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DOE OSTI2021

Application of molecular convergent close-coupling cross sections in a collisional radiative model for the triplet system of molecular hydrogen

Collisional radiative (CR) models for molecular hydrogen are of high relevance for performing qualitative and quantitative analysis of excited-state population densities measured in plasmas or predicting the dependence of plasma emission on parameter variations. Although the development of such models for H 2 started decades ago, major uncertainties still exist regarding the most important set of input parameters, namely the cross sections for electron-impact excitation. The deviations between cross sections from different datasets are particularly pronounced in the energy region close to the threshold energy, strongly increasing the uncertainty of CR models applied to low-temperature plasmas. This paper presents experimental validation of a set of newly calculated non ro-vibrationally resolved electron-impact cross sections calculated for the triplet system of H 2 using the molecular convergent close-coupling method in the adiabatic-nuclei formulation. These cross sections are implemented into a CR model based on the flexible solver Yacora. A first comparison of CR calculations with the different datasets to experimentally-determined population densities is performed at a planar ICP discharge for varying pressure (between 1 and 10 Pa) and RF power (between 700 and 1100 W). For the experimentally-accessible electron temperature and density range (2.5–10 eV and 1.8–3.3 × 10 16 m –3 , respectively), very good agreement between the model and experiment is obtained using the new data set, in contrast to previously used cross sections.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Electron–phonon coupling enhancement and displacive magnetostructural transition in SrCr 2 As 2 under magneto-Raman spectroscopy

Here, a Raman spectroscopy study on high quality single crystals of SrCr 2 A s 2 (SCA) in the temperature T range 4 K < T < 300 K and high applied magnetic fields up to H = 9 T is presented. The chromium B 1g phonon analysis reveals two anomalous shifts in the frequency, the first below T = 250 K at H = 0 T in the saturated AFM G -type order likely due to an enhanced electron–phonon coupling by the magnetic order, whereas the second anomaly occurs above H = 4 T at T = 4 K likely as a consequence of a magnetostructural displacive transition. Renormalization of the electronic Raman spectra in both studies reveals a decrease in the electronic density of states with decreasing T and increasing H , respectively, with consequent changes in the Fermi surface, which are intrinsically related to the observed anomalies.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Orbital hybridisation effects in B2 phase Cr doped Co 2 MnAl

Here we investigate here the magnetic, transport, local structural and electronic properties of Co 2 Mn 1−x Cr x Al (x = 0, 0.05, 0.1 and 0.2). Our results show that all the compounds stabilise in B2 phase and are ferromagnets. The results reveal disorder at the structural and magnetic levels. X-ray absorption near edge structure (XANES) analysis reveal signature of antisite disorder between Mn and Al atoms with equal ratio. The electronic structure calculations suggest enhancement in the half metallicity, localisation of electrons at the Fermi level and an increment in density of states with doping. The combined results of electronic structure calculations and XANES studies suggest transfer of electrons to the Co site. The results of high temperature resistivity measurements suggest the conduction electrons are undergoing transition from delocalisation to weak localisation to activated behaviour with Cr doping. The extended x-ray absorption spectroscopic analysis shows that the local structure around Mn atom is different from the global structure as obtained from the x-ray diffraction results. The behaviour of the edge region is in line with the trend as obtained from the compositional analysis. We observe link between the hybridisation of 3d like states at the Mn, Cr sites with that at the Co site and the transport properties. This could help in understanding the unusual decrement in the lattice parameter with doping. These results reveal the role of local structure in understanding the physical properties of such systems.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Lattice dynamics of 119 Sn impurity in a bcc-Cr crystal

The chromium crystal doped with 119 Sn isotope was studied using the nuclear resonance inelastic x-ray scattering and first principles calculations. The Sn partial phonon density of states (PDOS) was obtained for three temperatures that correspond to different magnetic states of Cr. At all temperatures, the energy spectrum consists of a broad band around 18 meV and a narrow peak at 43 meV. The additional peak around 39 meV is observed only in the magnetically ordered phases, indicating the influence of magnetic order in chromium on lattice dynamics. The partial PDOS calculated with the antiferromagnetic order on Cr atoms show a very good agreement with the experimental data. It is revealed that the high-energy peak is lying above the phonon spectra of the pure bcc-Cr crystal. These are the local modes with the increased energies due to a strongly reduced distance between Sn and the nearest-neighbor Cr atoms.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

The surface termination of a Fe (III) spin crossover molecular salt

From a comparison of the known molecular stoichiometry and x-ray photoemission spectroscopy, it is evident that the Fe(III) spin crossover salt [Fe(qsal) 2 Ni(dmit) 2 ] has a preferential surface termination with the Ni(dmit) 2 moiety, where qsal = N(8quinolyl)salicylaldimine, and dmit 2- = 1,3-dithiol-2-thione-4,5-dithiolato. This preferential surface termination leads to a significant surface to bulk core level shift for the Ni 2p x-ray photoemission core level, not seen in the corresponding Fe 2p core level spectra. A similar surface to bulk core level shift is seen in Pd 3d in the related [Fe(qsal) 2 ] 2 Pd(dmit) 2 . Inverse photoemission spectroscopy, compared with the x-ray absorption spectra at the Ni-L3,2 edge provides some indication of the density of states resulting from the dmit 2- = 1,3-dithiol-2-thione-4,5-dithiolato ligand unoccupied molecular orbitals and thus supports the evidence regarding surface termination in the Ni(dmit) 2 moiety.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Existence of a flat band in highly correlated metal BaCo 2 P 2

We report on the observation of a flat band situated at the Fermi level E F along with the structural, electrical transport, and magnetic properties of BaCo 2 P 2 that crystallizes in the ThCr 2 Si 2 -type body-center tetragonal structure. This compound has the largest inter-layer pnictide (Pn) distance d Pn–Pn as well as the largest c/a ratio among all the known ACo 2 Pn 2 (A = alkaline earth metal) compounds, where a and c are the tetragonal lattice parameters. Hence, the magnetic and electronic properties of this compound are expected to have a quasi-two-dimensional character. Despite the evidence of the presence of sizable magnetic interactions, magnetic susceptibility χ(T) of BaCo 2 P 2 does not show magnetic ordering down to 1.8 K. The material shows good metallic conduction with a large residual resistivity ratio ρ 300 K /ρ 1.8 K ≈ 70 and a Fermi liquid behavior at low temperature. Kadowaki–Woods ratio R KW of BaCo 2 P 2 suggests the presence of sizable electronic correlations within this system. Additionally, a large many-body enhancement of 2.3 of the experimental density of states D γ (E F ) over the band-structure D band (E F ) is inferred to arise from sizable electron-electron and/or electron-phonon interactions leading to a substantial deviation from the free-electron behavior.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Ab Initio modeling of Near-Edge EELS spectra for chemisorbed molecules

Abstract Electron energy loss spectroscopy (EELS) has recently been applied to probe chemisorbed molecules on metal nanostructures, but a fundamental understanding of the correlation between these spectra and the electronic structures of the adsorbates has been limited. We report here on the insights afforded by time-dependent density functional theory to decipher the energy loss near edge structure (ELNES) of EELS spectra associated with chemisorption. These first-principles calculations simulate the ELNES-EELS spectra for chemisorbed CO on various facets of Au and Pt. Computational predictions of key signatures such as the ‘red shift’ and reductions in the peak intensity of the 2 π * and 6 σ * peaks, as compared to free CO in the gas phase, are validated in comparison to experimentally collected EELS spectra. These signatures are revealed to arise from changes in the electronic structure in terms of unoccupied density of states associated with the chemisorption process. They are consistent with a Blyholder model that incorporates donation and back-donation of electrons. They are also characteristic of the chemisorption process, such as the choice of metal, site of adsorption and the coverage and distribution of adsorbates. Our simulations thus provide guidelines for the use of ELNES-EELS to characterize the atomic structure and adsorption property of nanostructured surfaces and facilitate the development of advanced nanomaterials for catalytic applications.

Materials Science↗
DOE OSTI2022

Optical fingerprints of the electronic band reconstruction in van der Waals magnetic materials

We report a broadband study of the charge dynamics in the van der Waals magnetic materials 2H-M x TaS 2 (M = Mn and Co), which span the onset of both long-range antiferromagnetic (AFM) and ferromagnetic (FM) order, depending on the intercalation M and its concentration x. We discover a spectral weight (SW) shift from high to low energy scales for FM compositions, while reversely SW is removed from low towards high spectral energies for AFM compounds. This maps the related reconstruction of the electronic band structure along the crossover from the FM to AFM order, which restores an occupation balance in the density of states between spin majority and minority bands of the intercalated 3d elements.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Distinguishing electronic contributions of surface and sub-surface transition metal atoms in Ti-based MXenes

MXenes are a rapidly-expanding family of 2D transition metal carbides and nitrides that have attracted attention due to their excellent performance in applications ranging from energy storage to electromagnetic interference shielding. Numerous other electronic and magnetic properties have been computationally predicted, but not yet realized due to the experimental difficulty in obtaining uniform surface terminations (T x ), necessitating new design approaches for MXenes that are independent of surface groups. In this study, we distinguished the contributions of surface and sub-surface Ti atoms to the electronic structure of four Ti-based MXenes (Ti 2 CT x , Ti 3 C 2 T x , Cr 2 TiC 2 T x , and Mo 2 TiC 2 T x ) using soft x-ray absorption spectroscopy, revealing minimal changes in the spectral features between the parent MAX phase and its MXene when no surface Ti atoms are present in the MXene, such as Mo 2 TiC 2 T x and Cr 2 TiC 2 T x . In contrast, for MXenes with surface Ti atoms, here Ti 3 C 2 T x and Ti 2 CT x , the Ti L-edge spectra are significantly modified compared to their parent MAX phase compounds. First principles calculations provide similar trends in the partial density of states derived from surface and interior Ti atoms, corroborating the spectroscopic measurements. Furthermore, these results reveal that electronic states derived from sub-surface M-site layers are largely unperturbed by the surface groups, indicating a relatively short length scale over which the T x groups alter the nominal electron count associated with Ti atoms and suggesting that desired band features should be hosted by sub-surface M-sites that are electronically more robust than their surface M-site counterparts.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Electric-field-tunable electronic nematic order in twisted double-bilayer graphene

Graphene-based moiré systems have attracted considerable interest in recent years as they display a remarkable variety of correlated phenomena. Besides insulating and superconducting phases in the vicinity of integer fillings of the moiré unit cell, there is growing evidence for electronic nematic order both in twisted bilayer graphene and twisted double-bilayer graphene (tDBG), as signaled by the spontaneous breaking of the threefold rotational symmetry of the moiré superlattices. Here, we combine symmetry-based analysis with a microscopic continuum model to investigate the structure of the nematic phase of tDBG and its experimental manifestations. First, we perform a detailed comparison between the theoretically calculated local density of states and recent scanning tunneling microscopy data (arXiv:2009.11645) to resolve the internal structure of the nematic order parameter in terms of the layer, sublattice, spin, and valley degrees of freedom. We find strong evidence that the dominant contribution to the nematic order parameter comes from states at the moiré scale rather than at the microscopic scale of the individual graphene layers, which demonstrates the key role played by the moiré degrees of freedom and confirms the correlated nature of the nematic phase in tDBG. Secondly, our analysis reveals an unprecedented tunability of the orientation of the nematic director in tDBG by an externally applied electric field, allowing the director to rotate away from high-symmetry crystalline directions. Here, we compute the expected fingerprints of this rotation in both STM and transport experiments, providing feasible ways to probe it. Rooted in the strong sensitivity of the flat bands of tDBG to the displacement field, this effect opens an interesting route to the electrostatic control of electronic nematicity in moiré systems.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Adaptive pruning-based optimization of parameterized quantum circuits

Abstract Variational hybrid quantum–classical algorithms are powerful tools to maximize the use of noisy intermediate-scale quantum devices. While past studies have developed powerful and expressive ansatze, their near-term applications have been limited by the difficulty of optimizing in the vast parameter space. In this work, we propose a heuristic optimization strategy for such ansatze used in variational quantum algorithms, which we call ‘parameter-efficient circuit training (PECT)’. Instead of optimizing all of the ansatz parameters at once, PECT launches a sequence of variational algorithms, in which each iteration of the algorithm activates and optimizes a subset of the total parameter set. To update the parameter subset between iterations, we adapt the Dynamic Sparse Reparameterization scheme which was originally proposed for training deep convolutional neural networks. We demonstrate PECT for the Variational Quantum Eigensolver, in which we benchmark unitary coupled-cluster ansatze including UCCSD and k -UpCCGSD, as well as the Low-Depth Circuit Ansatz (LDCA), to estimate ground state energies of molecular systems. We additionally use a layerwise variant of PECT to optimize a hardware-efficient circuit for the Sycamore processor to estimate the ground state energy densities of the one-dimensional Fermi-Hubbard model. From our numerical data, we find that PECT can enable optimizations of certain ansatze that were previously difficult to converge and more generally can improve the performance of variational algorithms by reducing the optimization runtime and/or the depth of circuits that encode the solution candidate(s).

Physics↗
DOE OSTI2024

Local models of two-temperature accretion disc coronae – II. Ion thermal conduction and the absence of disc evaporation

We use local stratified shearing-box simulations with magnetic field-aligned thermal conduction to study an idealized model of the coupling between a cold, radiatively efficient accretion disc, and an overlying, hot, two-temperature corona. Evaporation of a cold disc by conduction from the hot corona has been proposed as a means of mediating the soft-to-hard state transitions observed in X-ray binary systems. We model the coronal plasma in our local disc patch as an MHD fluid subject to both free-streaming ion conduction and a parametrized cooling function that captures the collisional transfer of energy from hot ions to colder, rapidly cooling leptons. In all of our models, independent of the initial net vertical magnetic flux (NF) threading the disc, we find no evidence of disc evaporation. The ion heat flux into the disc is radiated away before conduction can heat the disc’s surface layers. When an initial NF is present, steady-state temperature, density, and outflow velocities in our model coronae are unaffected by conduction. Instead of facilitating disc evaporation, thermal conduction is more likely to feed the disc with plasma condensing out of the corona, particularly in flows without NF. Our work indicates that uncertainties in the amount of NF threading the disc hold far greater influence over whether or not the disc will evaporate into a radiatively inefficient accretion flow compared to thermal conduction. We speculate that a change in net flux mediates disc truncation/evaporation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

XRISM high-resolution X-ray spectroscopy of Cygnus X-1: Orbital and short-term variability of iron absorption

We present the first high-resolution spectroscopy of the black hole high-mass X-ray binary Cygnus X-1 with XRISM, including orbital-phase-resolved analyses and tentative evidence of short-term variability in the Fe K band on second timescales. Using data from the Performance Verification phase in 2024 April, we analyzed spectral variability across orbital phases with the Resolve microcalorimeter and the Xtend CCD imager. The unprecedented resolution of Resolve reveals variability in highly ionized Fe absorption lines. The absorption features show orbital-phase-dependent variability in column density, ionization state, and blueshifted velocity, suggesting structural variations in the focused stellar wind along the line of sight. We also find indications of subtle broadening of the neutral Fe emission profile. In addition, intensity-sorted spectroscopy during dip phases suggests possible variability on timescales of a few seconds in the absorption features, consistent with cooler, denser, and lower-ionized gas clumps. Although the statistical significance is limited, these results hint that the stellar wind and the X-rays from the accretion disk around the black hole may interact on timescales as short as a few seconds. These XRISM results constrain wind-fed accretion in Cyg X-1 and highlight Resolve’s capability to probe plasma environments in high-mass X-ray binaries.

Astronomy and AstroPhysics↗
DOE OSTI2023

Colossal transverse magnetoresistance due to nematic superconducting phase fluctuations in a copper oxide

Electronic anisotropy (“nematicity”) has been detected in cuprate superconductors by various experimental techniques. Using angle-resolved transverse resistance (ARTR) measurements, a very sensitive and background-free technique that can detect 0.5% anisotropy in transport, we have observed it also in La 2-x Sr x CuO 4 (LSCO) for 0.02 ≤ x ≤ 0.25. A central enigma in LSCO is the rotation of the nematic director (orientation of the largest longitudinal resistance) with temperature; this has not been seen before in any material. Here, we address this puzzle by measuring the angle-resolved transverse magnetoresistance (ARTMR) in LSCO. We report the discovery of colossal transverse magnetoresistance (CTMR)—an order-of-magnitude drop in the transverse resistivity in the magnetic field of 6 T. We show that the apparent rotation of the nematic director is caused by anisotropic superconducting fluctuations, which are not aligned with the normal electron fluid, consistent with coexisting bond-aligned and diagonal nematic orders. We quantify this by modeling the (magneto-)conductivity as a sum of normal (Drude) and paraconducting (Aslamazov–Larkin) channels but extended to contain anisotropic Drude and Cooper-pair effective mass tensors. Strikingly, the anisotropy of Cooper-pair stiffness is much larger than that of the normal electrons. It grows dramatically on the underdoped side, where the fluctuations become quasi-one-dimensional. Our analysis is general rather than model dependent. Still, we discuss some candidate microscopic models, including coupled strongly-correlated ladders where the transverse (interladder) phase stiffness is low compared with the longitudinal intraladder stiffness, as well as the anisotropic superconducting fluctuations expected close to the transition to a pair-density wave state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Significance of the structural configuration of B2 disorder in Co and Ti based Heusler alloys

We investigate here structural (at local and global levels) and transport properties for 𝑋 2 ⁢MnAl (𝑋= Co and Ti). Additionally, the magnetic properties were also studied for Ti 2 ⁢MnAl. Our x-ray diffraction results show that both the compounds stabilize in B2 disordered phase with cubic structure of 𝑃⁢𝑚⁢$\overline{3}$⁢𝑚 space group. Further, the structural configuration of the above disordered phase for both the compounds was identified using combined studies of x-ray absorption spectroscopy and multiple scattering calculations at the transition metal 𝐾 edges. Upon such identification, in the case of Co 2 ⁢Mn 1−𝑦⁢ Cr 𝑦 ⁢Al (𝑦= 0, 0.05, 0.1, 0.2) with change in 𝑦, we are able to establish a better connection quantitatively between the inverse of Mn-Co bonds and peak in the temperature-dependent resistivity. This highlights the crucial importance of a detailed understanding of the nature of B2 disorder. In the case of 𝑦=0, in the temperature range of study, the resistivity is driven by the functional form associated with (a) three-dimensional enhanced electron-electron Coulomb interaction scattering mechanism and (b) an unconventional one-magnon process. For Ti 2 ⁢MnAl, the transport shows metallic glasslike behavior at high temperature, while at low temperature it follows both the Cote-Meisel's model and quantum correction model. In this compound, the magnetic studies suggest the formation of superparamagnetic clusters in the paramagnetic matrix at low temperatures. Our density functional theory results are in line with the transport and magnetic properties. In literature, the spin polarization percentage (𝑃) for 𝑋= Co in B2 disordered phase is 76%. However, the present results emphasize the fact that in B2 disordered phase, the value of 𝑃 can range from 90% to 71% depending on the structural configuration introduced by swapping of the atomic positions of Mn and Al. For the compound under study, the value of percentage spin polarization obtained ranges between 82% to 85%. In addition, we also identify the origin of the difference in the shape of the Mn 3⁢𝑑 density of states for both the alloys. In conclusion, our results for 𝑋= Co alloy highlights the importance of identifying the specific structural configuration associated with a particular disorder category especially in the estimation of 𝑇 𝑐 and 𝑃 and for 𝑋= Ti, the physical properties can be tuned by varying the position of 𝐸 𝐹 and thereby its utilization in device applications.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Thermodynamic origin of the pressure-induced Invar effect: General criterion and experimental study of Fe 68 ⁢Pd 32

Synchrotron X-ray diffraction measurements were performed on 57 Fe 68 Pd 32 at multiple pressures and two temperatures in a diamond-anvil cell. Between 4 and 11GPa, the thermal expansion was zero or slightly negative. This pressure-induced Invar effect was studied further with 57 Fe nuclear forward scattering and nuclear resonant inelastic X-ray scattering to obtain information on the pressure-induced changes in both the magnetization and the phonon density of states. Magnetic entropy and phonon entropy were obtained from these results, the latter with additional measurements from inelastic neutron scattering to account for the contributions from Pd atoms. The dependencies of these entropies on pressure gave the magnetic and phonon contributions to thermal expansion. These canceled in the region of pressure-induced Invar behavior, even though they individually increased by more than a factor of 2 below the Curie pressure. The behavior of phonons gives evidence for spin-phonon interactions in Fe 68 Pd 32 . A general explanation of the pressure-induced Invar effect is presented, showing that Invar behavior is typically expected at a pressure P* below a magnetic transition at pressure PC. The difference in pressure P C − P* scales with the fractional reduction in magnetic exchange interaction divided by the average Gr¨uneisen parameter.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Quantum critical point followed by Kondo-like behavior due to Cu substitution in the itinerant antiferromagnet La 2 ⁢(Cu 𝑥 ⁢Ni 1−𝑥 ) 7

La 2 ⁢Ni 7 is an itinerant magnetic system with a small ordered moment of ∼ 0.1⁢µ 𝐵 /Ni and a series of antiferromagnetic (AFM) transitions at 𝑇 1 = 61.0K, 𝑇 2 = 56.5K, and 𝑇 3 = 42.2K. 𝑀 ⁡(𝐻), and 𝜌 ⁡(𝐻) isotherms as well as constant field 𝑀⁡ (𝑇) and 𝜌 ⁡(𝑇) measurements on single-crystalline samples manifest a complex, anisotropic 𝐻−𝑇 phase diagram with multiple phase lines. Here, in this study, we present the growth and characterization of single crystals of the La 2 ⁢(Cu 𝑥 ⁢Ni 1−𝑥 ) 7 series for 0 ≤ 𝑥 ≤ 0.181. We measured powder x-ray diffraction and composition, as well as anisotropic temperature- and field-dependent resistivity, temperature- and field-dependent magnetization, and temperature-dependent heat capacity on these single crystals. Using the measured data we infer a transition temperature-composition (𝑇−𝑥) phase diagram for this system to study the evolution of the AFM ordering upon Cu substitution. For 0 ≤ 𝑥 ≤ 0.097, the system remains magnetically ordered at base temperature with 𝑥 ≤ 0.012, showing signs of multiple AFM ordering temperatures. For the higher substitution levels 0.125 ≤ 𝑥 ≤ 0.181, there are no signatures of magnetic ordering, but anomalous features in resistance and heat capacity data are observed which are consistent with the Kondo effect in this system. The intermediate 𝑥 = 0.105 sample lies between the magnetic ordered and the Kondo regime and is in the vicinity of the AFM quantum critical point (QCP). Thus, La 2⁢ (Cu 𝑥 ⁢Ni 1−𝑥 ) 7 is an example of a small moment system that can be tuned through a QCP. Given these data combined with the fact that the La 2⁢ Ni 7 structure has kagomelike, Ni sublattices running perpendicular to the crystallographic 𝑐 axis, and a predicted 3⁢𝑑-electron flat band that contributes to the density of states near the Fermi energy, La 2 ⁢(Cu 𝑥 ⁢Ni 1−𝑥 ) 7 becomes a promising system to host and study exotic physics.

Das, Atreyee [Ames Laboratory, and Iowa State Univ↗
DOE OSTI2025

Coherent phonon pairs and rotational symmetry breaking of charge density wave order in the kagome superconductor CsV 3 Sb 5

Here, in this work we perform ultrafast time-resolved reflectivity measurements to study the symmetry breaking in the charge-density wave (CDW) phase of CsV 3 ⁢Sb 5 . By extracting the coherent phonon spectrum in the CDW phase of CsV 3 ⁢Sb 5 , we discover close phonon pairs near 1.3 THz and 3.1 THz, as well as a new mode at 1.84 THz. The 1.3 THz phonon pair and the 1.84 THz mode are observed up to the CDW transition temperature. Combining density-functional theory calculations, we show that these phonon pairs arise from the coexistence of Star of David and inverse Star of David distortions combined with sixfold rotational symmetry breaking. An anisotropy in the magnitude of transient reflectivity change is also revealed at the onset of CDW order. Our results thus indicate broken sixfold rotational symmetry in the charge-density wave state of CsV 3⁢ Sb 5 , along with the absence of nematic fluctuation above 𝑇 CDW . Meanwhile, the measured coherent phonon spectrum in the CDW phase of CsV 3 ⁢Sb 5−𝑥 ⁢Sn 𝑥 with 𝑥 = 0.03–0.04 matches the staggered inverse Star of David with interlayer 𝜋 phase shift. This CDW structure contrasts with undoped CsV3⁢Sb5 and explains the evolution from a phonon pair to a single mode at 1.3 THz by 𝑥 = 0.03–0.04 Sn doping.

Deng, Qinwen [Univ. of Pennsylvania, Philadelphia,↗