arXiv subjects

A. H. Said

Publications and source records attributed to A. H. Said.

At least 19 recordsLinked to original sources

arXiv2025

Weak phonon coupling to nematic quantum critical mode in $BaFe2(As1-xPx)2$

In this work, we investigate the softening of the in-plane transverse acoustic phonon driven by electronic nematicity in BaFe$_2$(As$_{1-x}$P$_x$)$_2$ using inelastic X-ray scattering, with a focus on the optimally doped sample ($x = 0.31$) sample, a system exhibiting signatures of a putative nematic quantum critical point and minimal disorder among iron pnictides. We observe only a modest softening of the phonon frequency and no evidence of critical damping, suggesting that the nematic quantum critical fluctuations couple only weakly to the lattice from our quantum critical model. Given the close proximity of the structural and magnetic transition temperatures in the underdoped sample, which implies that spin-nematic fluctuations couple strongly to the lattice. We conjecture that the quantum critical nematic fluctuations are predominantly orbital in origin.

cond-mat.str-el↗

arXiv2024

Incommensurate Transverse Peierls Transition

In one-dimensional quantum materials, conducting electrons and the underlying lattices can undergo a spontaneous translational symmetry breaking, known as Peierls transition. For nearly a century, the Peierls transition has been understood within the paradigm of electron-electron interactions mediated by longitudinal acoustic phonons. This classical picture has recently been revised in topological semimetals, where transverse acoustic phonons can couple with conducting p-orbital electrons and give rise to an unconventional Fermi surface instability, dubbed the transverse Peierls transition (TPT). Most interestingly, the TPT induced lattice distortions can further break rotation or mirror/inversion symmetries, leading to nematic or chiral charge density waves (CDWs). Quantum materials that host the TPT, however, have not been experimentally established. Here, we report the experimental discovery of an incommensurate TPT in the tetragonal Dirac semimetal EuAl$_4$. Using inelastic x-ray scattering with meV resolution, we observe the complete softening of a transverse acoustic phonon at the CDW wavevector upon cooling, whereas the longitudinal acoustic phonon is nearly unchanged. Combining with first principles calculations, we show that the incommensurate CDW wavevector matches the calculated charge susceptibility peak and connects the nested Dirac bands with Al 3$p_{x}$ and 3$p_{y}$ orbitals. Supplemented by second harmonic generation measurements, we show that the CDW induced lattice distortions break all vertical and diagonal mirrors whereas the four-fold rotational symmetry is retained below the CDW transition. Our observations strongly suggest a chiral CDW in EuAl$_4$ and highlight the TPT as a new avenue for chiral quantum states.

cond-mat.str-el↗

arXiv2024

Charge Density Waves in the 2.5-Dimensional Quantum Heterostructure

Charge density wave (CDW) and their interplay with correlated and topological quantum states are forefront of condensed matter research. The 4$H_{b}$-TaS$_2$ is a CDW ordered quantum heterostructure that is formed by alternative stacking of Mott insulating 1T-TaS$_2$ and Ising superconducting 1H-TaS$_2$. While the $\sqrt{13}\times\sqrt{13}$ and 3$\times$3 CDWs have been respectively observed in the bulk 1T-TaS$_2$ and 2H-TaS$_2$, the CDWs and their pivotal role for unconventional superconductivity in the 4$H_{b}$-TaS$_2$ remain unsolved. In this letter, we reveal the 2-dimensional (2D) $\sqrt{13}\times\sqrt{13}$ chiral CDW in the 1T-layers and intra-unit cell coupled 2D 2$\times$2 CDW in the 1H and 1H' layers of 4$H_{b}$-TaS$_2$. Our results establish 4$H_{b}$-TaS$_2$ a novel 2.5D quantum heterostructure, where 2D quantum states emerge from 3D crystalline structure.

cond-mat.supr-con↗

arXiv2023

Electronic structure and lattice dynamics of 1T-VSe$_2$: origin of the 3D-CDW

In order to characterize in detail the charge density wave (CDW) transition of 1$T$-VSe$_2$, its electronic structure and lattice dynamics are comprehensively studied by means of x-ray diffraction, angle resolved photoemission (ARPES), diffuse and inelastic x-ray scattering (IXS), and state-of-the-art first principles density functional theory calculations. Resonant elastic x-ray scattering (REXS) does not show any resonant enhancement at either V or Se K-edges, indicating that the CDW peak describes a purely structural modulation of the electronic ordering. ARPES identifies (i) a pseudogap at T$>$T$_{CDW}$, which leads to a depletion of the density of states in the $ML-M'L'$ plane at T$<$T$_{CDW}$, and (ii) anomalies in the electronic dispersion reflecting a sizable impact of phonons on it. A diffuse scattering precursor, characteristic of soft phonons, is observed at room temperature (RT) and leads to the full collapse of the low-energy phonon ($ω_1$) with propagation vector (0.25 0 -0.3) r.l.u. We show that the frequency and linewidth of this mode are anisotropic in momentum space, reflecting the momentum dependence of the electron-phonon interaction (EPI), hence demonstrating that the origin of the CDW is, to a much larger extent, due to the momentum dependence EPI with a small contribution from nesting. The pressure dependence of the $ω_1$ soft mode remains nearly constant up to 13 GPa at RT, with only a modest softening before the transition to the high-pressure monoclinic $C2/m$ phase. The wide set of experimental data are well captured by our state-of-the art first-principles anharmonic calculations with the inclusion of van der Waals (vdW) corrections in the exchange-correlation functional. The description of the electronics and dynamics of VSe$_2$ reported here adds important pieces of information to the understanding of the electronic modulations of TMDs.

cond-mat.str-el↗

arXiv2023

Softening of a flat phonon mode in the kagome ScV$_6$Sn$_6$

The long range electronic modulations recently discovered in the geometrically frustrated kagome lattice have opened new avenues to explore the effect of correlations in materials with topological electron flat bands. The observation of the lattice response to the emergent new phases of matter, a soft phonon mode, has remained elusive and the microscopic origin of charge density waves (CDWs) is still unknown. Here, we show, for the first time, a complete melting of the ScV$_ 6$Sn$_ 6$ (166) kagome lattice. The low energy phonon with propagation vector $\frac{1}{3} \frac{1}{3} \frac{1}{2}$ collapses at 98 K, without the emergence of long-range charge order, which sets in with a propagation vector $\frac{1}{3} \frac{1}{3} \frac{1}{3}$. The CDW is driven (but locks at a different vector) by the softening of an overdamped phonon flat plane at k$_z$=$π$. We observe broad phonon anomalies in momentum space, pointing to (1) the existence of approximately flat phonon bands which gain some dispersion due to electron renormalization, and (2) the effects of the momentum dependent electron-phonon interaction in the CDW formation. Ab initio and analytical calculations corroborate the experimental findings to indicate that the weak leading order phonon instability is located at the wave vector $\frac{1}{3} \frac{1}{3} \frac{1}{2}$ of a rather flat collapsed mode. We analytically compute the phonon frequency renormalization from high temperatures to the soft mode, and relate it to a peak in the orbital-resolved susceptibility, obtaining an excellent match with both ab initio and experimental results, and explaining the origin of the approximately flat phonon dispersion. Our data report the first example of the collapse of a softening of a flat phonon plane and promote the 166 compounds of the kagome family as primary candidates to explore correlated flat phonon-topological flat electron physics.

cond-mat.str-el↗

arXiv2023

Order-disorder Peierls instability in the kagome metal (Cs,Rb)V$_3$Sb$_5$

The nature of the charge density wave phases in the kagome metal compound AV$_3$Sb$_5$ has raised many questions and their origin is still under debate. Here, we combine diffuse scattering (DS) and inelastic x-ray scattering (IXS) to identify a 3-dimensional (3D) precursor of the charge order with propagation vector (0.5 0 0.5), which condenses into a 3D-CDW through a first order phase transition. The quasi-elastic critical scattering indicates that the dominant contribution to the diffuse precursor is the elastic central peak without phonon softening. However, the inelastic spectra show a small broadening of the Einstein-type phonon mode on approaching the phase transition. Our results point to the situation where the Fermi surface instability at the \textit{L} point is of order-disorder type with a critical growth of quasi-static domains. The results go beyond the classical weak-coupling Peierls transition dynamics and are discussed within models including strong-electron phonon coupling and non-adiabaticity.

cond-mat.str-el↗

arXiv2022

Spin-phonon coupling driven Charge density wave in a Kagome Magnet

The intertwining between spin, charge, and lattice degrees of freedom can give rise to unusual macroscopic quantum states, including high-temperature superconductivity and quantum anomalous Hall effects. Recently, a charge density wave (CDW) is observed in the kagome antiferromagnet FeGe, indicative of possible intertwining physics. An outstanding question is that whether magnetic correlation is fundamental for the spontaneous spatial symmetry breaking orders. Here, utilizing elastic and high-resolution inelastic x-ray scattering, we discover a charge dimerization superlattice that coexists with the 2$\times$2$\times$1 CDW in the kagome sublattice. Most interestingly, between the magnetic and CDW transition temperature, the phonon dynamical structure factor shows a giant phonon-energy hardening and a substantial phonon linewidth broadening near the charge-dimerization wavevectors, both signaling the spin-phonon coupling. By first principles calculations, we show that both the static and dynamic spin excitations intertwine with the phonon to drive the spatial symmetry breaking.

cond-mat.str-el↗

arXiv2021

Spatial symmetry constraint of charge-ordered kagome superconductor CsV$_3$Sb$_5$

Elucidating the symmetry of intertwined orders in exotic superconductors is at the quantum frontier. Recent surface sensitive studies of the topological kagome superconductor CsV$_3$Sb$_5$ discovered a cascade 4a$_0$ superlattice below the charge density wave (CDW) ordering temperature, which can be related to the pair density modulations in the superconducting state. If the 4a$_0$ phase is a bulk and intrinsic property of the kagome lattice, this would form a striking analogy to the stripe order and pair density wave discovered in the cuprate high-temperature superconductors, and the cascade ordering found in twisted bilayer graphene. High-resolution X-ray diffraction has recently been established as an ultra-sensitive probe for bulk translational symmetry-breaking orders, even for short-range orders at the diffusive limit. Here, combining high-resolution X-ray diffraction, scanning tunneling microscopy and scanning transmission electron microscopy, we demonstrate that the 4a$_0$ superstructure emerges uniquely on the surface and hence exclude the 4a$_0$ phase as the origin of any bulk transport or spectroscopic anomaly. Crucially, we show that our detected 2$\times$2$\times$2 CDW order breaks the bulk rotational symmetry to C2, which can be the driver for the bulk nematic orders and nematic surface superlattices including the 4a$_0$ phase. Our high-resolution data impose decisive spatial symmetry constraints on emergent electronic orders in the kagome superconductor CsV$_3$Sb$_5$.

cond-mat.mtrl-sci↗

arXiv2021

Observation of van der Waals phonons in the single-layer cuprate (Bi,Pb)$_2$(Sr,La)$_2$CuO$_{6+δ}$

Interlayer van der Waals (vdW) coupling is generic in two-dimensional materials such as graphene and transition metal dichalcogenides, which can induce very low-energy phonon modes. Using high-resolution inelastic hard x-ray scattering, we uncover the ultra-low energy phonon mode along the Cu-O bond direction in the high-$T_c$ cuprate (Bi,Pb)$_2$(Sr,La)$_2$CuO$_{6+δ}$ (Bi2201). This mode is independent of temperature, while its intensity decreases with doping in accordance with an increasing c-axis lattice parameter. We compare the experimental results to first-principles density functional theory simulations and identify the observed mode as a van der Waals phonon, which arises from the shear motion of the adjacent Bi-O layers. This shows that Bi-based cuprate has similar vibrational properties as graphene and transition metal dichalcogenides, which can be exploited to engineer novel heterostructures.

cond-mat.supr-con↗

arXiv2020

Soft elastic constants from phonon spectroscopy in hole-doped Ba$_{1-x}$(K,Na)$_x$Fe$_2$As$_2$ and Sr$_{1-x}Na$_x$Fe$_2$As$_2$

We report inelastic x-ray scattering measurements of the in-plane polarized transverse acoustic phonon mode propagating along $q\parallel$[100] in various hole-doped compounds belonging to the 122 family of iron-based superconductors. The slope of the dispersion of this phonon mode is proportional to the square root of the shear modulus $C_{66}$ in the $q \rightarrow 0$ limit and, hence, sensitive to the tetragonal-to-orthorhombic structural phase transition occurring in these compounds. In contrast to a recent report for Ba(Fe$_{0.94}$Co$_{0.06}$)$_2$As$_2$ [F. Weber et al., Phys. Rev. B 98, 014516 (2018)], we find qualitative agreement between values of $C_{66}$ deduced from our experiments and those derived from measurements of the Youngs modulus in Ba$_{1-x}$(K,Na)$_x$Fe$_2$As$_2$ at optimal doping. These results provide an upper limit of about 50 Å for the nematic correlation length for the optimally hole-doped compounds. Furthermore, we also studied compounds at lower doping levels exhibiting the orthorhombic magnetic phase, where $C_{66}$ is not accessible by volume probes, as well as the C4 tetragonal magnetic phase.investigated

cond-mat.supr-con↗

arXiv2020

Phonon density of states in lanthanide-based nanocrystals

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.

cond-mat.mes-hall↗

arXiv2020

Phonon collapse and van der Waals melting of the 3D charge density wave of VSe$_2$

Among transition metal dichalcogenides (TMDs), VSe$_2$ is considered to develop a purely 3-dimensional (3D) charge-density wave (CDW) at T$_{CDW}$=110 K. Here, by means of high resolution inelastic x-ray scattering (IXS), we show that the CDW transition is driven by the collapse of an acoustic mode at the critical wavevector \textit{q}$_{CDW}$= (2.25 0 0.7) r.l.u. and critical temperature T$_{CDW}$=110 K. The softening of this mode starts to be pronounced for temperatures below 2$\times$ T$_{CDW}$ and expands over a rather wide region of the Brillouin zone, suggesting a large contribution of the electron-phonon interaction to the CDW formation. This interpretation is supported by our first principles calculations that determine a large momentum-dependence of the electron-phonon interaction, peaking at the CDW wavevector, in the presence of nesting. Fully anharmonic {\it ab initio} calculations confirm the softening of one acoustic branch at \textit{q}$_{CDW}$ as responsible for the CDW formation and show that van der Waals interactions are crucial to melt the CDW. Our work also highlights the important role of out-of-plane interactions to describe 3D CDWs in TMDs.

cond-mat.mtrl-sci↗

arXiv2020

Nematic correlation length in iron-based superconductors probed by inelastic x-ray scattering

Nematicity is ubiquitous in electronic phases of high-$T_c$ superconductors, particularly in the Fe-based systems. We used inelastic x-ray scattering to extract the temperature-dependent nematic correlation length $ξ$ from the anomalous softening of acoustic phonon modes in FeSe, underdoped Ba(Fe$_{0.97}$Co$_{0.03}$)$_2$As$_2$ and optimally doped Ba(Fe$_{0.94}$Co$_{0.06}$)$_2$As$_2$. In all cases, we find that $ξ$ is well described by a power law $(T-T_0)^{-1/2}$ extending over a wide temperature range. We attributed this mean-field behavior and the extended fluctuation regime to a sizable nemato-elastic coupling, which may be detrimental to superconductivity.

cond-mat.supr-con↗

arXiv2019

Phononic Helical Nodal Lines with $\mathcal{PT}$ Protection in MoB$_{2}$

While condensed matter systems host both Fermionic and Bosonic quasi-particles, reliably predicting and empirically verifying topological states is only mature for Fermionic electronic structures, leaving topological Bosonic excitations sporadically explored. This is unfortunate, as Bosonic systems such a phonons offer the opportunity to assess spinless band structures where nodal lines can be realized without invoking special additional symetries to protect against spin-orbit coupling. Here we combine first-principles calculations and meV-resolution inelastic x-ray scattering to demonstrate the first realization of parity-time reversal ($\mathcal{PT}$) symmetry protected helical nodal lines in the phonon spectrum of MoB$_{2}$. This structure is unique to phononic systems as the spin-orbit coupling present in electronic systems tends to lift the degeneracy away from high-symmetry locations. Our study establishes a protocol to accurately identify topological Bosonic excitations, opening a new route to explore exotic topological states in crystalline materials.

cond-mat.mtrl-sci↗

arXiv2019

Phonon Dispersion of Mo-stabilized $γ$-U measured using Inelastic X-ray Scattering

We have measured the room-temperature phonon spectrum of Mo-stabilized $γ-$U. The dispersion curves show unusual softening near the H point, q=[1/2,1/2,1/2], which may derive from the metastability of the $γ-$U phase or from strong electron-phonon coupling. Near the zone center, the dispersion curves agree well with theory, though significant differences are observed away from the zone center. The experimental phonon density of states is shifted to higher energy compared to theory and high-temperature neutron scattering. The elastic constants of $γ$-UMo are similar to those of body-centered cubic elemental metals.

cond-mat.mtrl-sci↗

arXiv2019

Electron-phonon coupling and superconductivity-induced distortion of the phonon lineshape in V$_3$Si

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)].

cond-mat.supr-con↗

arXiv2019

Suppression of charge density wave order by disorder in Pd-intercalated ErTe$_3$

Disorder is generically anticipated to suppress long range charge density wave (CDW) order. We report transport, thermodynamic, and scattering experiments on Pd$_x$ErTe$_3$, a model CDW system with disorder induced by intercalation. The pristine parent compound ($x=0$) shows two separate, mutually perpendicular, incommensurate unidirectional CDW phases setting in at 270 K and 165 K. Here we track the suppression of signatures corresponding to these two parent transitions as the Pd concentration increases. At the largest values of $x$, we observe complete suppression of long range CDW order in favor of superconductivity. We also report evidence from electron and x-ray diffraction which suggests a tendency toward short-range ordering along both wavevectors which persists even well above the crossover temperature. Pd$_x$ErTe$_3$ provides a promising model system for the study of the interrelation of charge order and superconductivity in the presence of quenched disorder.

cond-mat.str-el↗

arXiv2018

Competing soft phonon modes at the charge-density-wave transitions in DyTe$_3$

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° rotated analogue of the one appearing at high temperatures.

cond-mat.mtrl-sci↗