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We use diffuse and inelastic x-ray scattering to study the formation of an incommensurate charge-density-wave (I-CDW) in BaNi$_2$As$_2$, a candidate system for charge-driven electronic nematicity. Intense diffuse scattering is observed around the modulation vector of the I-CDW, $Q_{I-CDW}$. It is already visible at room temperature and collapses into superstructure reflections in the long-range ordered state where a small orthorhombic distortion occurs. A clear dip in the dispersion of a low-energy transverse optical phonon mode is observed around $Q_{I-CDW}$. The phonon continuously softens upon cooling, ultimately driving the transition to the I-CDW state. The transverse character of the soft-phonon branch elucidates the complex pattern of the I-CDW satellites observed in the current and earlier studies and settles the debated unidirectional nature of the I-CDW. The phonon instability and its reciprocal space position is well captured by our ${ab}$ ${initio}$ calculations. These however indicate that neither Fermi surface nesting, nor enhanced momentum-dependent electron-phonon coupling can account for the I-CDW formation, demonstrating its unconventional nature.% and suggest alternative origins of the I-CDW., Comment: Revised version - to appear in PRL

Following previous works reporting an anomalous behavior of several zone-center optical phonons across the magnetic transition of square lattice iridates Sr2IrO4 and Sr3Ir2O7, we have investigated the lattice dynamics as a function of momentum in these materials by means of high-resolution inelastic x-ray scattering (IXS). The observed phonon energies and scattering intensities across the Brillouin zone are in excellent agreement with ab-initio lattice dynamical calculations based on non-magnetic density-functional-perturbation theory (DFPT). Our results do not evidence any renormalization of the phonons at finite momentum across the magnetic transition of Sr2IrO4. The only anomalous behavior was detected for the in-plane polarized longitudinal-acoustic phonon branch in Sr3Ir2O7, which anomalously softens towards low temperatures and might be related to anisotropic negative thermal expansion in this compound. No anomalies related to potential charge ordering were observed.

Electronic nematicity is often found in unconventional superconductors, suggesting its relevance for electronic pairing. In the strongly hole-doped iron-based superconductors, the symmetry channel and strength of the nematic fluctuations, as well as the possible presence of long-range nematic order, remain controversial. Here, we address these questions using transport measurements under elastic strain. By decomposing the strain response into the appropriate symmetry channels, we demonstrate the emergence of a giant in-plane symmetric contribution, associated with the growth of both strong electronic correlations and the sensitivity of these correlations to strain. We find weakened remnants of the nematic fluctuations that are present at optimal doping, but no change in the symmetry channel of nematic fluctuations with hole doping. Furthermore, we find no evidence for a nematic-ordered state in the AFe$_2$As$_2$(A = K, Rb, Cs) superconductors. These results revise the current understanding of nematicity in hole-doped iron-based superconductors.

We report a combined inelastic neutron and X-ray scattering study of the phonon density of states of the nano- and microcrystalline lanthanide-based materials NaY$_{0.8}$Yb$_{0.18}$Er$_{0.02}$F$_4$ and NaGd$_{0.8}$Yb$_{0.18}$Er$_{0.02}$F$_4$. While large (20 nm) nanocrystals display the same vibrational spectra as their microcrystalline counterparts, we find an enhanced phonon density of states at low energies, $E \leq 15\,\rm{meV}$, in ultra-small (5 nm) NaGd$_{0.8}$Yb$_{0.18}$Er$_{0.02}$F$_4$ nanocrystals which we assign to an increased relative spectral weight of surface phonon modes. Based on our observations for ultra-small nanocrystals, we rationalize that an increase of the phonon density of states in large nanocrystals due to surface phonons is too small to be observed in the current measurements. The experimental approach described in this report constitutes the first step toward the rationalization of size effects on the modification of the absolute upconversion quantum yield of upconverting nanocrystals.

We study the elastoresistance of the highly correlated material CsFe2As2 in all symmetry channels. Neutralizing its thermal expansion by means of a piezoelectric-based strain cell is demonstrated to be essential. The elastoresistance response in the in-plane symmetric channel is found to be large, while the response in the symmetry-breaking channels is weaker and provides no evidence for a divergent nematic susceptibility. Rather, our results can be interpreted naturally within the framework of a coherence-incoherence crossover, where the low-temperature coherent state is sensitively tuned by the in-plane atomic distances.

We report on the lattice and spin dynamics in the monopnictide CrAs using polarized Raman scattering. This system exhibits a first-order magneto-structural phase transition at T_N~ 265 K, below which the magnetic moments of Cr form an incommensurate double helical magnetic structure while the unit cell volume abruptly expands. Across the transition, the frequencies of the fully symmetric Ag phonons strongly renormalize, which along with the results of first-principle calculations suggest the presence of a sizeable coupling of the phonons to the magnetic degrees of freedom in this compound. In addition, we observe two broad modes around 350 and 1700 cm-1 in the magnetic phase, which we associate with two-magnon Raman scattering. This work provides one of the few examples of magnetic Raman scattering from a non-collinear magnet.

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 dynamics in V$_3$Si with the focus on the temperature-dependent properties of low-energy acoustic phonon modes in several high-symmetry directions. We paid particular attention to the evolution of the soft phonon mode of the structural phase transition observed in our sample at $T_s=18.9\,\rm{K}$, i.e., just above the measured superconducting phase transition at $T_c=16.8\,\rm{K}$. Theoretically, we predict lattice dynamics including electron-phonon coupling based on density-functional-perturbation theory and discuss the relevance of the soft phonon mode with regard to the value of $T_c$. Furthermore, we explain superconductivityinduced anomalies in the lineshape of several acoustic phonon modes using a model proposed by Allen et al., [Phys. Rev. B 56, 5552 (1997)].

We investigate the three-dimensional electronic structure of the seminal charge-density-wave (CDW) material 2H-NbSe$_2$ by soft x-ray angle-resolved photoelectron spectroscopy and density-functional theory. Our results reveal the pronounced 3D character of the electronic structure formed in the quasi-two-dimensional layered crystal structure. In particular, we find a strong dispersion along $k_z$ excluding a nesting-driven CDW formation based on experimental data. The 3D-like band structure of 2H-NbSe$_2$ has strong implications for the intriguing phase competition of CDW order with superconductivity.

The family of rare-earth tritellurides RTe$_3$ features charge-density-wave (CDW) order related to strongly momentum-dependent electron-phonon coupling. Similar to other CDW compounds, superconductivity is observed when the CDW order is suppressed via hydrostatic pressure [1]. What sets the heavier members of the RTe3 series apart is the observation of a second CDW transition at lower temperatures having an in-plane ordering wavevector $q_{CDW,2}\parallel [100]$ of almost the same magnitude but orthogonal to the ordering wavevector $q_{CDW,1}\parallel [001]$ observed at higher temperatures [2]. Here, we report an inelastic x-ray scattering investigation of the lattice dynamics of DyTe$_3$. In particular, we show that there are several phonon modes along both in-plane directions, which respond to the onset of the CDW transition at $T_{CDW,1}=308\,\rm{K}$. Surprisingly, these soft modes close to $q_{CDW,2}=(0.68,0,0)$ show strong softening near $T_{CDW,1}$ but do not exhibit any response to the lower-temperature transition at $T_{CDW,2}=68\,\rm{K}$. Our results indicate that the low-temperature CDW order is not just the 90{\deg} rotated analogue of the one appearing at high temperatures.

While charge density wave (CDW) instabilities are ubiquitous to superconducting cuprates, the different ordering wavevectors in various cuprate families have hampered a unified description of the CDW formation mechanism. Here we investigate the temperature dependence of the low energy phonons in the canonical CDW ordered cuprate La$_{1.875}$Ba$_{0.125}$CuO$_{4}$. We discover that the phonon softening wavevector associated with CDW correlations becomes temperature dependent in the high-temperature precursor phase and changes from a wavevector of 0.238 reciprocal space units (r.l.u.) below the ordering transition temperature up to 0.3~r.l.u. at 300~K. This high-temperature behavior shows that "214"-type cuprates can host CDW correlations at a similar wavevector to previously reported CDW correlations in non-"214"-type cuprates such as YBa$_{2}$Cu$_{3}$O$_{6+\delta}$. This indicates that cuprate CDWs may arise from the same underlying instability despite their apparently different low temperature ordering wavevectors., Comment: Accepted in Phys. Rev. X; 9 pages; 5 figures; 3 pages of supplementary material

We calculate the effect of a static electric field on the critical temperature of a s-wave one band superconductor in the framework of proximity effect Eliashberg theory. In the weak electrostatic field limit the theory has no free parameters while, in general, the only free parameter is the thickness of the surface layer where the electric field acts. We conclude that the best situation for increasing the critical temperature is to have a very thin film of a superconducting material with a strong increase of electron-phonon (boson) constant upon charging., Comment: 9 pages, 5 figures

The competition between superconductivity and other ground states of solids is one of the challenging topics in condensed matter physics. Apart from high-temperature superconductors [1,2] this interplay also plays a central role in the layered transition-metal dichalcogenides, where superconductivity is stabilized by suppressing charge-density-wave order to zero temperature by intercalation [3] or applied pressure [4-7]. 1T-TiSe$_2$ forms a prime example, featuring superconducting domes on intercalation as well as under applied pressure. Here, we present high energy-resolution inelastic x-ray scattering measurements of the CDW soft phonon mode in intercalated Cu$_x$TiSe$_2$ and pressurized 1T-TiSe$_2$ along with detailed ab-initio calculations for the lattice dynamical properties and phonon-mediated superconductivity. We find that the intercalation-induced superconductivity can be explained by a solely phonon-mediated pairing mechanism, while this is not possible for the superconducting phase under pressure. We argue that a hybridization of phonon and exciton modes in the pairing mechanism is necessary to explain the full observed temperature-pressure-intercalation phase diagram. These results indicate that 1T-TiSe$_2$ under pressure is close to the elusive state of the excitonic insulator.

We present a high energy-resolution inelastic x-ray scattering data investigation of the charge-density-wave (CDW) soft phonon mode upon entering the superconducting state in $2H$-NbSe$_2$. Measurements were done close to the CDW ordering wavevector $\mathbf{q}_{CDW}$ at $\mathbf{q}=\mathbf{q}_{CDW}+(0,0,l)$,$0.15\leq l \leq 0.5$, for $T=10\,\rm{K}$ (CDW order) and $3.8\,\rm{K}$ (CDW order + superconductivity). We observe changes of the phonon lineshape that are characteristic for systems with strong electron-phonon coupling in the presence of a superconducting energy gap $2\Delta_c$ and from which we can demonstrate an $l$-dependence of the superconducting gap. Reversely, our data imply that the CDW energy gap is strongly localized along the $c^*$ direction. The confinement of the CDW gap to a very small momentum region explains the rather low competition and easy coexistence of CDW order and superconductivity in $2H$-NbSe$_2$. However, the energy gained by opening $\Delta_{CDW}$ seems to be too small to be the driving force of the phase transition at $T_{CDW}=33\,\rm{K}$ , which is better described as an electron-phonon coupling driven structural phase transition.

We study the possibility of pressure-induced transitions from a normal semiconductor to a topological insulator (TI) in bismuth tellurohalides using density functional theory and tight-binding method. In BiTeI this transition is realized through the formation of an intermediate phase, a Weyl semimetal, that leads to modification of surface state dispersions. In the topologically trivial phase, the surface states exhibit a Bychkov-Rashba type dispersion. The Weyl semimetal phase exists in a narrow pressure interval of 0.2 GPa. After the Weyl semimetal--TI transition occurs, the surface electronic structure is characterized by gapless states with linear dispersion. The peculiarities of the surface states modification under pressure depend on the band-bending effect. We have also calculated the frequencies of Raman active modes for BiTeI in the proposed high-pressure crystal phases in order to compare them with available experimental data. Unlike BiTeI, in BiTeBr and BiTeCl the topological phase transition does not occur. In BiTeBr, the crystal structure changes with pressure but the phase remains a trivial one. However, the transition appears to be possible if the low-pressure crystal structure is retained. In BiTeCl under pressure, the topological phase does not appear up to 18 GPa due to a relatively large band gap width in this compound.

Recent advances in strain engineering at the nanoscale have shown the feasibility to modulate the properties of graphene. Although the electron-phonon (e-ph) coupling and Kohn anomalies in graphene define the phonon branches contributing to the resonance Raman scattering, and is relevant to the electronic and thermal transport as a scattering source, the evolution of the e-ph coupling as a function of strain has been less studied. In this work, the Kohn anomalies and the e-ph coupling in uniaxially strained graphene along armchair (AC) and zigzag (ZZ) directions were studied by means of density functional perturbation theory calculations. In addition to the phonon anomaly at the transversal optical (TO) phonon branch in the K point for pristine graphene, we found that uniaxial strain induces a discontinuity in the frequency derivative of the longitudinal acoustic (LA) phonon branch. This behavior corresponds to the emergence of a Kohn anomaly, as a consequence of a strain-enhanced e-ph coupling. Thus, the present results for uniaxially strained graphene contrast with the commonly assumed view that the e-ph coupling around the K point is only present in the TO phonon branch., Comment: Accepted for publication in Physical Review B (12 July 2016)

We study \textit{ab initio} a pyrochlore compound, CsW$_{2}$O$_{6}$, which exhibits a yet unexplained metal-insulator transition. We find that (1) the reported low-$T$ structure is likely inaccurate and the correct structure has a twice larger cell; (2) the insulating phase is not of a Mott or dimer-singlet nature, but a rare example of a 3D Peierls transition, with a simultaneous condensation of three density waves; (3) spin-orbit interaction plays a crucial role, forming well-nested bands. The high-$T$ (HT) phase, if stabilized, could harbor a unique $e_{g}+ie_{g}$ superconducting state that breaks the time reversal symmetry, but is not chiral. This state was predicted in 1999, but never observed. We speculate about possible ways to stabilize the HT phase while keeping the conditions for superconductivity.

We present a comprehensive study of the low-temperature heat capacity and thermal expansion of single crystals of the hole-doped Ba1-xKxFe2As2 series (0

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 $\lambda \sim 2$. 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 experiments ($2\Delta_0 / k_{\mathrm{B}}T_c \sim 5$). The low-lying phonon modes observed in the experiments are approximately 1.5 meV harder than the corresponding calculated phonon branch. Moreover, we do not find any changes in the spectra upon entering the superconducting phase. We conclude that current theoretical calculations underestimate the energy of the lowest band of phonon modes indicating that the coupling of these modes to the electronic subsystem is overestimated., Comment: 5 pages, 3 figures

Motivated by model calculations for the heavy fermion superconductor CePt3Si predicting phonon anomalies because of anti-symmetric spin-orbit coupling we performed a detailed experimental study of the lattice dynamical properties of CePt3Si. In particular, we investigated the dispersion of transverse acoustic and low energy optic phonon branches along the [110] direction using inelastic neutron scattering. In these branches, we found deviations from our ab-initio lattice dynamical calculations, which overall give a good description of the phonon dispersion in CePt3Si. However, the agreement for the [110] transverse modes can be improved if we neglect the Ce 4f states, done in an additional calculation. We conclude that the lattice dynamics of CePt3Si are conventional and that the observed deviations are not related to effects of anti-symmetric spin-orbit-coupling. More likely, ab-initio calculations overestimate the exchange between different phonon branches, particularly in the presence of 4f electron states. Our results imply that the ASOC plays less a role in non-centrosymmetric superconductors than commonly believed., Comment: accepted by PRB

We present a high energy-resolution inelastic x-ray scattering investigation of the soft phonon mode in the charge-density-wave system TbTe$_3$. We analyze our data based on lattice dynamical calculations using density-functional-perturbation-theory and find clear evidence that strongly momentum dependent electron-phonon-coupling defines the periodicity of the CDW superstructure: Our experiment reveals strong phonon softening and increased phonon line widths over a large part in reciprocal space adjacent to the CDW ordering vector $q_{CDW} = (0, 0, 0.3)$. Further, $q_{CDW}$ is clearly offset from the wave vector of (weak) Fermi surface nesting $q_{FS} = (0, 0, 0.25)$ and our detailed analysis indicates that electron-phonon-coupling is responsible for this shift. Hence, we can add TbTe$_3$, which was previously considered as a canonical CDW compound following the Peierls scenario, to the list of distinct charge-density-wave materials characterized by momentum dependent electron-phonon coupling.

We present a comprehensive ab initio study of structural, electronic, lattice dynamical and electron-phonon coupling properties of the Bi(111) surface within density functional perturbation theory. Relativistic corrections due to spin-orbit coupling are consistently taken into account. As calculations are carried out in a periodic slab geometry, special attention is given to the convergence with respect to the slab thickness. Although the electronic structure of Bi(111) thin films varies significantly with thickness, we found that the lattice dynamics of Bi(111) is quite robust and appears converged already for slabs as thin as 6 bilayers. Changes of interatomic couplings are confined mostly to the first two bilayers, resulting in super-bulk modes with frequencies higher than the optic bulk spectrum, and in an enhanced density of states at lower frequencies for atoms in the first bilayer. Electronic states of the surface band related to the outer part of the hole Fermi surfaces exhibit a moderate electron-phonon coupling of about 0.45, which is larger than the coupling constant of bulk Bi. States at the inner part of the hole surface as well as those forming the electron pocket close to the zone center show much increased couplings due to transitions into bulk projected states near Gamma_bar. For these cases, the state dependent Eliashberg functions exhibit pronounced peaks at low energy and strongly deviate in shape from a Debye-like spectrum, indicating that an extraction of the coupling strength from measured electronic self-energies based on this simple model is likely to fail., Comment: 30 pages, 11 figures

We present a combined density-functional-perturbation-theory and inelastic neutron scattering study of the lattice dynamical properties of YNi2B2C. In general, very good agreement was found between theory and experiment for both phonon energies and line widths. Our analysis reveals that the strong coupling of certain low energy modes is linked to the presence of large displacements of the light atoms, i.e. B and C, which is unusual in view of the rather low phonon energies. Specific modes exhibiting a strong coupling to the electronic quasiparticles were investigated as a function of temperature. Their energies and line widths showed marked changes on cooling from room temperature to just above the superconducting transition at Tc = 15.2 K. Calculations simulating the effects of temperature allow to model the observed temperature dependence qualitatively.

The ferropnictide superconductors exhibit a sensitive interplay between the lattice and magnetic degrees of freedom, including a number of phonon modes that are much softer than predicted by nonmagnetic calculations using density functional theory (DFT). However, it is not known what effect, if any, the long-range magnetic order has on phonon frequencies above 23 meV, where several phonon branches are very closely spaced in energy and it is challenging to isolate them from each other. We measured these phonons using inelastic time-of-flight neutron scattering in ~40 Brillouin zones, and developed a technique to determine their frequencies. We find this method capable of determining phonon energies to ~0.1 meV accuracy, and that the DFT calculations using the experimental structure yield qualitatively correct energies and eigenvectors. We do not find any effect of the magnetic transition on these phonons., Comment: To be published in Physical Review B

The electron-phonon interaction is a major factor influencing the competition between collective instabilities in correlated-electron materials, but its role in driving high-temperature superconductivity in the cuprates remains poorly understood. We have used high-resolution inelastic x-ray scattering to monitor low-energy phonons in YBa$_2$Cu$_3$O$_{6.6}$ (superconducting $\bf T_c = 61$ K), which is close to a charge density wave (CDW) instability. Phonons in a narrow range of momentum space around the CDW ordering vector exhibit extremely large superconductivity-induced lineshape renormalizations. These results imply that the electron-phonon interaction has sufficient strength to generate various anomalies in electronic spectra, but does not contribute significantly to Cooper pairing. In addition, a quasi-elastic "central peak" due to CDW nanodomains is observed in a wide temperature range above and below $\bf T_c$, suggesting that the gradual onset of a spatially inhomogeneous CDW domain state with decreasing temperature is a generic feature of the underdoped cuprates.

KFe2As2 single crystals are studied using specific-heat, high-resolution thermal-expansion, magnetization, and magnetostriction measurements. The magnetization and magnetostriction data provide clear evidence for strong Pauli limiting effects for magnetic fields parallel to the FeAs planes, suggesting that KFe2As2 may be a good candidate to search for the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. Using standard thermodynamic relations, the uniaxial pressure derivatives of the critical temperature ($T_{c}$), the normal-state Sommerfeld coefficient ($\gamma_{n}$), the normal-state susceptibility ($\chi$), and the thermodynamic critical field ($H_{c}$) are calculated from our data. We find that the close relationship between doping and pressure as found in other Fe-based systems does not hold for KFe2As2.

We present an investigation of the lattice dynamics of the charge-density-wave compound 2H-NbSe2. We analyze the precise nature of the wave vector dependent electron-phonon coupling (EPC) and derive the bare dispersion of the charge-density-wave (CDW) soft phonon mode using inelastic x-ray scattering combined with ab-initio calculations. Experimentally, phonon modes along the {\Gamma} - M line, i.e. q = (h, 0, 0) with 0 <= h <= 0.5, with the same longitudinal symmetry ({\Sigma}1) as the CDW soft mode were investigated up to 32 meV. In agreement with our calculations we observe significant EPC in the optic modes at h <= 0.2. We analyze the EPC in the optic as well as acoustic modes and show that the q dependences stem from scattering processes between two bands at the Fermi surface both having Nb 4d character. Finally, we demonstrate that the soft mode dispersion at T = 33 K (= {T_{CDW}}) can be well described on the basis of a strongly q dependent EPC matrix element and an acoustic-like bare phonon dispersion in agreement with observations near room temperature., Comment: accepted as regular article in Physical Review B

Using resistivity, heat-capacity, thermal-expansion, and susceptibility measurements we study the normal-state behavior of KFe2As2. We find that both the Sommerfeld coefficient gamma = 103 mJ mol-1 K-2 and the Pauli susceptibility chi = 4x10-4 are strongly enhanced, which confirm the existence of heavy quasiparticles inferred from previous de Haas-van Alphen and ARPES experiments. We discuss this large enhancement using a Gutzwiller slave-boson mean-field calculation, which reveals the proximity of KFe2As2 to an orbital-selective Mott transition. The temperature dependence of the magnetic susceptibility and the thermal expansion provide strong experimental evidence for the existence of a coherence-incoherence crossover, similar to what is found in heavy fermion and ruthenate compounds, due to Hund's coupling between orbitals.

We report an inelastic neutron scattering investigation of phonons with energies up to 159 meV in the conventional superconductor YNi$_2$B$_2$C. Using the SWEEP mode, a newly developed time-of-flight technique involving the continuous rotation of a single crystal specimen, allowed us to measure a four dimensional volume in (Q,E) space and, thus, determine the dispersion surface and linewidths of the $A_{1g}$ (~ 102 meV) and $A_u$ (~ 159 meV) type phonon modes for the whole Brillouin zone. Despite of having linewidths of $\Gamma = 10 meV$, $A_{1g}$ modes do not strongly contribute to the total electron-phonon coupling constant $\lambda$. However, experimental linewidths show a remarkable agreement with ab-initio calculations over the complete phonon energy range demonstrating the accuracy of such calculations in a rare comparison to a comprehensive experimental data set., Comment: accepted for publication in PRL

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 with a uniaxial charge-density modulation and does not mediate d-wave superconductivity., Comment: to appear in PRL

We report high-resolution inelastic x-ray measurements of the soft phonon mode in the charge-density-wave compound TiSe$_2$. We observe a complete softening of a transverse optic phonon at the L point, i.e. q = (0.5, 0, 0.5), at T ~ T_{CDW}. Renormalized phonon energies are observed over a large wavevector range $(0.3, 0, 0.5) \le \mathbf{q} \le (0.5, 0, 0.5)$. Detailed ab-initio calculations for the electronic and lattice dynamical properties of TiSe2 are in quantitative agreement with experimental frequencies for the phonon branch involving the soft mode. The observed broad range of renormalized phonon frequencies is directly related to a broad peak in the electronic susceptibility stabilizing the charge-density-wave ordered state. Our analysis demonstrates that a conventional electron-phonon coupling mechanism can explain a structural instability and the charge-density-wave order in TiSe_2 although other mechanisms might further boost the transition temperature.

We report inelastic x-ray scattering measurements of the temperature dependence of phonon dispersion in the prototypical charge-density-wave (CDW) compound NbSe2. Surprisingly, acoustic phonons soften to zero frequency and become overdamped over an extended region around the CDW wavevector. This extended phonon collapse is dramatically different from the sharp cusp in the phonon dispersion expected from Fermi surface nesting. Instead, our experiments combined with ab initio calculations, show that it is the wavevector dependence of the electron-phonon coupling that drives the CDW formation in NbSe$_2$ and determines its periodicity. This mechanism explains the so far enigmatic behavior of CDW in NbSe$_2$ and may provide a new approach to other strongly correlated systems where electron-phonon coupling is important.

We have studied the electron-phonon and superconducting properties of the Mg{1-x}AlxB2 and MgB{2(1-y)}C{2y} alloys within the framework of density functional theory using the self-consistent virtual-crystal approximation. For both alloys, the Eliashberg spectral functions and the electron-phonon coupling constants have been calculated in the two-band model for several concentrations up to x(Al)=0.55 and y(C)=0.175. We solved numerically the two-band Eliashberg gap equations without considering interband scattering. Using a single parameter for the Coulomb pseudopotential, which was determined for the undoped compound, we were able to reproduce the experimental doping dependence of Delta_sigma, Delta_pi, and T_c for both alloys on a quantitative level. In particular, the observed differences in the doping range of superconductivity between Al and C doping indicate a pronounced influence of the doping site, which can be explained naturally in the present approach without the need to invoke interband scattering, suggesting that this factor plays only a minor role., Comment: 18 pages, 6 figures

An extensive calorimetric study of the normal- and superconducting-state properties of Ba(Fe1-xCox)2As2 is presented for 0 < x < 0.2. The normal-state Sommerfeld coefficient increases (decreases) with Co doping for x < 0.06 (x > 0.06), which illustrates the strong competition between magnetism and superconductivity to monopolize the Fermi surface in the underdoped region and the filling of the hole bands for overdoped Ba(Fe1-xCox)2As2. All superconducting samples exhibit a residual electronic density of states of unknown origin in the zero-temperature limit, which is minimal at optimal doping but increases to the normal-state value in the strongly under- and over-doped regions. The remaining specific heat in the superconducting state is well described using a two-band model with isotropic s-wave superconducting gaps., Comment: Submitted to Europhysics Letters

The pressure dependence of a large number of phonon modes in CaFe2As2 with energies covering the full range of the phonon spectrum has been studied using inelastic x-ray and neutron scattering. The observed phonon frequency changes are in general rather small despite the sizable changes of the lattice parameters at the phase transition. This indicates that the bonding properties are not profoundly altered by the phase transition. The transverse acoustic phonons propagating along the c-direction are an exception because they stiffen very significantly in response to the large contraction of the c-axis. The lattice parameters are found to change significantly as a function of pressure before, during and after the first-order phase transition. However, the frequencies change nearly uniformly with the change in the lattice parameters due to pressure, with no regard specifically to the first-order phase transition. Density functional theory describes the frequencies in both the zero pressure and in the collapsed phase in a satisfactory way if based on the respective crystal structures.

Interactions with electronic excitations can soften and/or broaden phonons. They are greatly amplified at wavevectors Q+- that connect parallel (nested) sheets of the Fermi surface. In such a case, called a Kohn anomaly, the phonon dispersion sharply dips and its linewidth has a maximum at Q+-. Here we present results of inelastic x-ray scattering measurements that uncovered soft phonons in chromium far from Q+-. They appear in addition to the previously reported soft phonons at Q+-. Calculations in the local density approximation (LDA) show that the new anomalies originate from enhanced electron-phonon coupling. A similar mechanism may explain phonon anomalies away from nesting wavevectors in copper oxide superconductors and other compounds.

We measured phonon frequencies and linewidths in doped and undoped BaFe2As2 single crystals by inelastic x-ray scattering and compared our results with density functional theory (DFT) calculations. In agreement with previous work, the calculated frequencies of some phonons depended on whether the ground state was magnetic or not and, in the former case, whether phonon wavevector was parallel or perpendicular to the magnetic ordering wavevector. The experimental results agreed better with the magnetic calculation than with zero Fe moment calculations, except the peak splitting expected due to magnetic domain twinning was not observed. Furthermore, phonon frequencies were unaffected by the breakdown of the magnetic ground state due to either doping or increased temperature. Based on these results we propose that phonons strongly couple not to the static order, but to high frequency magnetic fluctuations., Comment: Minor revision of the text

Extensive inelastic neutron scattering measurements of phonons on a single crystal of CaFe2As2 allowed us to establish a fairly complete picture of phonon dispersions in the main symmetry directions. The phonon spectra were also calculated by density functional theory (DFT) in the local density approximation (LDA). There are serious discrepancies between calculations done for the optimized structure and experiment, because the optimised structure is not the ambient pressure structure but is very close to the collapsed structure reached at p = 3.5 kbar. However, if the experimental crystal structure is used the calculation gives correct frequencies of most phonons. The most important new result is that linewidths/frequencies of certain modes are larger/softer than predicted by DFT-LDA. We also observed strong temperature dependence of some phonons near the structural phase transition near 173K. This behavior may indicate anomalously strong electron phonon coupling and/or anharmonicity, which may be important to the mechanism of superconductivity., Comment: 12 pages, 3 figues Revised version, Final version, Accepted for publication in Physical Review Letters

We show that the superconducting energy gap $\Delta$ can be directly observed in phonon spectra, as predicted by recent theories. In addition, since each phonon probes the gap on only a small part of the Fermi surface, the gap anisotropy can be studied in detail. Our neutron scattering investigation of the anisotropic conventional superconductor YNi$_2$B$_2$C demonstrates this new application of phonon spectroscopy., Comment: 4 pages, 5 figures

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.

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 consistently with the superconductivity., Comment: 4 pages, 4 figures, to be published in Phys. Rev. B (Rapid Communications)

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., Comment: 8 Pages, 4 Figures Please reference Phys. Rev. B 75, 020505(R), 2007

We present a detailed study of the lattice dynamics and electron-phonon coupling for a (3,3) carbon nanotube which belongs to the class of small diameter based nanotubes which have recently been claimed to be superconducting. We treat the electronic and phononic degrees of freedom completely by modern ab-initio methods without involving approximations beyond the local density approximation. Using density functional perturbation theory we find a mean-field Peierls transition temperature of approx 40K which is an order of magnitude larger than the calculated superconducting transition temperature. Thus in (3,3) tubes the Peierls transition might compete with superconductivity. The Peierls instability is related to the special 2k_F nesting feature of the Fermi surface. Due to the special topology of the (n,n) tubes also a q=0 coupling between the two bands crossing the Fermi energy at k_F is possible which leads to a phonon softening at the Gamma point., Comment: 4 pages, 3 figures; to be published in Phys. Rev. Lett

Temperature dependent inelastic neutron-scattering measurements of the generalized phonon density-of-states for superconducting MgCNi_3, T_c=8 K, give evidence for a soft-mode behavior of low-frequency Ni phonon modes. Results are compared with ab initio density functional calculations which suggest an incipient lattice instability of the stoichiometric compound with respect to Ni vibrations orthogonal to the Ni-C bond direction., Comment: 4 pages, 5 figures

We study phonons in MgB2 using inelastic x-ray scattering (1.6 and 6 meV resolution). Our measurements show excellent agreement with theory for the dispersion and line-width: we clearly observe the softening and broadening of the crucial E2g mode through the Kohn anomaly along GM. Low temperature measurements (just above and below Tc) show negligible changes for the momentum-transfers investigated, and no change in the E2g mode at A between room temperature and 16K. We report the presence of a longitudinal mode along GA near in energy to the E2g mode that is not predicted by theory., Comment: 7 Pages of text and references 4 Figures in 4 pages

The phonon density-of-states of transition metal diborides TMB2 with TM = Ti, V, Ta, Nb and Y has been measured using the technique of inelastic neutron scattering. The experimental data are compared with ab initio density functional calculations whereby an excellent agreement is registered. The calculations thus can be used to obtain electron-phonon spectral functions within the isotropic limit. A comparison to similar data for MgB2 and AlB2 which were subject of prior publications as well as parameters important for the superconducting properties are part of the discussion., Comment: 4 pages, 3 figures

We have investigated the lattice dynamics of LiBC. Experimental Raman and inelastic neutron scattering results are confronted with density functional calculations. The excellent agreement between experiment and theory indicates that we have attained a high level of understanding for LiBC, which by its structure is closely related to superconducting MgB2 We will show that annealing of the sample is insufficient to cause Li deficiency and thus produce the expected superconductivity., Comment: 4 pages, 3 figures

The dynamical properties of the high-density Ru(001)-(1$\times$1)-O phase has been investigated by a combined high-resolution electron energy loss spectroscopy and density functional theory study. Due to a strong static outward relaxation of the first Ru layer a soft Rayleigh phonon mode is expected. However, a Rayleigh mode stiffening together with a new high energy in-plane phonon mode above the bulk bands is found which is related to a strong adsorbate-induced intralayer force constant stiffening which counteracts an interlayer softening. This structurally rather simple system with one surface atom per (1$\times$1) unit cell demonstrates the limited applicability of previously adopted models., Comment: 3 figures; submitted to Phys.Rev