Charge Density Wave Amplitude Research Articles

Pressure effect of the charge density wave transition on Raman spectra and transport properties of 2H−NbSe2

Charge density wave (CDW) order is widely existing and fundamentally important in solid-state physics. However, several critical issues regarding the vibrational and electronic subsystems and their coupling still need to be better understood. Here, we tune the electrical transport and collective vibrational excitation, i.e., phonon and amplitude mode, by pressure in a prototype charge density wave material, $2H\text{\ensuremath{-}}{\mathrm{NbSe}}_{2}$. A complete pressure-temperature phase diagram is revisited. The anomaly in Hall and magnetoresistivity at CDW critical temperature, ${T}_{\mathrm{CDW}}$, was suppressed by the pressure. In the Raman spectroscopy measurements, the appearance of CDW amplitude mode is accompanied by the freezing of the two-phonon mode. The frequency of CDW amplitude mode under pressure follows modified mean-field theory with power-law scaling $(\ensuremath{\beta}=0.18)$. The renormalization of the Raman phonon across the CDW transition and the mean-field temperature dependence of CDW amplitude mode emphasized the importance of electron-phonon coupling in the formation of CDW state in $2H\text{\ensuremath{-}}{\mathrm{NbSe}}_{2}$. Our work clarifies the complex vibrational and electronic subsystems and sheds light on the mechanism of the charge density state in $2H\text{\ensuremath{-}}{\mathrm{NbSe}}_{2}$.

Ultrafast melting of charge-density wave fluctuations at room temperature in 1T-TiSe2 monitored under non-equilibrium conditions

We investigate the ultrafast lattice dynamics in 1T-TiSe2 using femtosecond reflection pump–probe and pump–pump–probe techniques at room temperature. The time-domain signals and Fourier-transformed spectra show the A1g phonon mode at 5.9 THz. Moreover, we observe an additional mode at ≈ 3 THz, corresponding to the charge-density wave (CDW) amplitude mode (AM), which is generally visible below Tc≈200 K. We argue that the emergence of the CDW amplitude mode at room temperature can be a consequence of fluctuations of order parameters based on the additional experiment using the pump–pump–probe technique, which exhibited suppression of the AM signal within the ultrafast timescale of ∼0.5 ps.

Phase-resolved frequency-domain analysis of the photoemission spectra for photoexcited 1T-TaS2 in the Mott insulating charge density wave state

We investigate the nonequilibrium electronic structure of 1T-TaS2 by time- and angle-resolved photoemission spectroscopy. We observe that strong photoexcitation induces the collapse of the Mott gap, leading to the photo-induced metallic phase. It is also found that the oscillation of photoemission intensity occurs as a result of the excitations of coherent phonons corresponding to the amplitude mode of the charge density wave (CDW). To study the dynamical change in the band dispersions modulated by the CDW amplitude mode, we perform analyses by using frequency-domain angle-resolved photoemission spectroscopy (FDARPES). We find that two different peak structures exhibit anti-phase oscillation with respect to each other by retrieving the amplitude and phase parts of the FDARPES spectra. They are attributed to the minimum and maximum band positions in energy, where the single band is oscillating between them synchronizing with the CDW amplitude mode. We further find that the flatband constructed as a result of CDW band folding survives during the oscillation while the Mott gap is significantly reduced. Our results suggest the CDW phase is robust, and the lattice modulation corresponding to the CDW amplitude mode dynamically modulates the Mott gap.

Enhanced charge density wave with mobile superconducting vortices in La1.885Sr0.115CuO4

Superconductivity in the cuprates is found to be intertwined with charge and spin density waves. Determining the interactions between the different types of order is crucial for understanding these important materials. Here, we elucidate the role of the charge density wave (CDW) in the prototypical cuprate La1.885Sr0.115CuO4, by studying the effects of large magnetic fields (H) up to 24 Tesla. At low temperatures (T), the observed CDW peaks reveal two distinct regions in the material: a majority phase with short-range CDW coexisting with superconductivity, and a minority phase with longer-range CDW coexisting with static spin density wave (SDW). With increasing magnetic field, the CDW first grows smoothly in a manner similar to the SDW. However, at high fields we discover a sudden increase in the CDW amplitude upon entering the vortex-liquid state. Our results signify strong coupling of the CDW to mobile superconducting vortices and link enhanced CDW amplitude with local superconducting pairing across the H − T phase diagram.

Super-resolved time–frequency measurements of coupled phonon dynamics in a 2D quantum material

Methods to probe and understand the dynamic response of materials following impulsive excitation are important for many fields, from materials and energy sciences to chemical and neuroscience. To design more efficient nano, energy, and quantum devices, new methods are needed to uncover the dominant excitations and reaction pathways. In this work, we implement a newly-developed superlet transform—a super-resolution time-frequency analytical method—to analyze and extract phonon dynamics in a laser-excited two-dimensional (2D) quantum material. This quasi-2D system, 1T-TaSe2, supports both equilibrium and metastable light-induced charge density wave (CDW) phases mediated by strongly coupled phonons. We compare the effectiveness of the superlet transform to standard time-frequency techniques. We find that the superlet transform is superior in both time and frequency resolution, and use it to observe and validate novel physics. In particular, we show fluence-dependent changes in the coupled dynamics of three phonon modes that are similar in frequency, including the CDW amplitude mode, that clearly demonstrate a change in the dominant charge-phonon couplings. More interestingly, the frequencies of the three phonon modes, including the strongly-coupled CDW amplitude mode, remain time- and fluence-independent, which is unusual compared to previously investigated materials. Our study opens a new avenue for capturing the coherent evolution and couplings of strongly-coupled materials and quantum systems.

Spectrally Resolving the Phase and Amplitude of Coherent Phonons in the Charge Density Wave State of 1T‐TaSe2

AbstractThe excitation and detection of coherent phonons have given unique insights into the condensed matter, in particular for materials with strong electron–phonon coupling. A study of coherent phonons is reported in the layered charge density wave (CDW) compound 1T‐TaSe2 performed using transient broadband reflectivity spectroscopy, in the photon energy range 1.75–2.65 eV. Several intense and long‐lasting (>20 ps) oscillations, arising from the CDW superlattice reconstruction, are observed allowing for detailed analysis of the spectral dependence of their amplitude and phase. For energies above 2.4 eV, where transitions involve Ta d‐bands, the CDW amplitude mode at 2.19 THz is found to dominate the coherent response. At lower energies, instead, beating arises between additional frequencies, with a particularly intense mode at 2.95 THz. Interestingly, the spectral analysis reveals a π phase shift at 2.4 eV. Results are discussed considering the selective coupling of specific modes to energy bands involved in the optical transitions seen in steady‐state reflectivity. The work demonstrates how coherent phonon spectroscopy can distinguish and resolve optical states strongly coupled to the CDW order and provide additional information normally hidden in conventional steady‐state techniques.

Observation of anomalous amplitude modes in the kagome metal CsV3Sb5

The kagome lattice provides a fertile platform to explore novel symmetry-breaking states. Charge-density wave (CDW) instabilities have been recently discovered in a new kagome metal family, commonly considered to arise from Fermi-surface instabilities. Here we report the observation of Raman-active CDW amplitude modes in CsV3Sb5, which are collective excitations typically thought to emerge out of frozen soft phonons, although phonon softening is elusive experimentally. The amplitude modes strongly hybridize with other superlattice modes, imparting them with clear temperature-dependent frequency shift and broadening, rarely seen in other known CDW materials. Both the mode mixing and the large amplitude mode frequencies suggest that the CDW exhibits the character of strong electron-phonon coupling, a regime in which phonon softening can cease to exist. Our work highlights the importance of the lattice degree of freedom in the CDW formation and points to the complex nature of the mechanism.

Emergent nematicity and intrinsic versus extrinsic electronic scattering processes in the kagome metal CsV3Sb5

Fermi surface fluctuations and lattice instabilities in the 2D metallic kagome superconductor CsV$_3$Sb$_5$ are elucidated via polarization-resolved Raman spectroscopy. The presence of a weak electronic continuum in high-quality samples marks the cross-over into the charge-density-wave (CDW) ordered phase, while impurity-rich samples promote strong defect-induced electronic scattering processes that affect the coherence of the CDW phase. CDW-induced phonon anomalies appear below $T_{\mathrm{CDW}}$, with emergent $C2$ symmetry for one of the CDW amplitude modes, alluding to nematicity. In conjunction with symmetry-breaking lattice distortions, a kink-like hardening of the A$_{1g}$ phonon energy at $T_{\mathrm{CDW}}$ signifies a concerted interplay of electronic correlations and electron-phonon coupling in the exotic CDW order.

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.

Unveiling Unequivocal Charge Stripe Order in a Prototypical Cuprate Superconductor.

In the cuprates, high-temperature superconductivity, spin-density-wave order, and charge-density-wave (CDW) order are intertwined, and symmetry determination is challenging due to domain formation. We investigated the CDW in the prototypical cuprate La_{1.88}Sr_{0.12}CuO_{4} via x-ray diffraction employing uniaxial pressure as a domain-selective stimulus to establish the unidirectional nature of the CDW unambiguously. A fivefold enhancement of the CDW amplitude is found when homogeneous superconductivity is partially suppressed by magnetic field. This field-induced state provides an ideal search environment for a putative pair-density-wave state.

Optical spectroscopy and ultrafast pump-probe study of a quasi-one-dimensional charge density wave in CuTe

CuTe is a two-dimensional (2D) layered material; yet it forms a quasi-one-dimensional (quasi-1D) charge-density-wave (CDW) along the $a$ axis in the $ab$ plane at high transition temperature ${T}_{\mathrm{CDW}}=335\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. However, the anisotropic properties of CuTe remain to be explored. Here, we performed combined transport, polarized infrared reflectivity, and ultrafast pump-probe spectroscopy studies to investigate the underlying CDW physics of CuTe. Polarized optical measurements clearly revealed that an energy gap gradually forms along the $a$ axis upon cooling, while optical evidence of a gap signature is absent along the $b$ axis, suggesting pronounced electronic anisotropy in this quasi-2D material. Time-resolved optical reflectivity measurements revealed that the amplitude and relaxation time of photoexcited quasiparticles change dramatically across the CDW phase transition. Performing fast Fourier transformation of the oscillation signals arising from collective excitations, we identify the 1.65-THz mode as the CDW amplitude mode, whose energy softens gradually at elevated temperatures. Consequently, we provide further evidence for the formation of completely anisotropic CDW order in CuTe, which is quite rare in quasi-2D materials.

Restored strange metal phase through suppression of charge density waves in underdoped YBa2Cu3O7-δ.

The normal state of optimally doped cuprates is dominated by the “strange metal” phase that shows a linear temperature (T) dependence of the resistivity persisting down to the lowest T. For underdoped cuprates, this behavior is lost below the pseudogap temperature T*, where charge density waves (CDWs), together with other intertwined local orders, characterize the ground state. We found that the T-linear resistivity of highly strained, ultrathin, underdoped YBa2Cu3O7–δ films is restored when the CDW amplitude, detected by resonant inelastic x-ray scattering, is suppressed. This observation suggests an intimate connection between the onset of CDWs and the departure from T-linear resistivity in underdoped cuprates. Our results illustrate the potential of using strain control to manipulate the ground state of quantum materials.

The charge-density-wave signature on the superfluid density of cuprate superconductors

The superfluid density or superconducting (SC) carrier concentration n sc of cuprates has been the subject of intense investigations but there is not any single theory capable to explain all the available data. Here we show that the behavior of n sc in under and overdoped cuprates are a consequence of an SC interaction based on charge fluctuations in the incommensurate charge-density-waves (CDW) domains. We have shown that this interaction scales with the CDW amplitude or the pseudogap (PG) energy, yielding local SC amplitudes and Josephson currents. The average Josephson energy is proportional to the phase stiffness or superfluid density ρ sc ∝ n sc. We find that n sc(p) increases almost linearly with doping p in the underdoped region and in the charge abundant overdoped only a few fractions of the holes condense leading to two kinds of carriers, a recently confirmed feature. The calculations and the ρ sc data uncover how the PG–CDW–SC intertwined orders operate to yield cuprates properties.

Amplitude mode of charge density wave in TTF[Ni(dmit)2]2 observed by electronic Raman scattering

We measured the optical signature of the charge density waves (CDWs) in the multiband conductor TTF[Ni(dmit)2]2 by electronic Raman scattering. At low energies, a hump develops below 60 K. This hump is associated to the amplitude mode of the CDW with an energy around 9 meV. Raman symmetry-resolved measurements show that the CDW amplitude mode is anisotropic and that the CDW can be associated to the band nesting of Ni(dmit)2 chains.

Coherent phonons and the interplay between charge density wave and Mott phases in 1T−TaSe2

1$T$-TaSe$_{2}$ is host to coexisting strongly-correlated phases including charge density waves (CDWs) and an unusual Mott transition at low temperature. Here, we investigate coherent phonon oscillations in 1$T$-TaSe$_{2}$ using a combination of time- and angle-resolved photoemission spectroscopy (TR-ARPES) and time-resolved reflectivity (TRR). Perturbation by a femtosecond laser pulse triggers a modulation of the valence band binding energy at the $\Gamma$-point, related to the Mott gap, that is consistent with the in-plane CDW amplitude mode frequency. By contrast, TRR measurements show a modulation of the differential reflectivity comprised of multiple frequencies belonging to the distorted CDW lattice modes. Comparison of the temperature dependence of coherent and spontaneous phonons across the CDW transition shows that the amplitude mode intensity is more easily suppressed during perturbation of the CDW state by the optical excitation compared to other modes. Our results clearly identify the relationship of the in-plane CDW amplitude mode with the Mott phase in 1$T$-TaSe$_{2}$ and highlight the importance of lattice degrees of freedom.

Renormalization of the Mott gap by lattice entropy: The case of 1T- TaS2

In many transition-metal oxides and dichalcogenides, the electronic and lattice degrees of freedom are strongly coupled, giving rise to remarkable phenomena, such as metal-insulator transition (MIT) and charge-density wave (CDW) order. We study this interplay by tracing the instant electronic structure under ab initio molecular dynamics. Applying this method to a 1T-TaS2 layer, we show that the CDW-triggered Mott gap undergoes a continuous reduction as the lattice temperature raises, despite a nearly constant CDW amplitude. Before the CDW order undergoes a sharp first-order transition around the room temperature, the dynamical CDW fluctuation already shrinks the Mott gap size by half. The gap size reduction is one order of magnitude larger than the lattice temperature variation. Our calculation not only provides an important clue to understand the thermodynamics behavior in 1T-TaS2, but also demonstrates a general approach to quantify the lattice entropy effect in MIT.

Amplitude dynamics of the charge density wave in LaTe3 : Theoretical description of pump-probe experiments

We formulate a dynamical model to describe a photo-induced charge density wave (CDW) quench transition and apply it to recent multi-probe experiments on LaTe$_3$ [A. Zong et al., Nat. Phys. 15, 27 (2019)]. Our approach relies on coupled time-dependent Ginzburg-Landau equations tracking two order parameters that represent the modulations of the electronic density and the ionic positions. We aim at describing the amplitude of the order parameters under the assumption that they are homogeneous in space. This description is supplemented by a three-temperature model, which treats separately the electronic temperature, temperature of the lattice phonons with stronger couplings to the electronic subsystem, and temperature of all other phonons. The broad scope of available data for LaTe$_3$ and similar materials as well as the synergy between different time-resolved spectroscopies allow us to extract model parameters. The resulting calculations are in good agreement with ultra-fast electron diffraction experiments, reproducing qualitative and quantitative features of the CDW amplitude evolution during the initial few picoseconds after photoexcitation.

Dynamical Metal to Charge-Density-Wave Junctions in an Atomic Wire Array

We investigated the atomic scale electronic phase separation emerging from a quasi-1D charge-density-wave (CDW) state of the In atomic wire array on a Si(111) surface. Spatial variations of the CDW gap and amplitude are quantified for various interfaces of metallic and insulating CDW domains by scanning tunneling microscopy and spectroscopy (STS). The strong anisotropy in the metal-insulator junctions is revealed with an order of magnitude difference in the interwire and intrawire junction lengths of 0.4 and 7 nm, respectively. The intrawire junction length is reduced dramatically by an atomic scale impurity, indicating the tunability of the metal-insulator junction in an atomic scale. Density functional theory calculations disclose the dynamical nature of the intrawire junction formation and tunability.

Short-range charge density wave order in 2H−TaS2

$2H\text{\ensuremath{-}}\mathrm{Ta}{\mathrm{S}}_{2}$ undergoes a charge density wave (CDW) transition at ${T}_{\mathrm{CDW}}\ensuremath{\sim}75$ K, however key questions regarding the onset of CDW order remain under debate. In this study, we explore the CDW transition through a combination of temperature and excitation-dependent Raman spectroscopy, angle resolved photoemission spectroscopy (ARPES), and density functional theory (DFT). Below ${T}_{\mathrm{CDW}}$ we identify two CDW amplitude modes that redshift and broaden with increasing temperature and one zone-folded mode that disappears above ${T}_{\mathrm{CDW}}$. Above ${T}_{\mathrm{CDW}}$, we observe a strong two-phonon mode that softens substantially upon cooling, which suggests the presence of substantial lattice distortions at temperatures as high as 250 K. This correlates with the ARPES observation of the persistence of a CDW energy gap above ${T}_{\mathrm{CDW}}$ and finite-temperature DFT calculations of the phonon band structure that indicate an instability occurring well above the CDW transition temperature. DFT also provides the atomic displacements of the CDW amplitude modes and reproduces their temperature dependence. From these observations we suggest that short range CDW order exists well above ${T}_{\mathrm{CDW}}$, which poses new questions regarding the interplay between electronic structure and vibrational modes in layered CDW materials.

Pretopological fractional excitations in the two-leg flux ladder

Topological order, the hallmark of fractional quantum Hall states, is primarily defined in terms of ground-state degeneracy on higher-genus manifolds, e.g. the torus. We investigate analytically and numerically the smooth crossover between this topological regime and the Tao-Thouless thin torus quasi-1D limit. Using the wire-construction approach, we analyze an emergent charge density wave (CDW) signifying the break-down of topological order, and relate its phase shifts to Wilson loop operators. The CDW amplitude decreases exponentially with the torus circumference once it exceeds the transverse correlation length controllable by the inter-wire coupling. By means of numerical simulations based on the matrix product states (MPS) formalism, we explore the extreme quasi-1D limit in a two-leg flux ladder and present a simple recipe for probing fractional charge excitations in the $\nu=1/2$ Laughlin-like state of hard-core bosons. We discuss the possibility of realizing this construction in cold-atom experiments. We also address the implications of our findings to the possibility of producing non-Abelian zero modes. As known from rigorous no-go theorems, topological protection for exotic zero modes such as parafermions cannot exist in 1D fermionic systems and the associated degeneracy cannot be robust. Our theory of the 1D-2D crossover allows to calculate the splitting of the degeneracy, which vanishes exponentially with the number of wires, similarly to the CDW amplitude.