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Electronic structure and lattice dynamics of 1⁢𝑇−VSe 2 : Origin of the three-dimensional charge density wave

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, muon spectroscopy, angle resolved photoemission (ARPES), diffuse and inelastic x-ray scattering, and state-of-the-art first-principles density functional theory calculations. Resonant elastic x-ray scattering does not show any resonant enhancement at either V or Se, indicating that the CDW peak at the 𝐾 edges describes a purely structural modulation of the electronic ordering. ARPES experiments identify (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. Here, 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 dependent 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 is well captured by our state-of-the art first-principles anharmonic calculations with the inclusion of van der Waals corrections in the exchange-correlation functional. The comprehensive description of the electronic and dynamical properties of VSe 2 reported here adds important pieces of information to the understanding of the electronic modulations in the family of transition-metal dichalcogenides.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Universal Stripe Symmetry of Short-Range Charge Density Waves in Cuprate Superconductors

The omnipresence of charge density waves (CDWs) across almost all cuprate families underpins a common organizing principle. However, a longstanding debate of whether its spatial symmetry is stripe or checkerboard remains unresolved. While CDWs in lanthanum- and yttrium-based cuprates possess a stripe symmetry, distinguishing these two scenarios is challenging for the short-range CDW in bismuth-based cuprates. Here, high-resolution resonant inelastic x-ray scattering is employed to uncover the spatial symmetry of the CDW in Bi 2 Sr 2-x La x CuO 6 + δ . Across a wide range of doping and temperature, anisotropic CDW peaks with elliptical shapes are found in reciprocal space. Based on Fourier transform analysis of real-space models, the results are interpreted as evidence of unidirectional charge stripes, hosted by mutually 90°-rotated anisotropic domains. This work paves the way for a unified symmetry and microscopic description of CDW order in cuprates.

36 MATERIALS SCIENCE↗

Theoretical investigation of charge density wave instability in CuS 2

The existence of a charge density wave (CDW) in transition-metal dichalcogenide (TMDC) CuS 2 has remained undetermined since its first experimental synthesis nearly 50 years ago. Despite conflicting experimental literature regarding its low-temperature structure, there exists no theoretical investigation of the phonon properties and lattice stability of this material. By studying the first-principles electronic structure and phonon properties of CuS 2 at various electronic temperatures, we identify temperature-sensitive soft phonon modes which unveil a previously unreported Kohn anomaly at approximately 100 K. Variation of the electronic temperature shows the presence of two distinct phases, characterized at low electronic temperature by a 2 × 2 × 2 periodic charge modulation associated with the motion of the S 2 dimers. We find this is driven by a slight orbital occupation imbalance of the copper d and sulfur p orbitals, reminiscent of the Jahn-Teller effect in finite systems. Investigation of the Fermi surface presents a potential Fermi surface nesting vector related to the location of the Kohn anomaly and observed band splittings in the unfolded band structure. The combination of these results suggests a strong possibility of CDW order in CuS 2 . Further study of CuS 2 in monolayer form finds no evidence of a CDW phase, as the identified bulk periodic distortions cannot be realized in two dimensions. This behavior sets this material apart from other transition-metal dichalcogenide materials, which exhibit a charge density wave phase down to the two-dimensional limit. As CDW in TMDC materials is considered to compete with superconductivity, the lack of a CDW in monolayer CuS 2 suggests the possibility of enhanced superconductivity relative to other transition-metal dichalcogenides. Altogether, our work identifies CuS 2 as a previously unrealized candidate to study the interplay of superconductivity, CDW order, and dimensionality.

36 MATERIALS SCIENCE↗

Real-space visualization of a defect-mediated charge density wave transition

Here, we study the coupled charge density wave (CDW) and insulator-to-metal transitions in the 2D quantum material 1T-TaS 2 . By applying in situ cryogenic 4D scanning transmission electron microscopy with in situ electrical resistance measurements, we directly visualize the CDW transition and establish that the transition is mediated by basal dislocations (stacking solitons). We find that dislocations can both nucleate and pin the transition and locally alter the transition temperature T c by nearly ~75 K. This finding was enabled by the application of unsupervised machine learning to cluster five-dimensional, terabyte scale datasets, which demonstrate a one-to-one correlation between resistance—a global property—and local CDW domain-dislocation dynamics, thereby linking the material microstructure to device properties. This work represents a major step toward defect-engineering of quantum materials, which will become increasingly important as we aim to utilize such materials in real devices.

4D-STEM↗

Room temperature depinning of the charge-density waves in quasi-two-dimensional 1T-TaS 2 devices

Here we report on the depinning of nearly commensurate charge-density waves in 1T-TaS 2 thin films at room temperature. A combination of the differential current–voltage measurements with the low-frequency noise spectroscopy provides unambiguous means for detecting the depinning threshold field in quasi-2D materials. The depinning process in 1T-TaS 2 is not accompanied by an observable abrupt increase in electric current—in striking contrast to depinning in the conventional charge-density-wave materials with quasi-1D crystal structure. We explained it by the fact that the current density from the charge-density waves in the 1T-TaS 2 devices is orders of magnitude smaller than the current density of the free carriers available in the discommensuration network surrounding the commensurate charge-density wave islands. The depinning fields in 1T-TaS 2 thin-film devices are several orders of magnitude larger than those in quasi-1D van der Waals materials. Obtained results are important for the proposed applications of the charge-density wave devices in electronics.

2D materials↗

Anharmonic strong-coupling effects at the origin of the charge density wave in CsV 3 Sb 5

The formation of charge density waves is a long-standing open problem, particularly in dimensions higher than one. Various observations in the vanadium antimonides discovered recently further underpin this notion. Here, we study the Kagome metal CsV3Sb5 using polarized inelastic light scattering and density functional theory calculations. We observe a significant gap anisotropy with 2Δ max /κ B T CDW ≈ 20, far beyond the prediction of mean-field theory. The analysis of the A 1g and E 2g phonons, including those emerging below T CDW , indicates strong phonon-phonon coupling, presumably mediated by a strong electron-phonon interaction. Similarly, the asymmetric Fano-type lineshape of the A 1g amplitude mode suggests strong electron-phonon coupling below T CDW . The large electronic gap, the enhanced anharmonic phonon-phonon coupling, and the Fano shape of the amplitude mode combined are more supportive of a strong-coupling phonon-driven charge density wave transition than of a Fermi surface instability or an exotic mechanism in CsV 3 Sb 5 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Bidirectional Ultrafast Control of Charge Density Waves via Phase Competition

The intricate competition between coexisting charge density waves (CDWs) can lead to rich phenomena, offering unique opportunities for phase manipulation through electromagnetic stimuli. Here, leveraging time-resolved x-ray diffraction, we demonstrate ultrafast control of a CDW in EuTe 4 upon optical excitation. At low excitation intensities, the amplitude of one of the coexisting CDW orders increases at the expense of the competing CDW, whereas at high intensities, it exhibits a nonmonotonic temporal evolution characterized by both enhancement and reduction. This transient bidirectional controllability, tunable by adjusting photoexcitation intensity, arises from the interplay between optical quenching and phase-competition-induced enhancement. Our findings, supported by phenomenological time-dependent Ginzburg-Landau theory simulations, not only clarify the relationship between the two CDWs in EuTe 4 , but also highlight the versatility of optical control over order parameters enabled by phase competition.

charge density waves↗

Landau-Ginzburg theory of charge density wave formation accompanying lattice and electronic long-range ordering

Here we propose an analytical Landau-Ginzburg (LG) theory of the charge density waves coupled with lattice and electronic long-range order parameters. Examples of long-range order include the electronic wave function of superconducting Cooper pairs, structural distortions, electric polarization, and magnetization. We formulate the LG free energy density as a power expansion with respect to the charge density and other long-range order parameters as well as their spatial gradients and biquadratic coupling terms. We introduced a biquadratic coupling between the charge density gradient and long-range order parameters as well as nonlinear higher gradients of the long-range order parameters. The biquadratic gradient coupling is critical to the appearance of different spatially modulated phases in charge-ordered ferroics and high-temperature superconductors. We derived the thermodynamic conditions for the stability of the spatially modulated phases, which are the intertwined spatial waves of charge density and lattice/electronic long-range order. The analytical expressions for the energies of different phases, corresponding order parameters, charge density waves amplitudes, and modulation periods obtained in this paper can be employed to guide the comprehensive physical explanation, deconvolution, and Bayesian analysis of experimental data on quantum materials ranging from charge-ordered ferroics to high-temperature superconductors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Charge density waves in two-dimensional transition metal dichalcogenides

Charge density wave (CDW is one of the most ubiquitous electronic orders in quantum materials. While the essential ingredients of CDW order have been extensively studied, a comprehensive microscopic understanding is yet to be reached. Recent research efforts on the CDW phenomena in two-dimensional (2D) materials provide a new pathway toward a deeper understanding of its complexity. This review provides an overview of the CDW orders in 2D with atomically thin transition metal dichalcogenides (TMDCs) as the materials platform. We mainly focus on the electronic structure investigations on the epitaxially grown TMDC samples with angle-resolved photoemission spectroscopy and scanning tunneling microscopy/spectroscopy as complementary experimental tools. Finally, we discuss the possible origins of the 2D CDW, novel quantum states coexisting with them, and exotic types of charge orders that can only be realized in the 2D limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Mapping the nonequilibrium order parameter of a quasi-two dimensional charge density wave system

The driving force of a charge density wave (CDW) transition in quasi-two dimensional systems is still debated, while being crucial in understanding electronic correlation in such materials. Here we use femtosecond time- and angle-resolved photoemission spectroscopy combined with computational methods to investigate the coherent lattice dynamics of a prototypical CDW system. The photo-induced temporal evolution of the periodic lattice distortion associated with the amplitude mode reveals the dynamics of the free energy functional governing the order parameter. Our approach establishes that optically-induced screening rather than CDW melting at the electronic level leads to a transiently modified potential which explains the anharmonic behaviour of the amplitude mode and discloses the structural origin of the symmetry-breaking phase transition.

electronic properties and materials↗

Charge density waves in the 2.5-dimensional quantum heterostructure

Charge density wave (CDW) and their interplay with correlated and topological quantum states are at the forefront of condensed matter research. The 4H 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 $\sqrt{13}$ ×$\sqrt{13}$ and 3 × 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⁢Hb-TaS 2 remain unsolved. In this Letter, we reveal the two-dimensional (2D) $\sqrt{13}$ ×$\sqrt{13}$ chiral CDW in the 1T layers and intraunit cell coupled 2D 2 × 2 CDW in the 1H and 1H' layers of 4⁢H b -TaS 2 . Here, our results establish 4⁢H b -TaS 2 a 2.5D quantum heterostructure, where 2D quantum states emerge from 3D crystalline structure.

36 MATERIALS SCIENCE↗

Strongly Correlated Charge Density Wave in La 2 – x Sr x CuO 4 Evidenced by Doping-Dependent Phonon Anomaly

The discovery of charge-density-wave-related effects in the resonant inelastic x-ray scattering spectra of cuprates holds the tantalizing promise of clarifying the interactions that stabilize the electronic order. In this paper, we report a comprehensive resonant inelastic x-ray scattering study of La 2 – x Sr x CuO 4 finding that charge-density wave effects persist up to a remarkably high doping level of x = 0.21 before disappearing at x = 0.25 . The inelastic excitation spectra remain essentially unchanged with doping despite crossing a topological transition in the Fermi surface. This indicates that the spectra contain little or no direct coupling to electronic excitations near the Fermi surface, rather they are dominated by the resonant cross section for phonons and charge-density-wave-induced phonon softening. We interpret our results in terms of a charge-density wave that is generated by strong correlations and a phonon response that is driven by the charge-density-wave-induced modification of the lattice.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Inhomogeneous high temperature melting and decoupling of charge density waves in spin-triplet superconductor UTe 2

Charge, spin and Cooper-pair density waves have now been widely detected in exotic superconductors. Understanding how these density waves emerge — and become suppressed by external parameters — is a key research direction in condensed matter physics. Here we study the temperature and magnetic-field evolution of charge density waves in the rare spin-triplet superconductor candidate UTe 2 using scanning tunneling microscopy/spectroscopy. We reveal that charge modulations composed of three different wave vectors gradually weaken in a spatially inhomogeneous manner, while persisting to surprisingly high temperatures of 10–12 K. We also reveal an unexpected decoupling of the three-component charge density wave state. Our observations match closely to the temperature scale potentially related to short-range magnetic correlations, providing a possible connection between density waves observed by surface probes and intrinsic bulk features. Importantly, charge density wave modulations become suppressed with magnetic field both below and above superconducting T c in a comparable manner. Our work points towards an intimate connection between hidden magnetic correlations and the origin of the unusual charge density waves in UTe 2 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Direct observation of the collective modes of the charge density wave in the kagome metal CsV 3 Sb 5

A recently discovered group of kagome metals AV 3 Sb 5 (A = K, Rb, Cs) exhibit a variety of intertwined unconventional electronic phases, which emerge from a puzzling charge density wave phase. Understanding of this charge-ordered parent phase is crucial for deciphering the entire phase diagram. However, the mechanism of the charge density wave is still controversial, and its primary source of fluctuations—the collective modes—has not been experimentally observed. Here, we use ultrashort laser pulses to melt the charge order in CsV 3 Sb 5 and record the resulting dynamics using femtosecond angle-resolved photoemission. We resolve the melting time of the charge order and directly observe its amplitude mode, imposing a fundamental limit for the fastest possible lattice rearrangement time. These observations together with ab initio calculations provide clear evidence for a structural rather than electronic mechanism of the charge density wave. Our findings pave the way for a better understanding of the unconventional phases hosted on the kagome lattice.

36 MATERIALS SCIENCE↗

Chirality locking charge density waves in a chiral crystal

In Weyl semimetals, charge density wave (CDW) order can spontaneously break the chiral symmetry, gap out the Weyl nodes, and drive the material into the axion insulating phase. Investigations have however been limited since CDWs are rarely seen in Weyl semimetals. Here, using scanning tunneling microscopy/spectroscopy (STM/S), we report the discovery of a novel unidirectional CDW order on the (001) surface of chiral crystal CoSi – a unique Weyl semimetal with unconventional chiral fermions. The CDW is incommensurate with both lattice momentum and crystalline symmetry directions, and exhibits an intra unit cell π phase shift in the layer stacking direction. The tunneling spectrum shows a particle-hole asymmetric V-shaped energy gap around the Fermi level that modulates spatially with the CDW wave vector. Combined with first-principle calculations, we identify that the CDW is locked to the crystal chirality and is related by a mirror reflection between the two enantiomers of the chiral crystal. Our findings reveal a novel correlated topological quantum state in chiral CoSi crystals and raise the potential for exploring the unprecedented physical behaviors of unconventional chiral fermions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Efficient simulations of charge density waves in the transition metal Dichalcogenide TiSe 2

Charge density waves (CDWs) in transition metal dichalcogenides are the subject of growing scientific interest due to their rich interplay with exotic phases of matter and their potential technological applications. Here, using density functional theory with advanced meta-generalized gradient approximations (meta-GGAs) and linear response time-dependent density functional theory (TDDFT) with state-of-the-art exchange-correlation kernels, we investigate the electronic, vibrational, and optical properties in 1T-TiSe 2 with and without CDW. In both bulk and monolayer TiSe 2 , the electronic bands and phonon dispersions in either normal or CDW (semiconducting) phase are described well via meta-GGAs, which separate the valence and conduction bands just as HSE06 does but with significantly more computational feasibility. The experimentally observed humps of electron energy loss spectroscopy are successfully reproduced in TDDFT. Our work opens the door to simulating these complexities in CDW compounds from first principles by revealing meta-GGAs as an accurate low-cost alternative to HSE06.

Electronic properties and materials↗

Aspects of symmetry and topology in the charge density wave phase of 1T–TiSe 2

Abstract The charge density wave (CDW) in 1 T –TiSe 2 harbors a nontrivial symmetry configuration. It is important to understand this underlying symmetry both for gaining a handle on the mechanism of CDW formation and for probing the CDW experimentally. Here, based on first-principles computations within the framework of the density functional theory, we unravel the connection between the symmetries of the normal and CDW states and the electronic structure of 1 T –TiSe 2 . Our analysis highlights the key role of irreducible representations of the electronic states and the occurrence of band gaps in the system in driving the CDW. By showing how symmetry-related topology can be obtained directly from the electronic structure, our study provides a practical pathway in search of topological CDW insulators.

Physics↗

In-Plane Anisotropy of Charge Density Wave Fluctuations in 1⁢𝑇−TiSe 2

We report measurements of anisotropic triple-𝑞 charge density wave (CDW) fluctuations in the transition metal dichalcogenide 1⁢𝑇−TiSe 2 over a large volume of reciprocal space with x-ray diffuse scattering. Above the transition temperature, 𝑇 CDW , the in-plane diffuse scattering is marked by ellipses which reveal that the in-plane fluctuations are anisotropic. In addition, the out-of-plane diffuse scattering is characterized by rodlike structures which indicate that the CDW fluctuations in neighboring layers are largely decoupled. Furthermore, our analysis of the diffuse scattering line shapes and orientations suggests that the three charge density wave components contain independent phase fluctuations with a hierarchy of length scales, leading to intricate fluctuation patterns that go beyond the conventional 2D-to-3D crossover picture.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗