Charge Density Wave Systems Research Articles

Unusual Geometric and Electronic Structures at Domain Boundaries in a Heterochiral Charge Density Wave Superlattice.

Domain boundaries (DBs) in charge density wave (CDW) systems not only are important for understanding the mechanism of how CDW interplays with other quantum phases but also have potential for future CDW-based nanodevices. However, current research on DBs in CDW materials has been mainly limited to those between homochiral CDW domains, whereas DBs between heterochiral CDW domains, especially in the atomic layers, remain largely unexplored. Here, we have studied the geometric and electronic states of heterochiral DBs in single-layer and bilayer 1T-NbSe2 using scanning tunneling microscopy/spectroscopy. We observe the existence of diverse CDW configurations in a single heterochiral CDW DB with atomic resolution and reveal the corresponding electronic states. In addition, interlayer stacking further enriches the electronic properties of the DB. Our results offer deep insights into the relationship between the detailed CDW nanostructures and electronic behaviors, which has significant implications for DB engineering in strongly correlated CDW systems and related nanodevices.

Theoretical Description of Pump-Probe Experiments in Charge-Density-Wave Materials out to Long Times

We describe coupled nonequilibrium electron-phonon systems semiclassically—Ehrenfest dynamics for the phonons and quantum mechanics for the electrons—using a classical Monte Carlo approach that determines the nonequilibrium response to a large pump field. The semiclassical approach is expected to be accurate, because the phonons are excited to average energies much higher than the phonon frequency, eliminating the need for a quantum description. The numerical efficiency of this method allows us to perform a self-consistent time evolution out to very long times (tens of picoseconds), enabling us to model pump-probe experiments of a charge-density-wave (CDW) material. Our system is a half-filled, one-dimensional (1D) Holstein chain that exhibits CDW ordering due to a Peierls transition. The chain is subjected to a time-dependent electromagnetic pump field that excites it out of equilibrium, and then a second probe pulse is applied after a time delay. By evolving the system to long times, we capture the complete process of lattice excitation and subsequent relaxation to a new equilibrium, due to an exchange of energy between the electrons and the lattice, leading to lattice relaxation at finite temperatures. We employ an indirect (impulsive) driving mechanism of the lattice by the pump pulse due to the direct driving of the electrons. We identify two driving regimes, where the pump can either cause small perturbations or completely invert the initial CDW order. Our work successfully describes the ringing of the amplitude mode in CDW systems that has long been seen in experiment but never successfully explained by microscopic theory. We also describe the fluence-dependent crossover that inverts the CDW order parameter and changes the phonon dynamics. Finally, we illustrate how this method can examine a number of different types of experiments including photoemission, x-ray diffraction, and two-dimensional (2D) spectroscopy. Published by the American Physical Society 2024

Depinning of charge density waves of different dimensionalities in 1T-TiSe2 and NbSe3

Nonlinear transport behavior is one of the signatures of the formation of electronic crystals such as charge density wave (CDW), as it provides evidence for their collective motion. Such experimental evidence has been widely reported in quasi-one-dimensional (1D) materials but is rarely studied in 2D systems. Only a few studies on the RTe3materials have been previsouly reported. Here we report for the first time the observation of CDW depinning and sliding in the layered 1T-TiSe2compound, based on the observation of (1) nonlinear voltage-current characteristics and (2) the electrical noise, which are associated with the CDW depinning and sliding process. Similar measurements are also conducted on quasi-1D system NbSe3. The depinning behavior of the CDWs with different dimensionalities in these two systems are compared. It is found that the threshold electric field (ET) increases linearly with decreasing temperature for the 2D case, consistent with previous results on RTe3, while it demonstrated an activated behavior in 1D, as expected within the weak-pinning Fukuyama-Lee-Rice framework. Such a distinction of the threshold behavior in CDW systems of different dimensions therefore indicates a possible strong pinning picture in higher-dimensional CDW systems in general.ETis found to be much higher in 1T-TiSe2, consistent with a strong pinning picture, and could account for the scarcity of the depinning study in these 2D systems. Our results thus pave the way for a unified understanding of the CDW collective motion in different dimensionalities.

Magnetic field mediated charge density wave transport in Ni doped NbSe3 nanowires

Controllable manipulation of the transition between many-body ground states or metastable states in charge density wave (CDW) systems by external stimuli such as an electric field or optical pulse is of great interest to distinguish delicate interplay of quantum states and to design functional devices. Here, we report magnetization-induced transport anomalies in magnetic impurity Ni doped NbSe3 nanowires, which is toward suppressing the anomalous features of pristine CDW states and inducing the typical transport characteristics of disordered metallic phase accompanied by new emergent metastable CDW states or a tunneling-like transport behavior. These transport switching phenomena are ascribed to out-of-equilibrium disorder introduced by the reorientation of local charge/spin-density-wave domains, which partly retain even after switching off the magnetic field. Our observation will promote the understanding of the interaction between the CDW and the magnetic field coupled by magnetic impurities and pave a way to tune the CDW transport by magnetization, which may contribute to the development of CDW-based devices.

Three-dimensional ultrafast charge-density-wave dynamics in CuTe

Charge density waves (CDWs) involved with electronic and phononic subsystems simultaneously are a common quantum state in solid-state physics, especially in low-dimensional materials. However, CDW phase dynamics in various dimensions are yet to be studied, and their phase transition mechanism is currently moot. Here we show that using the distinct temperature evolution of orientation-dependent ultrafast electron and phonon dynamics, different dimensional CDW phases are verified in CuTe. When the temperature decreases, the shrinking of c-axis length accompanied with the appearance of interchain and interlayer interactions causes the quantum fluctuations (QF) of the CDW phase until 220 K. At T < 220 K, the CDWs on the different ab-planes are finally locked with each other in anti-phase to form a CDW phase along the c-axis. This study shows the dimension evolution of CDW phases in one CDW system and their stabilized mechanisms in different temperature regimes.

Structural dynamics at surfaces by ultrafast reflection high-energy electron diffraction.

Many fundamental processes of structural changes at surfaces occur on a pico- or femtosecond timescale. In order to study such ultrafast processes, we have combined modern surface science techniques with fs-laser pulses in a pump-probe scheme. Grazing incidence of the electrons ensures surface sensitivity in ultrafast reflection high-energy electron diffraction (URHEED). Utilizing the Debye-Waller effect, we studied the nanoscale heat transport from an ultrathin film through a hetero-interface or the damping of vibrational excitations in monolayer adsorbate systems on the lower ps-timescale. By means of spot profile analysis, the different cooling rates of epitaxial Ge nanostructures of different size and strain state were determined. The excitation and relaxation dynamics of a driven phase transition far away from thermal equilibrium is demonstrated using the In-induced (8 × 2) reconstruction on Si(111). This Peierls-distorted surface charge density wave system exhibits a discontinuous phase transition of first order at 130 K from a (8 × 2) insulating ground state to (4 × 1) metallic excited state. Upon excitation by a fs-laser pulse, this structural phase transition is non-thermally driven in only 700 fs into the excited state. A small barrier of 40 meV hinders the immediate recovery of the ground state, and the system is found in a metastable supercooled state for up to few nanoseconds.

Atomistic Origin of Diverse Charge Density Wave States in CsV_{3}Sb_{5}.

Kagome metals AV_{3}Sb_{5} (A=K, Rb, or Cs) exhibit intriguing charge density wave (CDW) instabilities, which interplay with superconductivity and band topology. However, despite firm observations, the atomistic origins of the CDW phases, as well as hidden instabilities, remain elusive. Here, we adopt our newly developed symmetry-adapted cluster expansion method to construct a first-principles-based effective Hamiltonian of CsV_{3}Sb_{5}, which not only reproduces the established inverse star of David (ISD) phase, but also predict a series of D_{3h}-n states under mild tensile strains. With such atomistic Hamiltonians, the microscopic origins of different CDW states are revealed as the competition of the second-nearest neighbor V-V pairs versus the first-nearest neighbor V-V and V-Sb couplings. Interestingly, the effective Hamiltonians also reveal the existence of ionic Dzyaloshinskii-Moriya interaction in the high-symmetry phase of CsV_{3}Sb_{5} and drives the formation of noncollinear CDW patterns. Our work thus not only deepens the understanding of the CDW formation in AV_{3}Sb_{5}, but also demonstrates that the effective Hamiltonian is a suitable approach for investigating CDW mechanisms, which can be extended to various CDW systems.

Ab initio electron-lattice downfolding: Potential energy landscapes, anharmonicity, and molecular dynamics in charge density wave materials

The interplay of electronic and nuclear degrees of freedom presents an outstanding problem in condensed matter physics and chemistry. Computational challenges arise especially for large systems, long time scales, in nonequilibrium, or in systems with strong correlations. In this work, we show how downfolding approaches facilitate complexity reduction on the electronic side and thereby boost the simulation of electronic properties and nuclear motion-in particular molecular dynamics (MD) simulations. Three different downfolding strategies based on constraining, unscreening, and combinations thereof are benchmarked against full density functional calculations for selected charge density wave (CDW) systems, namely 1H-TaS_22, 1T-TiSe_22, 1H-NbS_22, and a one-dimensional carbon chain. We find that the downfolded models can reproduce potential energy surfaces on supercells accurately and facilitate computational speedup in MD simulations by about five orders of magnitude in comparison to purely ab initio calculations. For monolayer 1H-TaS_22 we report classical and path integral replica exchange MD simulations, revealing the impact of thermal and quantum fluctuations on the CDW transition.

Stacking and spin order in a van der Waals Mott insulator 1T-TaS2

Quasi-two-dimensional charge density wave system of 1T-TaS2 has attracted recent interest due to topological excitations, emergent superconductivity, ultrafast synaptic functionality, and the possibility of a quantum spin liquid state. While electron correlation has been known to be essential in this system, the nature of its insulating phase is currently under debate. Here, we reinvestigate the origin of the insulating band structures of the 1T-TaS2 surface using density-functional theory calculations to consider the recently-raised issues such as interlayer coupling, surface effect, and interlayer spin ordering. We identify four distinct electronic states of the surface layer such as a 2D Mott phase, a strongly-coupled antiferromagnetic insulator, a weakly-coupled ferromagnetic insulator, and a small-gap semiconductor, depending on types of the surface termination and the interlayer spin configuration. These distinct surface electronic states explain the different sizes of spectroscopic band gaps observed in scanning tunneling microscopy, revealing the complexity of the interlayer charge and spin couplings in layered correlated materials.

Surface properties of 1T-TaS2 and contrasting its electron-phonon coupling with TlBiTe2 from helium atom scattering.

We present a detailed helium atom scattering study of the charge-density wave (CDW) system and transition metal dichalcogenide 1T-TaS2. In terms of energy dissipation, we determine the electron-phonon (e-ph) coupling, a quantity that is at the heart of conventional superconductivity and may even "drive" phase transitions such as CDWs. The e-ph coupling of TaS2 in the commensurate CDW phase (λ = 0.59 ± 0.12) is compared with measurements of the topo-logical insulator TlBiTe2 (λ = 0.09 ± 0.01). Furthermore, by means of elastic He diffraction and resonance/interference effects in He scattering, the thermal expansion of the surface lattice, the surface step height, and the three-dimensional atom-surface interaction potential are determined including the electronic corrugation of 1T-TaS2. The linear thermal expansion coefficient is similar to that of other transition-metal dichalcogenides. The He-TaS2 interaction is best described by a corrugated Morse potential with a relatively large well depth and supports a large number of bound states, comparable to the surface of Bi2Se3, and the surface electronic corrugation of 1T-TaS2 is similar to the ones found for semimetal surfaces.

Combined investigation of collective amplitude and phase modes in a quasi-one-dimensional charge density wave system over a wide spectral range

Combined investigation of collective amplitude and phase modes in a quasi-one-dimensional charge density wave system over a wide spectral range

Coexistence of Unidirectional Charge Density Waves in LaTe3

The classic rare-earth tritelluride provides an ideal platform to study the strong correlation state owing to its stable structures and abundance of orders. Here we report the observation of an undiscovered charge density wave (CDW) in LaTe3 under 4.2 K, the transition temperature of the CDW states is fitted to be 35 K, and confirmed by the evanishment of this CDW at 77 K via using temperature-dependent scanning tunneling microscope/spectroscopy. The coexistence of these CDWs is confirmed by the atomic resolution and beating pattern simulation. It is the first time to observe the coexistence of unidirectional charge density waves system, providing a new platform to understand the competition and evolution between strong correlation states, and get a deeper sight into the phase lag between different order parameters.

Decisive role of electron-phonon coupling for phonon and electron instabilities in transition metal dichalcogenides

The origin of the charge density wave (CDW) in transition metal dichalcogenides has been hotly debated, and no conclusive agreement has been reached. Here, we propose an ab initio framework for an accurate description of both Fermi surface nesting and electron-phonon coupling (EPC) and systematically investigate their roles in the formation of the CDW. Using monolayer $1H\text{\ensuremath{-}}{\mathrm{NbSe}}_{2}$ and $1T\text{\ensuremath{-}}{\mathrm{VTe}}_{2}$ as representative examples, we show that it is the momentum-dependent EPC that softens the phonon frequencies, which become imaginary (phonon instabilities) at CDW vectors (indicating CDW formation). In addition, the distribution of the CDW gap opening (electron instabilities) can be correctly predicted only if EPC is included in the mean-field model. These results emphasize the decisive role of EPC in the CDW formation. Our analytical process is general and can be applied to other CDW systems.

Realization of Multiple Charge-Density Waves in NbTe2 at the Monolayer Limit.

Layered transition-metal dichalcogenides down to the monolayer (ML) limit provide a fertile platform for exploring charge-density waves (CDWs). Here, we experimentally unveil the richness of the CDW phases in ML-NbTe2 for the first time. Not only the theoretically predicted 4 × 4 and 4 × 1 phases but also two unexpected and phases are realized. For such a complex CDW system, we establish an exhaustive growth phase diagram via systematic efforts in the material synthesis and scanning tunneling microscope characterization. Moreover, the energetically stable phase is the larger-scale order (), which is surprisingly in contradiction to the prior prediction (4 × 4). These findings are confirmed using two different kinetic pathways: i.e., direct growth at proper growth temperatures (T) and low-T growth followed by high-T annealing. Our results provide a comprehensive diagram of the "zoo" of CDW orders in ML-NbTe2.

Dramatic Plasmon Response to the Charge-Density-Wave Gap Development in 1T-TiSe_{2}.

1T-TiSe_{2} is one of the most studied charge density wave (CDW) systems, not only because of its peculiar properties related to the CDW transition, but also due to its status as a promising candidate of exciton insulator signaled by the proposed plasmon softening at the CDW wave vector. Using high-resolution electron energy loss spectroscopy, we report a systematic study of the temperature-dependent plasmon behaviors of 1T-TiSe_{2}. We unambiguously resolve the plasmon from phonon modes, revealing the existence of Landau damping to the plasmon at finite momentums, which does not support the plasmon softening picture for exciton condensation. Moreover, we discover that the plasmon lifetime at zero momentum responds dramatically to the band gap evolution associated with the CDW transition. The interband transitions near the Fermi energy in the normal phase are demonstrated to serve as a strong damping channel of plasmons, while such a channel in the CDW phase is suppressed due to the CDW gap opening, which results in the dramatic tunability of the plasmon in semimetals or small-gap semiconductors.

Surface enhanced electron correlation on the trivial quasi-two-dimensional bulk insulator 1T−TaS2

While the prototypical quasi-two-dimensional charge density wave system of $1T\text{\ensuremath{-}}{\mathrm{TaS}}_{2}$ has been known as a Mott insulator with a possibility of quantum spin liquid, recent band-structure calculations and spectroscopic works in parallel suggested a metallic system or a spin-singlet insulator due to the interlayer coupling. Here, we carefully reinvestigate the out-of-plane electron dispersion, which reflects the interlayer electronic coupling, with angle-resolved photoelectron spectroscopy. We identify two distinct branches for the topmost valence band, which can be unambiguously related to the surface and the bulk layers with different band gaps. Density functional theory calculations clearly indicate a trivial band insulator due to the interlayer coupling for the bulk but the surface band gap affected substantially by the electron correlation. The surface-bulk electronic dichotomy consistently incorporates most of the theoretical and spectroscopic results reported so far and has wide implications for van der Waals materials with nontrivial interlayer interactions.

Axial Higgs mode detected by quantum pathway interference in RTe3.

The observation of the Higgs boson solidified the standard model of particle physics. However, explanations of anomalies (for example, dark matter) rely on further symmetry breaking, calling for an undiscovered axial Higgs mode1. The Higgs modewas also seen in magnetic, superconducting and charge density wave (CDW) systems2,3. Uncovering thevector properties of a low-energy mode is challenging, and requires going beyond typical spectroscopic or scattering techniques. Here we discover an axial Higgs mode in the CDW system RTe3 using the interference of quantum pathways. In RTe3 (R = La, Gd), the electronic ordering couples bands of equal or different angular momenta4-6. As such, the Raman scattering tensor associated with the Higgs mode contains both symmetric and antisymmetric components, which are excited via two distinct but degenerate pathways. This leads to constructive or destructive interference of these pathways, depending on the choice of the incident and Raman-scattered light polarization. The qualitative behaviour of the Raman spectra is well captured by an appropriate tight-binding model, including an axial Higgs mode. Elucidation of the antisymmetric component is direct evidence that the Higgs mode contains an axial vector representation (that is, a pseudo-angular momentum) and hints that the CDW is unconventional. Thus, we provide a means for measuring quantum properties of collective modes without resorting to extreme experimental conditions.

Dynamics of collective modes in an unconventional charge density wave system BaNi2As2

BaNi2As2 is a non-magnetic analogue of BaFe2As2, the parent compound of a prototype pnictide high-temperature superconductor, displaying superconductivity already at ambient pressure. Recent diffraction studies demonstrated the existence of two types of periodic lattice distortions above and below the triclinic phase transition, suggesting the existence of an unconventional charge-density-wave (CDW) order. The suppression of CDW order upon doping results in a sixfold increase in the superconducting transition temperature and enhanced nematic fluctuations, suggesting CDW is competing with superconductivity. Here, we apply time-resolved optical spectroscopy to investigate collective dynamics in BaNi2As2. We demonstrate the existence of several CDW amplitude modes. Their smooth evolution through the structural phase transition implies the commensurate CDW order in the triclinic phase evolves from the high-temperature unidirectional incommensurate CDW, and may indeed trigger the structural phase transition. Excitation density dependence reveals exceptional resilience of CDW against perturbation, implying an unconventional origin of the underlying electronic instability.

Mapping the dispersion of the occupied and unoccupied band structure in photoexcited 1T-TiSe2

Charge density waves (CDW) are states of broken symmetry with a periodic modulation of charge and lattice typically leading to the opening of a gap in the band structure. In the model CDW system 1T-TiSe2 such a gap opens up between its Se4p valence and Ti3d conduction band, accompanied by a change of dispersion. These changes are crucial in understanding the CDW phase, as they provide a measure of the Se4p-Ti3d hybridization strength and characteristic mechanistic features. Using time- and angle-resolved photoelectron spectroscopy (trARPES), the unoccupied band structure is populated with near-infrared (NIR) pump pulses which allows to directly visualize the parabolically-shaped Ti3d conduction band. Furthermore, we observe a transient change of effective mass in the Se4p valence band following photoexcitation. This occurs alongside an overall reduction due to weakening of the CDW phase and is accompanied by an oscillating component with the frequency of the characteristic A1g phonon. These observations, enabled by trAPRES, highlight the importance of the lattice contributions in establishing the CDW order in 1T-TiSe2.

Orthorhombic charge density wave on the tetragonal lattice of EuAl4.

EuAl4 possesses the BaAl4 crystal structure type with tetragonal symmetry I4/mmm. It undergoes a charge density wave (CDW) transition at T CDW= 145 K and features four consecutive antiferromagnetic phase transitions below 16 K. Here we use single-crystal X-ray diffraction to determine the incommensurately modulated crystal structure of EuAl4 in its CDW state. The CDW is shown to be incommensurate with modulation wave vector q= (0,0,0.1781 (3)) at 70 K. The symmetry of the incommensurately modulated crystal structure is orthorhombic with superspace group Fmmm(00σ)s00, where Fmmm is a subgroup of I4/mmm of index 2. Both the lattice and the atomic coordinates of the basic structure remain tetragonal. Symmetry breaking is entirely due to the modulation wave, where atoms Eu and Al1 have displacements exclusively along a, while the fourfold rotation would require equal displacement amplitudes along a and b. The calculated band structure of the basic structure and interatomic distances in the modulated crystal structure both indicate the Al atoms as the location of the CDW. The tem-per-ature dependence of the specific heat reveals an anomaly at T CDW= 145 K of a magnitude similar to canonical CDW systems. The present discovery of orthorhombic symmetry for the CDW state of EuAl4 leads to the suggestion of monoclinic instead of orthorhombic symmetry for the third AFM state.