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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Revealing rotational symmetry breaking charge density wave order in the kagome superconductor (Rb, K)⁢V 3 ⁢Sb 5 by ultrafast pump-probe experiments

The recently discovered Kagome superconductor 𝐴⁢V 3 ⁢Sb 5 (where 𝐴 refers to K, Rb, Cs) has stimulated widespread research interest due to its interplay of nontrivial topology and unconventional correlated physics including charge-density waves (CDW) and superconductivity. The essential prerequisite to understanding the microscopic mechanisms of this complex electronic landscape is to unveil the configuration and symmetry of the charge-density wave order. As to now, little consensus has been made on what symmetry is broken. Herein, we clarify the microscopic structure and symmetry breaking of the CDW phase in RbV 3 ⁢Sb 5 and KV 3 ⁢Sb 5 by ultrafast time-resolved reflectivity. Our approach is based on extracting coherent phonon spectra induced by three-dimensional CDW and comparing them to calculated phonon frequencies via density-functional theory. The combination of these experimental results and calculations provides compelling evidence that the CDW structure of both compounds prevailing up to 𝑇 CDW is the 2 × 2 × 2 staggered inverse Star-of-David pattern with interlayer 𝜋 phase shift, in which the sixfold rotational symmetry is broken. Finally, these observations thus corroborate sixfold rotational symmetry breaking throughout the CDW phase of RbV 3 ⁢Sb 5 and KV 3⁢ Sb 5 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
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,↗
DOE OSTI2026

Kramers nodal line in the charge density wave state of YTe 3 and the influence of twin domains

Recent studies have focused on the relationship between charge density wave (CDW) collective electronic ground states and nontrivial topological states. YTe 3 , a nonmagnetic quasi-two-dimensional chalcogenide, has been reported to exhibit a CDW state below 334 K. Using angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT), we establish that YTe 3 is a CDW-induced Kramers nodal line (KNL) metal, a recently proposed topological state of matter. Scanning tunneling microscopy and low energy electron diffraction reveal two orthogonal domains, each with a unidirectional CDW and a similar wave vector (𝐪 CDW ). When the influence of twin domains is considered, the effective band structure (EBS) computations that utilize DFT-calculated bands using a noncentrosymmetric structure determined by x-ray crystallography, show excellent agreement with ARPES. The noncentrosymmetry of YTe 3 is established by Raman spectroscopy. The Fermi surface and ARPES intensity plots show weak shadow bands displaced by 𝐪 CDW from the main bands. Furthermore, these are linked to CDW modulation, as the EBS calculation confirms. Bilayer split main and shadow bands suggest the existence of crossings, according to theory and experiment. DFT bands, including spin-orbit coupling, indicate existence of a KNL along the Σ direction from multiple crossings of bands dispersing perpendicular to it. Additionally, doubly degenerate bands are only found along the KNL at all energies, with some bands dispersing through the Fermi level.

Angle-resolved photoemission spectroscopy↗
DOE OSTI2024

Absence of a bulk signature of a charge density wave in hard x-ray measurements of UTe 2

The long-sought pair density wave (PDW) is an exotic phase of matter in which charge density wave (CDW) order is intertwined with the amplitude or phase of coexisting, superconducting order. Originally predicted to exist in copper-oxides, circumstantial evidence for PDW order now exists in a variety of materials. Recently, scanning tunneling microscopy (STM) studies have reported evidence for a three-component CDW at the surface of the heavy-fermion superconductor, UTe 2 , persisting below its superconducting transition temperature [Aishwarya et al., Nature 618, 928933 (2023); Gu et al., Nature 618, 921927 (2023); LaFleur et al., Nat. Commun. 15, 4456 (2024)]. Here, in this study, we use hard x-ray diffraction measurements on crystals of UTe 2 at 𝑇 = 1.9 and 12 K to search for a bulk signature of this CDW. Using STM measurements as a constraint, we calculate the expected locations of CDW superlattice peaks and sweep a large volume of reciprocal space in search of a signature. We fail to find any evidence for a CDW near any of the expected superlattice positions in many Brillouin zones. We estimate an upper bound on the CDW lattice distortion of 𝑢 max ≲ 4×10 −3 Å. Our results suggest that the CDW observed in STM is either purely electronic, somehow lacking a signature in the lattice, or is restricted to the material surface.

Kengle, Caitlin S.↗
DOE OSTI2025

Charge Density Wave and Ferromagnetism in Intercalated CrSBr

In materials with 1D electronic bands, electron–electron interactions can produce intriguing quantum phenomena, including spin-charge separation and charge density waves (CDW). Most of these systems, however, are non-magnetic, motivating a search for anisotropic materials where the coupling of charge and spin may affect emergent quantum states. Here, in this study, chemical intercalation of the van der Waals magnetic semiconductor CrSBr yields Li 0.17(2) (tetrahydrofuran) 0.26(3) CrSBr, which possesses an electronically driven quasi-1D CDW with an onset temperature above room temperature. Concurrently, electron doping increases the magnetic ordering temperature from 132 to 200 K and switches its interlayer magnetic coupling from antiferromagnetic to ferromagnetic. The spin-polarized nature of the anisotropic bands that give rise to this CDW enforces an intrinsic coupling of charge and spin. The coexistence and interplay of ferromagnetism and charge modulation in this exfoliatable material provide a promising platform for studying tunable quantum phenomena across a range of temperatures and thicknesses.

2D magnets↗
DOE OSTI2024

Dynamical decoding of the competition between charge density waves in a kagome superconductor

The kagome superconductor CsV 3 Sb 5 hosts a variety of charge density wave (CDW) phases, which play a fundamental role in the formation of other exotic electronic instabilities. However, identifying the precise structure of these CDW phases and their intricate relationships remain the subject of intense debate, due to the lack of static probes that can distinguish the CDW phases with identical spatial periodicity. Here, we unveil the competition between two coexisting 2×2×2 CDWs in CsV 3 Sb 5 harnessing time-resolved X-ray diffraction. By analyzing the light-induced changes in the intensity of CDW superlattice peaks, we demonstrate the presence of both phases, each displaying a significantly different amount of melting upon excitation. The anomalous light-induced sharpening of peak width further shows that the phase that is more resistant to photo-excitation exhibits an increase in domain size at the expense of the other, thereby showcasing a hallmark of phase competition. Our results not only shed light on the interplay between the multiple CDW phases in CsV 3 Sb 5 , but also establish a non-equilibrium framework for comprehending complex phase relationships that are challenging to disentangle using static techniques.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Realignment and suppression of charge density waves in the rare-earth tritellurides 𝑅⁢Te 3 (𝑅 = La, Gd, Er)

The rare-earth tritellurides have a rich phase diagram that includes charge density waves (CDWs), superconductivity, and magnetic order, offering a platform to study the interplay between these phases on a square-net system. Prior studies have shown that defects can affect the CDW characteristics in these materials, yet coupling between the CDW order and the underlying microstructure has not been studied at the nanoscale. Here we use scanning transmission electron microscopy at cryogenic temperatures to directly visualize the effects of defects on the CDW order and provide a spatially resolved microscopic correlation between the CDW transition and structural defects. Here, we show that in the presence of extended defects, such as dislocations and stacking faults, the weak orthorhombicity of the rare-earth tritellurides is lost and the material becomes pseudotetragonal. Since the orthorhombicity acts as a symmetry breaking field for the CDW transitions in rare-earth tritellurides, the presence of these extended defects modulates the energetics of the CDWs and suppresses the ground-state CDW phase at low temperature.

Charge density waves↗
DOE OSTI2025

Incommensurate Transverse Peierls Transition and Signature of Chiral Charge Density Wave in EuAl 4

In one-dimensional quantum materials, electrons and lattices can undergo a Peierls transition, a translational symmetry-breaking instability traditionally understood through electron coupling to longitudinal acoustic phonons. Recently, this paradigm has been revised in topological semimetals, where transverse acoustic phonons couple to p-orbital electrons, giving rise to a transverse Peierls transition. Importantly, transverse Peierls transition-induced distortions can further break mirror or inversion symmetries, producing nematic or chiral charge density waves. Here, we report the experimental identification of an incommensurate transverse Peierls transition in EuAl 4 . Using meV-resolution inelastic x-ray scattering, we observe complete softening of a transverse acoustic phonon upon cooling, while the longitudinal acoustic mode remains unaffected. First-principles calculations reveal that the transverse Peierls transition wavevector coincides with a charge susceptibility peak connecting nested Dirac bands. Second harmonic generation confirms mirror symmetry breaking, supporting a chiral charge density wave stabilized by the transverse Peierls transition.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Fluctuating charge-density-wave correlations in the three-band Hubbard model

The high-temperature superconducting cuprates host unidirectional spin- and charge-density-wave orders that can intertwine with superconductivity in nontrivial ways. While the charge components of these stripes have now been observed in nearly all cuprate families, their detailed evolution with doping varies across different materials and at high and low temperatures. We address this problem using nonperturbative determinant quantum Monte Carlo calculations for the three-band Hubbard model. Using an efficient implementation, we can resolve the model’s fluctuating spin and charge modulations and map their evolution as a function of the charge transfer energy and doping. We find that the incommensurability of the charge modulations is decoupled from the spin modulations and decreases with hole doping, consistent with experimental measurements at high temperatures. These findings support the proposal that the high-temperature charge correlations are distinct from the intertwined stripe order observed at low-temperature and in the single-band Hubbard model.

42 ENGINEERING↗
DOE OSTI2024

Understanding the superconductivity and charge density wave interaction through quasi-static lattice fluctuations

In unconventional superconductors, coupled charge and lattice degrees of freedom can manifest in ordered phases of matter that are intertwined. In the cuprate family, fluctuating short-range charge correlations can coalesce into a longer-range charge density wave (CDW) order which is thought to intertwine with superconductivity, yet the nature of the interaction is still poorly understood. Here, by measuring subtle lattice fluctuations in underdoped YBa 2 Cu 3 O 6+y on quasi-static timescales (thousands of seconds) through X-ray photon correlation spectroscopy, we report sensitivity to both superconductivity and CDW. The atomic lattice shows remarkably faster relaxational dynamics upon approaching the superconducting transition at T c ≈ 65 K. By tracking the momentum dependence, we show that the intermediate scattering function almost monotonically scales with the relaxation distance of atoms away from their average positions above T c and in the presence of the CDW state, while this peculiar trend is reversed for other temperatures. These observations are consistent with an incipient CDW stabilized by local strain. This work provides insights into the crucial role of relaxational atomic fluctuations for understanding the electronic physics cuprates, which are inherently disordered due to carrier doping.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Interplay of Kondo physics with incommensurate charge density waves in CeTe 3

CeTe 3 is a 2-dimensional (2D) Van der Waals (VdW) material with incommensurate charge density waves (CDW), extremely high transition temperature (T CDW ), and a large momentum-dependent CDW gap that leaves a significant portion of the Fermi surface intact. It is also considered to be a weak Kondo system, a property unexpected for a material with incommensurate CDW, where each atomic site is slightly different. Here, we study the properties of the CDW state in several RTe3 (R is rare earth) materials and examine the hybridization of itinerant states with the localized Ce 4f multiplet in CeTe 3 by using angle resolved photoemission spectroscopy. We find that the renormalization of the itinerant states originating from the hybridization with the deeper localized 4f states at −260 meV is k−dependent and extends to the Fermi level. As these localized states are far from the Fermi level, the observed hybridization affects the effective masses only marginally and does not lead to heavy fermions. However, since the same renormalizing mechanism normally leads to the heavy fermion physics when the localized 4f states are near the Fermi level, our observation of its strong k−dependence suggests that this could be the reason for discrepancy between the heavy masses in specific heat and light ones in Shubnikov de Haas oscillations, often observed in heavy fermions.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Data Files for P. Mai et al., "Fluctuating charge-density-wave correlations in the three-band Hubbard model" (2024)

The high-temperature superconducting cuprates host unidirectional spin- and charge-density-wave orders that can intertwine with superconductivity in nontrivial ways. While the charge components of these stripes have now been observed in nearly all cuprate families, their detailed evolution with doping varies across different materials and at high and low temperatures. We address this problem using nonperturbative determinant quantum Monte Carlo calculations for the three-band Hubbard model. Using an efficient implementation, we can resolve the model’s fluctuating spin and charge modulations and map their evolution as a function of the charge transfer energy and doping. We find that the incommensurability of the charge modulations is decoupled from the spin modulations and decreases with hole doping, consistent with experimental measurements at high temperatures. These findings support the proposal that the high-temperature charge correlations are distinct from the intertwined stripe order observed at low-temperature and in the single-band Hubbard model.

cuprates↗
DOE OSTI2025

One-Dimensional Electron Gas Confined along Nanowrinkles in a Unidirectional Charge Density Wave Material

Two-dimensional (2D) materials inherently exhibit instabilities. Structurally, this may lead to modulations along the third dimension, e.g., wrinkles. Electronically, 2D instabilities can manifest themselves as charge density waves (CDWs). Although wrinkles can alter anisotropic electronic structures susceptible to forming CDWs, less is known about their impact on broken-symmetry ground states. Here, in this study, using scanning tunneling microscopy and spectroscopy, we investigate the CDW states on the wrinkled surface of DyTe 3 . We identify elongated, parallel nanoscale wrinkles stabilized by ribbon-shaped defects. Interestingly, the CDW order persists across the nanowrinkles with a gradual phase shift but is locally suppressed near the defects, where phase windings occur. In addition, these defects induce quantum confinement effects along the nanowrinkles, indicating the presence of one-dimensional metallic states with hole- like dispersion, while angle-resolved photoemission spectroscopy identifies a gap along the wrinkle direction. We ascribe this discrepancy to strain-induced changes in the Fermi surface, which lead to the closure of the gap at the sites of the nanowrinkles. Taken together, our results underscore the complex interplay between structural features and Fermi surface topology, allowing for the deliberate manipulation of quantum states in strongly correlated systems via local crystal deformations.

nanowrinkles↗
DOE OSTI2025

Genesis and atomic structure of the charge density wave phase of 1T-VSe 2

Using variable temperature total x-ray scattering, we study the emergence of charge density wave (CDW) order in the archetypal transition-metal dichalcogenide (TMDC) 1⁢𝑇−VSe 2 . Here, we find that a CDW precursor phase (PF) appears at 𝑇 CDW⁡(PF) of 200(5) K, where V and Se atoms experience in- and out-of-plane static displacements from their position in the undistorted lattice, respectively. The displacements increase with decreasing temperature and a little-known superstructure of V triatomic clusters emerges below 𝑇 CDW⁡(3⁢D) of 100(5) K, where three-dimensional CDW order sets in. Concurrently, Se atoms form less well-defined dimers. Thus, similarly to other TMDCs, 1⁢𝑇−VSe 2 appears to exhibit a two-step CDW transition. The finding underlines the key contribution of lattice distortions to the emergence of CDW order in 1⁢𝑇−VSe 2 and generally in TMDCs.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Observation of room-temperature charge density wave correlations via coherent phonon spectroscopy in the Sn-doped kagome superconductor CsV 3 ⁢Sb 5

In this study, we perform ultrafast time-resolved reflectivity measurements to track the evolution of charge density wave (CDW) correlations in Sn-doped Kagome superconductor CsV 3⁢ Sb 5−𝑥 ⁢Sn 𝑥 . By extracting the coherent phonon spectrum, we evidence robust signatures of CDW correlations at temperature and doping ranges far beyond the phase boundary of long-range CDW order. Remarkably, we show that short-range CDW correlations survive up to room temperature in 𝑥 = 0.32 Sn-doped CsV 3 ⁢Sb 5 , supported by synchrotron x-ray diffraction measurements. We point out that the introduction of quenched disorder by Sn doping can pin the CDW and form static short-range CDW, which can explain the observed persistent CDW signatures. Our results thus corroborate the ubiquity and robustness of CDW correlations in Sn-doped CsV 3⁢ Sb 5 and provide new insights on the role of disorders on the CDW correlations in AV 3 ⁢Sb 5 family.

Charge density waves↗
DOE OSTI2025

Large Kohn Anomaly and Phonon Collapse Induced by Charge Density Wave in UPt 2⁢ Si 2

Using high-energy-resolution inelastic x-ray scattering, we observe anomalous softening and damping of the transverse acoustic phonon in UPt 2 ⁢Si 2 as the system is cooled toward the charge density wave (CDW) transition temperature 𝑇 CDW . The phonon exhibits a marked Kohn-type anomaly around the CDW wave vector 𝑄 CDW and becomes overdamped within a finite momentum range already well above 𝑇 CDW . The dispersion anomaly is consistent with potential Fermi surface nesting, which together with the extended phonon collapse indicates strong electron-phonon coupling. The transition temperature estimated from the phonon softening is markedly lower than 𝑇 CDW , consistent with a primarily electronic instability rather than a phonon-driven transition. In conclusion, our results establish UPt 2⁢ Si 2 as a prime example of a strongly correlated electron CDW system with exceptionally strong electron-phonon coupling driving phonon softening and collapse.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Spin-Charge-Lattice Coupling across the Charge Density Wave Transition in a Kagome Lattice Antiferromagnet

Understanding spin and lattice excitations in a metallic magnetic ordered system forms the basis to unveil the magnetic and lattice exchange couplings and their interactions with itinerant electrons. Kagome lattice antiferromagnet FeGe is interesting because it displays a rare charge density wave (CDW) deep inside the antiferromagnetic ordered phase that interacts with the magnetic order. Here, we use neutron scattering to study the evolution of spin and lattice excitations across the CDW transition 𝑇 CDW in FeGe. While spin excitations below ∼100 meV can be well described by spin waves of a spin-1 Heisenberg Hamiltonian, spin excitations at higher energies are centered around the Brillouin zone boundary and extend up to ∼180 meV consistent with quasiparticle excitations across spin-polarized electron-hole Fermi surfaces. Furthermore, 𝑐-axis spin wave dispersion and Fe-Ge optical phonon modes show a clear hardening below 𝑇 CDW due to spin-charge-lattice coupling but with no evidence of a phonon Kohn anomaly. By comparing our experimental results with density functional theory calculations in absolute units, we conclude that FeGe is a Hund’s metal in the intermediate correlated regime where magnetism has contributions from both itinerant and localized electrons arising from spin polarized electronic bands near the Fermi level.

charge density waves↗
DOE OSTI2024

Cooling rate dependence of charge density wave phases in 1 T -TaS 2 studied by scanning tunneling microscopy and x-ray diffraction

The role of dynamics in the charge density wave (CDW) phases of 1T-TaS 2 , especially in accessing metastable phases, is still under scrutiny. We investigated cooling rate dependence on low-temperature CDW phases in this material by scanning tunneling microscopy and x-ray diffraction. In the majority of cases, we found the typical low temperature commensurate CDW and identified no other differences between samples that were fast cooled vs slow cooled from room temperature. In rare cases (1/18 STM experiments and 1/30 XRD experiments), we found a multi-domain structure in the low temperature CDW. The domain structure and metallic behavior revealed by STM and STS measurements of this phase are in excellent agreement with the previously reported metallic mosaic CDW phase.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗