC6. Additional IXS intensity is observed below 15 meV in both BaC6 and CaC6. It has been previously suggested that this additional inelastic intensity may arise from defect or vacancy modes in these compounds, unpredicte…
Inelastic x-ray scattering (IXS) with very high (meV) energy resolution has become a valuable spectroscopic tool, complementing the well established coherent inelastic neutron scattering (INS) technique for phonon dispersion investigations. In the study of crystalline systems IXS is a viable alternative to INS, especially in cases where only small samples are available. Using IXS, we have measured the phonon dispersion of Nd_{1.86}Ce_{0.14}CuO_{4+δ} along the [x,0,0] and [x,x,0] in-plane directions. Compared to the undoped parent compound, the two highest longitudinal optical (LO) phonon branc…
Metamaterial approach is capable of drastically increasing the critical temperature, Tc, of composite metal-dielectric superconductors. Tripling of Tc was observed in bulk Al-Al2O3 core-shell metamaterials. A theoretical model based on the Maxwell-Garnett approximation provides a microscopic explanation of this effect in terms of electron-electron pairing mediated by a hybrid plasmon-phonon excitation. We report the first observation of this excitation in Al-Al2O3 core-shell metamaterials using inelastic neutron scattering. This result provides support for this novel mechanism of superconducti…
The tunneling path between the CuO2-layers in cuprate superconductors and a scanning tunneling microscope tip passes through a barrier made from other oxide layers. This opens up the possibility that inelastic processes in the barrier contribute to the tunneling spectra. Such processes cause one or possibly more peaks in the second derivative current-voltage spectra displaced by phonon energies from the density of states singularity associated with superconductivity. Calculations of inelastic processes generated by apical O-phonons show good qualitative agreement with recent experiments report…
We report inelastic x-ray scattering experiments on the lattice dynamics in SmFeAsO and superconducting SmFeAsO$_{0.6}$F$_{0.35}$ single crystals. Particular attention was paid to the dispersions along the [100] direction of three optical modes close to 23 meV, polarized out of the FeAs planes. Remarkably, two of these modes are strongly renormalized upon fluorine doping. These results provide significant insight into the energy and momentum dependence of the coupling of the lattice to the electron system and underline the importance of spin-phonon coupling in the superconducting iron-pnictide…
We report here first extensive measurements of the temperature dependence of phonon density of states of BaFe2As2, the parent compound of the newly discovered FeAs-based superconductors, using inelastic neutron scattering. The experiments were carried out on the thermal time-of-flight neutron spectrometer IN4 at the ILL on a polycrystalline sample. There is no appreciable change in the spectra between T = 10 K and 200 K, although the sample undergoes a magnetic as well as a tetragonal-to-orthorhombic structural phase transition at 140 K. This indicates a rather harmonic phonon system. Shell mo…
We have performed extensive ab initio calculations to investigate phonon dynamics and their possible role in superconductivity in BaFe2As2 and related systems. The calculations are compared to inelastic neutron scattering data that offer improved resolution over published data [Mittal et al., PRB 78 104514 (2008)], in particular at low frequencies. Effects of structural phase transition and full/partial structural relaxation, with and without magnetic ordering, on the calculated vibrational density of states are reported. Phonons are best reproduced using either the relaxed magnetic structures…
We report measurements of the phonon density of states as measured with inelastic x-ray scattering in SmFeAsO$_{1-x}$F$_y$ powders. An unexpected strong renormalization of phonon branches around 23 meV is observed as fluorine is substituted for oxygen. Phonon dispersion measurements on SmFeAsO$_{1-x}$F$_y$ single crystals allow us to identify the 21 meV A$_{1g}$ in-phase (Sm,As) and the 26 meV B$_{1g}$ (Fe,O) modes to be responsible for this renormalization, and may reveal unusual electron-phonon coupling through the spin channel in iron-based superconductors.
We investigate the low energy acoustical and optical modes in $\mathrm{HgBa_2CuO_{4+δ}}$ using inelastic x-ray scattering (IXS). The experimental phonon dispersion and the dynamical structure factor are compared with an atomic shell model, and the set of the atomic potentials obtained are discussed. Our results are also compared with those obtained by Raman spectroscopy and with density-of-state data measured by inelastic neutron scattering.
We study the $τ_1$-impurity induced $\mathbf{q}$-space pattern of the energy derivative local density of states (LDOS) in a d-wave superconductor. We are motivated in part by the recent scanning tunneling microscopy (STM) observation of strong gap inhomogeneity with weak charge density variation in Bi$_{2}$Sr$_2$CaCu$_2$O$_{8+δ}$ (BSCCO). The hypothesis is that the gap inhomogeneity might be triggered by the disorder in pair potential. We focus on the effects of electron coupling to various bosonic modes, at the mode energy shifted by the d-wave superconducting gap. The pattern due to a highly…
Electron-boson coupling plays a key role in superconductivity for many systems. However, in copper-based high-temperature ($T_c$) superconductors, its relation to superconductivity remains controversial despite strong spectroscopic fingerprints. Here we use angle-resolved photoemission spectroscopy to find a striking correlation between the superconducting gap and the bosonic coupling strength near the Brillouin zone boundary in Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$. The bosonic coupling strength rapidly increases from the overdoped Fermi-liquid regime to the optimally doped strange metal, concomitant…
Bulk charge density waves are now reported in nearly all high-temperature superconducting cuprates, with the noticeable exception of one particular family: the copper oxychlorides. Here, we used resonant inelastic X-ray scattering to reveal a bulk charge density waves in these materials. Combining resonant inelastic X-ray scattering with non-resonant inelastic X-ray scattering, we investigate the interplay between the lattice excitations and the charge density wave, and evidence the phonon anomalies of the Cu-O bond-stretching mode at the charge density wave wave-vector. We propose that such e…
The coupling between lattice and charge degrees of freedom in condensed matter materials is ubiquitous and can often result in interesting properties and ordered phases, including conventional superconductivity, charge density wave order, and metal-insulator transitions. Angle-resolved photoemission spectroscopy and both neutron and non-resonant x-ray scattering serve as effective probes for determining the behavior of appropriate, individual degrees of freedom -- the electronic structure and lattice excitation, or phonon dispersion, respectively. However, each provides less direct information…
The in-plane oxygen vibrations in La2NiO4 are investigated for several hole-doping concentrations both theoretically and experimentally via inelastic neutron scattering. Using an inhomogeneous Hartree-Fock plus RPA numerical method in a two-dimensional Peierls-Hubbard model, it is found that the doping induces stripe ordering of localized charges, and that the strong electron-lattice coupling causes the in-plane oxygen modes to split into two subbands. This result agrees with the phonon band splitting observed by inelastic neutron scattering in La2-xSrxNiO4. Predictions of strong electron-latt…
The coupling between lattice vibration quanta and valence electrons can induce charge density modulations and decisively influence the transport properties of materials, e.g. leading to conventional superconductivity. In high critical temperature superconductors, where electronic correlation is the main actor, the actual role of electron-phonon coupling (EPC) is being intensely debated theoretically and investigated experimentally. We present an in-depth study of how the EPC strength can be obtained directly from resonant inelastic x-ray scattering (RIXS) data through the theoretical approach …
Phonon-assisted electronic tunnelings through a vibrating quantum dot embedded between normal and superconducting leads are studied in the Kondo regime. In such a hybrid device, with the bias applied to the normal lead, we find a series of Kondo sidebands separated by half a phonon energy in the differential conductance, which are distinct from the phonon-assisted sidebands previously observed in the conventional Andreev tunnelings and in systems with only normal leads. These Kondo sidebands originate from the Kondo-Andreev cooperative cotunneling mediated by phonons, which exhibit a novel Kon…
