C-axis Phonons in Fe-As Based Superconductors Investigated by Inelastic X-ray Scattering
D. Reznik, K. Lokshin, D. C. Mitchell, D. Parshall, W. Dmowski, D. Lamago, R. Heid, K. -P. Bohnen, A. S. Sefat, M. A. McGuire, B. C. Sales, D. G. Mandrus, A. As… 展开作者
D. Reznik, K. Lokshin, D. C. Mitchell, D. Parshall, W. Dmowski, D. Lamago, R. Heid, K. -P. Bohnen, A. S. Sefat, M. A. McGuire, B. C. Sales, D. G. Mandrus, A. Asubedi, D. J. Singh, A. Alatas, M. H. Upton, A. H. Said, Yu. Shvyd'ko, T. Egami
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 of the As-As vibrations (Raman active at the zone center) but not for the Fe-As vibrations (infrared-active at the zone center). This behavior cannot be explained by a 10% softening of Fe-As interaction strength as proposed previously for in-plane polarized vibrations.
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…
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…
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 w…
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…
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…
In our recent paper we presented empirical evidences suggesting that electrons in cuprate superconductors are strongly coupled to unscreened c-axis polar phonons. In the overdoped regime the c-axis metallizes and we present here simple theoretical arguments demonstrating that the observed effect of the metallic c-axis screening on the polar electron-phonon coupling is consistent with a strongly overdamped c-axis charge dynamics in the optimally doped system, becoming less dissipative in the overdoped regime.
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.
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.
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…
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…
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…
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…
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.
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…
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）
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…
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…
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…
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 conductivity spectra of c-axis oriented thin RuSr$_2$GdCu$_2$O$_8$ film on SrTiO$_3$ substrate, prepared by pulsed-laser deposition, are obtained from the analysis of the reflectivity spectra over broad frequency range and temperatures between 10 and 300 K. The free charge carriers are found to be strongly overdamped with their scattering rate (1.0 eV at room temperature) exceeding the plasma frequency (0.55 eV). Four phonon lines are identified in the experimental spectra and assigned to the specific oxygen related in-plane polarized vibrations based on the comparison with the results of …
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.
Inelastic x-ray scattering (IXS) was used to study the Cu-O bond-stretching vibrations in the static stripe phase compound La1.48Nd0.4Sr0.12CuO4. It was found that the intrinsic width in Q-space of the previously reported huge anomalous phonon softening and broadening is approximately 0.08r.l.u HWHM. A detailed comparison was also made to inelastic neutron scattering (INS) studies, which indicate a two-peak lineshape (with superimposed broad and narrow peaks) in the vicinity of the anomaly. The high resolution IXS data show that the narrow peak is mostly an artifact of the poor transverse Q-re…
The out-of-plane intercalate phonons of superconducting YbC6 have been measured with inelastic x-ray scattering. Model fits to this data, and previously measured out-of-plane intercalate phonons in graphite intercalation compounds (GICs), reveal surprising trends with the superconducting transition temperature. These trends suggest that superconducting GICs should be viewed as electron-doped graphite.
Phonon measurements in the A15-type superconductors were complicated in the past because of the unavailability of large single crystals for inelastic neutron scattering, e.g., in the case of Nb$_3$Sn, or unfavorable neutron scattering properties in the case of V$_3$Si. Hence, only few studies of the lattice dynamical properties with momentum resolved methods were published, in particular below the superconducting transition temperature $T_c$. Here, we overcome these problems by employing inelastic x-ray scattering and report a combined experimental and theoretical investigation of lattice dyna…
Magnetic excitations in the optimally doped high-$T_\mathrm{c}$ superconductor Bi$_{1.5}$Pb$_{0.55}$Sr$_{1.6}$La$_{0.4}$CuO$_{6+δ}$ (OP-Bi2201, $T_\mathrm{c}\simeq 34$ K) are investigated by Cu $L_3$ edge resonant inelastic x-ray scattering (RIXS), below and above the pseudogap opening temperature. At both temperatures the broad spectral distribution disperses along the (1,0) direction up to $\sim$350~meV at zone boundary, similarly to other hole-doped cuprates. However, above $\sim$0.22 reciprocal lattice units, we observe a concurrent intensity decrease for magnetic excitations and quasi-ela…
We present grazing incidence reflectivity measurements in the far infrared region at temperatures above and below Tc for a series of thallium (Tl2Ba2CuO6, Tl2Ba2CaCu2O8) and bismuth (Bi2Sr2CuO6, Bi2Sr2CaCu2O8, and Bi(2-x)Pb(x)Sr2CaCu2O8) based cuprate superconductors. From the spectra, which are dominated by the c-axis phonons, longitudinal frequencies (LO) are directly obtained. The reflectivity curves are well fitted by a series of Lorentz oscillators. In this way the transverse (TO) phonon frequencies were accurately determined. On the basis of the comparative study of the Bi and Tl based c…
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.
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…
We study the influence of inelastic rare-earth impurity scattering on electron-phonon mediated superconductivity and mass renormalization in (La$_{1-x}$Pr$_{x}$)Os$_{4}$Sb$_{12}$ compounds. Solving the strong coupling Eliashberg equations we find that the dominant quadrupolar component of the inelastic scattering on Pr impurities yields an enhancement of the superconducting transition temperature T$_c$ in LaOs$_{4}$Sb$_{12}$ and increases monotonically as a function of Pr concentration. The calculated results are in good agreement with the experimentally observed T$_c (x)$ dependence. Our anal…
The c-axis polarized phonon spectra of single crystals of YBCO_{6+x} have been measured for the doping range x=0.5 -> 0.95, between 10 K and 300 K. The low background electronic conductivity, determined by Kramers-Kronig analysis of the reflectance, leads to a rich phonon structure. With decreased doping the five normally-active B_{1u} modes broaden and the high-frequency apical oxygen mode splits into two components. We associate the higher of these with the two-fold coordinated copper-oxygen sticks. The 155 cm^{-1} low-frequency mode, which involves the apical and chain-oxygens, splits into …
In a superconductor with magnetic impurities, Kondo scattering results in the formation of localized states inside the superconducting gap. We show that inelastic electronic transitions involving quasiparticle scattering into and out of the localized states may result in significant changes in the non equilibrium properties of the superconductor. Using the model of Muller-Hartmann and Zittartz for the extreme dilute limit, and including both deformation potential and spin-lattice coupling we have calculated the rates of such inelastic transitions between continuum and discrete states, and show…
Emergence of an orbital-selective Mott phase (OSMP) found in multi-band correlated systems leads to a non-perturbative obliteration of the Landau Fermi liquid in favor of a novel metallic state exhibiting anomalous infra-red (branch-cut) continuum features in one- and two-particle responses. We use a combination of $(1)$ dynamical mean-field theory (DMFT) using the continuous-time-quantum Monte-Carlo (CTQMC) solver for a two-band Hubbard model and $(2)$ analytic arguments from an effective bosonized description to investigate strange metal features in inelastic neutron scattering studies for c…
