Commensurate Charge Density Wave Research Articles

Two distinct charge density waves in the quasi-one-dimensional metal Sr0.95NbO3.37 revealed by resonant soft X-ray scattering

The interplay of electron-electron and electron-lattice interactions plays an important role in determining exotic properties in strongly correlated electron systems. Of particular interest is quasi-one-dimensional SrNbOx metals, which are perovskite-related layered Carpy-Galy phases. Quasi-one-dimensional metals often exhibit a charge density wave (CDW) accompanied by lattice distortion; however, to date, the presence of a CDW in a quasi-one-dimensional metallic Carpy-Galy phase has not been detected. Here, we report the discovery of two distinct and simultaneous commensurate CDWs in Sr0.95NbO3.37 using resonant soft X-ray scattering (RSXS), namely, an electronic-(001) superlattice below ~ 200 K and an electronic-(002) Bragg peak. We also observe a non-electronic-(002) Bragg peak showing lattice distortion below ~ 150 K. Through the temperature dependence and resonance profile of these CDWs and the lattice distortion, as well as the relationship between the wavelength and charge density, these CDWs are determined to be Wigner crystals and Peierls-like instabilities, respectively. The electron‒electron interaction is strong and dominant even up to 350 K, and upon cooling, it drives the electron–lattice interaction. The correlation length of the electronic-(001) superlattice is surprisingly larger than that of the electronic-(002) Bragg peak, and the superlattice is highly anisotropic. Supported by theoretical calculations, the CDWs are determined by the charge anisotropy and redistribution between the O-2p and Nb-4d orbitals, and the strength of the electronic-(001) superlattice is within the strong coupling limit.

Photodoping-modified charge density wave phase transition in WS2/1T-TaS2 heterostructure

Abstract Controlling collective electronic states holds great promise for the development of innovative devices. Here, we experimentally detect the modification of the charge density wave (CDW) phase transition within a 1T-TaS2 layer in a WS2/1T-TaS2 heterostructure using time-resolved ultrafast spectroscopy. Laser-induced charge transfer doping strongly suppresses the commensurate CDW (CCDW) phase, which results in a significant decrease in both the phase transition temperature (T c) and phase transition stiffness (PTS). We interpret that photo-induced hole doping, when surpassing a critical threshold value of ~1018/cm3, sharply decreases the phase transition energy barrier. Our results provide new insights into controlling the CDW phase transition, paving the way for optical-controlled novel devices based on CDW materials.

Superconductivity and charge density wave in Cu0.06TiSe2: A low-temperature STM/STS investigation

As one of the earliest discovered two-dimensional materials possessing charge density wave (CDW), TiSe2 has attracted wide attention due to its superconductivity induced by Cu intercalation. Until now, the relationship between superconductivity and CDW remains unclear, largely due to insufficient research at extremely low temperatures and magnetic fields. In this study, spatially resolved electronic density of states (DOS) of Cu0.06TiSe2 is investigated using low-temperature scanning tunneling microscopy/spectroscopy measurements. It is found that short-ranged commensurate CDW coexists with a homogeneous superconductivity exhibiting an anisotropic s-wave gap with an amplitude of 0.5 meV. Compared to the parent compound TiSe2, the spectra of Cu0.06TiSe2 exhibit a clear electron doping effect, as evidenced by a 70 meV shift of Fermi energy. Interestingly, the DOS is found to be strongly modified near the Fermi energy, despite its overall rigid band nature. These findings suggest that it is the remnant electron–hole coupling that sustains the short-ranged CDW, while the doping enhanced DOS facilitates superconductivity. This reveals a momentum space competition between the two microscopically coexistent orders.

Absence of 3a0 charge density wave order in the infinite-layer nickelate NdNiO2

A hallmark of many unconventional superconductors is the presence of many-body interactions that give rise to broken-symmetry states intertwined with superconductivity. Recent resonant soft X-ray scattering experiments report commensurate 3a0 charge density wave order in infinite-layer nickelates, which has important implications regarding the universal interplay between charge order and superconductivity in both cuprates and nickelates. Here we present X-ray scattering and spectroscopy measurements on a series of NdNiO2+x samples, which reveal that the signatures of charge density wave order are absent in fully reduced, single-phase NdNiO2. The 3a0 superlattice peak instead originates from a partially reduced impurity phase where excess apical oxygens form ordered rows with three-unit-cell periodicity. The absence of any observable charge density wave order in NdNiO2 highlights a crucial difference between the phase diagrams of cuprate and nickelate superconductors.

In operando cryo-STEM of pulse-induced charge density wave switching in TaS2

The charge density wave material 1T-TaS2 exhibits a pulse-induced insulator-to-metal transition, which shows promise for next-generation electronics such as memristive memory and neuromorphic hardware. However, the rational design of TaS2 devices is hindered by a poor understanding of the switching mechanism, the pulse-induced phase, and the influence of material defects. Here, we operate a 2-terminal TaS2 device within a scanning transmission electron microscope at cryogenic temperature, and directly visualize the changing charge density wave structure with nanoscale spatial resolution and down to 300 μs temporal resolution. We show that the pulse-induced transition is driven by Joule heating, and that the pulse-induced state corresponds to the nearly commensurate and incommensurate charge density wave phases, depending on the applied voltage amplitude. With our in operando cryogenic electron microscopy experiments, we directly correlate the charge density wave structure with the device resistance, and show that dislocations significantly impact device performance. This work resolves fundamental questions of resistive switching in TaS2 devices, critical for engineering reliable and scalable TaS2 electronics.

Pair density wave and superconductivity in a kinetically frustrated doped Emery model on a square lattice

The quest to understand the nature of superconductivity in the cuprates has spotlighted the pair density wave (PDW)–a superconducting state characterized by a spatially modulated order parameter. Despite significant advances in understanding PDW properties, conclusively demonstrating its presence in systems pertinent to cuprate superconductors remains elusive. In this study, we present a systematic density-matrix renormalization group study to investigate the Emery model (or the three-band Hubbard model) on two-leg square cylinders with negative electron hopping term tpp between adjacent oxygen sites. Kinetic frustration - introduced by changing the sign of oxygen-oxygen hopping - leads to a much reduced Cu-Cu antiferromagnetic exchange along with an enlarged charge transfer energy that changes the local properties of the model. At light doping levels, our findings reveal a ground state remarkably consistent with a PDW, exhibiting mutually commensurate superconducting (SC), charge, and spin density wave correlations. Intriguingly, the dominant SC pairing is observed between neighboring oxygen sites, diverging from the expected Cu sites in the positive tpp case. When the system incorporates moderate near-neighbor interactions, particularly an attractive Vpp between adjacent oxygen sites, the SC correlations become quasi-long-ranged, accompanied by a pronounced divergence in the PDW susceptibility. When the attractive Vpp increases further, the system gives way to an unconventional d-wave superconductivity.

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.

Selective Electron-Phonon Coupling in Dimerized 1T-TaS2 Revealed by Resonance Raman Spectroscopy.

The layered transition-metal dichalcogenide material 1T-TaS2 possesses successive phase transitions upon cooling, resulting in strong electron-electron correlation effects and the formation of charge density waves (CDWs). Recently, a dimerized double-layer stacking configuration was shown to form a Peierls-like instability in the electronic structure. To date, no direct evidence for this double-layer stacking configuration using optical techniques has been reported, in particular through Raman spectroscopy. Here, we employ a multiple excitation and polarized Raman spectroscopy to resolve the behavior of phonons and electron-phonon interactions in the commensurate CDW lattice phase of dimerized 1T-TaS2. We observe a distinct behavior from what is predicted for a single layer and probe a richer number of phonon modes that are compatible with the formation of double-layer units (layer dimerization). The multiple-excitation results show a selective coupling of each Raman-active phonon with specific electronic transitions hidden in the optical spectra of 1T-TaS2, suggesting that selectivity in the electron-phonon coupling must also play a role in the CDW order of 1T-TaS2.

Electronic dispersion, correlations and stacking in the photoexcited state of 1T-TaS2

Here we perform angle and time-resolved photoelectron spectroscopy on the commensurate charge density wave (CDW) phase of 1T-TaS2. Data with different probe pulse polarization are employed to map the dispersion of electronic states below and above the chemical potential. Upon photoexcitation, the fluctuations of CDW order erase the band dispersion and squeeze the electronic states near to the chemical potential. This transient phase sets within half a period of the coherent lattice motion and is favored by strong electronic correlations. The experimental results are compared to density-functional theory calculations with a self-consistent evaluation of the Coulomb repulsion. Our simulations indicate that the screening of Coulomb repulsion depends on the stacking order of the TaS2 layers. The entanglement of such degrees of freedom suggest that both the structural order and electronic repulsion are locally modified by the photoinduced CDW fluctuations.

Observation of the metallic mosaic phase in 1T−TaS2 at equilibrium

The transition-metal dichalcogenide tantalum disulphide ($1\mathit{T}\text{\ensuremath{-}}\mathrm{TaS}{}_{2}$) hosts a commensurate charge density wave (CCDW) at temperatures below 165 K where it also becomes insulating. The low temperature CCDW phase can be driven into a metastable ``mosaic'' phase by means of either laser or voltage pulses, which shows a large density of CDW domain walls as well as a closing of the electronic band gap. The exact origins of this pulse-induced metallic mosaic are not yet fully understood. Here, using scanning tunneling microscopy and spectroscopy (STM/STS), we observe the occurrence of such a metallic mosaic phase on the surface of $\mathrm{TaS}{}_{2}$ without prior pulse excitation over continuous areas larger than $100\ifmmode\times\else\texttimes\fi{}100\phantom{\rule{0.16em}{0ex}}\mathrm{nm}{}^{2}$ and macroscopic areas on the millimeter scale. We attribute the appearance of the mosaic phase to the presence of surface defects which cause the formation of the characteristic dense domain wall network. Based on our STM measurements, we further argue how the appearance of the metallic behavior in the mosaic phase could be explained by local stacking differences of the top layer. Thus we provide a potential avenue to explain the origin of the pulse-induced mosaic phase.

Incommensurate charge density wave in multiband intermetallic systems exhibiting competing orders

The appearance of an incommensurate charge density wave vector $\textbf{Q} = (Q_x,Q_y)$ on multiband intermetallic systems presenting commensurate charge density wave (CDW) and superconductivity (SC) orders is investigated. We consider a two-band model in a square lattice, where the bands have distinct effective masses. The incommensurate CDW (inCDW) and CDW phases arise from an interband Coulomb repulsive interaction, while the SC emerges due to a local intraband attractive interaction. For simplicity, all the interactions, the order parameters and hybridization between bands are considered $\textbf{k}$-independent. The multiband systems that we are interested are intermetallic systems with a $d$-band coexisting with a large $c$-band, for which a mean-field approach has proved suitable. We obtain the eigenvalues and eigenvectors of the Hamiltonian numerically and minimize the free energy density with respect to the diverse parameters of the model by means of the Hellmann-Feynman theorem. We investigate the system in real as well as momentum space and we find an inCDW phase with wave vector $\textbf{Q} = (\pi, Q_y) = (Q_x, \pi)$. Our numerical results show that the arising of an inCDW state depends on parameters, such as the magnitude of the inCDW and CDW interactions, band filling, hybridization and the relative depth of the bands. In general, inCDW tends to emerge at low temperatures, away from half-filling. We also show that, whether the CDW ordering is commensurate or incommensurate, large values of the relative depth between bands may suppress it. We discuss how each parameter of the model affects the emergence of an inCDW phase.

Atomic Visualization of the 3D Charge Density Wave Stacking in 1T-TaS2 by Cryogenic Transmission Electron Microscopy.

Charge density waves (CDWs) in 1T-TaS2 maintain 2D ordering by forming periodic in-plane star-of-David (SOD) patterns, while they also intertwined with orbital order in the c axis. Recent theoretical calculations and surface measurements have explored 3D CDW configurations, but interlayer intertwining of a 2D CDW order remains elusive. Here, we investigate the in- and out-of-plane ordering of the commensurate CDW superstructure in a 1T-TaS2 thin flake in real space, using aberration-corrected cryogenic transmission electronic microscopy (cryo-TEM) in low-dose mode, far below the threshold dose for an electron-induced CDW phase transition. By scrutinizing the phase intensity variation of modulated Ta atoms, we visualize the penetrative 3D CDW stacking structure, revealing an intertwining multidomain structure with three types of vertical CDW stacking configurations. Our results provide microstructural evidence for the coexistence of local Mott insulation and metal phases and offer a paradigm for studying the CDW structure and correlation order in condensed-matter physics using cryo-TEM.

Electronic states of domain walls in commensurate charge density wave ground state and mosaic phase in 1T -TaS2

Domain walls (DWs) in the charge-density-wave (CDW) Mott insulator 1T-TaS2 have unique localized states, which play an important role in exploring the electronic properties of the material. However, the electronic states in DWs in 1T-TaS2 have not been clearly understood, mostly due to the complex structures, phases, and interlayer stacking orders in the DW areas. Here, we explored the electronic states of DWs in the large-area CDW phase and mosaic phase of 1T-TaS2 by scanning tunneling spectroscopy. Due to the different densities of DWs, the electronic states of DWs show distinct features in these phases. In the large area CDW phase, both the domain and the DWs (DW1, DW2, DW4) have zero conductance at the Fermi level; while in the mosaic phase, they can be metallic or insulating depending on their environments. In areas with a high density of DWs, some electronic states were observed both on the DWs and within the domains, indicating delocalized states over the whole region. Our work contributes to further understanding of the interplay between CDW and electron correlations in 1T-TaS2.

Proximity-induced charge density wave in a metallic system

Non-local quasiparticles in correlated quantum materials can exhibit the proximity effect. For instance, in metal superconductor hybrid systems, the leaking of cooper pairs to the metallic region induces superconducting correlations in a standard metal. This paper explores the proximity effects of charge density wave (CDW) on metal using the attractive Hubbard model, which harbors CDW state at half-filling. Our fully self-consistent calculations demonstrate that periodic charge modulations develop in a metal due to the tunneling of finite momentum particle-hole pairs from the CDW region. Upon doping the normal region, the commensurate CDW changes to an incommensurate one by incorporating regular phase shifts. Furthermore, the induced CDW produces a soft gap in the density of states and thus can be detected in tunneling experiments. We discuss our results in light of recent reports of such proximity-induced charge order in different two-dimensional heterostructures.

Charge density wave and crystalline electric field effects inTmNiC2

Single crystals of ${\mathrm{TmNiC}}_{2}$ were grown by the optical floating-zone technique and were investigated by x-ray diffraction (XRD), thermal expansion, electrical resistivity, specific heat, and magnetic susceptibility measurements. Single-crystal XRD reveals the formation of a commensurate charge density wave (CDW) characterized by a CDW modulation vector ${\mathbf{q}}_{\mathbf{2}\mathbf{c}}=(0.5,0.5,0.5)$, which is accompanied by a symmetry change from the orthorhombic space group $Amm2$ to the monoclinic space group $Cm$, i.e., to a CDW superstructure which is isostructural with that of ${\mathrm{LuNiC}}_{2}$. For all transport and thermodynamic properties, anomalies related to a second order-type thermodynamic CDW phase transition are observed at around ${T}_{\mathrm{CDW}}\ensuremath{\simeq}375\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The large specific heat anomaly at ${T}_{\mathrm{CDW}}, \mathrm{\ensuremath{\Delta}}C\ensuremath{\simeq}6.2\phantom{\rule{4pt}{0ex}}\mathrm{J}\phantom{\rule{0.16em}{0ex}}{\mathrm{mol}}^{\ensuremath{-}1}{\mathrm{K}}^{\ensuremath{-}1}$, together with noticeable changes in entropy and enthalpy related to the CDW transition, suggests that this point group symmetry breaking CDW phase transition affects more significant parts of the Fermi surface as compared to the incommensurate CDW transition of, e.g., ${\mathrm{SmNiC}}_{2}$ with no change in point group symmetry. The results on the antiferromagnetic and paramagnetic state of ${\mathrm{TmNiC}}_{2}$ obtained by the above macroscopic techniques were complemented by microscopic studies via inelastic neutron scattering. A crystalline electric field modeling of macroscopic susceptibility and magnetic specific heat and entropy contributions as well as microscopic neutron scattering data, reveal crystal field eigenstates and eigenvalues with a ground-state doublet of the Tm-$4f$ electrons, which is well separated by about 25 meV from exited states of the $J=6$ ground-state multiplet.

Distinguishing and controlling Mottness in 1T−TaS2 by ultrafast light

Distinguishing and controlling the extent of Mottness is important for materials where the energy scales of the on-site Coulomb repulsion $U$ and the bandwidth $W$ are comparable. Here, we report the ultrafast electronic dynamics of $1T\text{\ensuremath{-}}{\mathrm{TaS}}_{2}$ by ultrafast time- and angle-resolved photoemission spectroscopy. A comparison of the electron dynamics for the intermediate phase (I-phase) as well as the low-temperature commensurate charge density wave (C-CDW) phase shows distinctive dynamics. While the I-phase is characterized by an instantaneous response and nearly time-resolution-limited fast relaxation ($\ensuremath{\sim}200$ fs), the C-CDW phase shows a delayed response and a slower relaxation (a few ps). Such distinctive dynamics reflect the different relaxation mechanisms and provide nonequilibrium signatures to distinguish the Mott insulating I-phase from the C-CDW band insulating phase. Moreover, a light-induced bandwidth reduction is observed in the C-CDW phase, pushing it toward the Mott insulating phase. Our work demonstrates the power of an ultrafast light-matter interaction in both distinguishing and controlling the extent of Mottness on the ultrafast timescale.

Nanoscale phase-slip domain walls in the charge density wave state of the Weyl semimetal candidate NbTe4

The transition-metal tetrachalcogenides are a model system to explore the conjunction of correlated electronic states such as charge density waves (CDWs) with topological phases of matter. Understanding the connection between these phases requires a thorough understanding of the individual states, which for the case of the CDW in this system, is still missing. In this paper we combine phonon-structure calculations and scanning tunneling microscopy measurements of ${\mathrm{NbTe}}_{4}$ in order to provide a full characterization of the CDW state. We find that, at short range, the superstructure formed by the CDW is fully commensurate with the lattice parameters. Moreover, our data reveals the presence of phase-slip domain walls separating regions of commensurate CDWs in the nanoscale, indicating that the CDW in this compound is discommensurate at long range. Our results solve a long-standing discussion about the nature of the CDW in these materials and provide a strong basis for the study of the interplay between this state and other novel quantum electronic states.

Nanoscale Friction across the First-Order Charge Density Wave Phase Transition of 1T-TaS2.

Nanotribology using atomic force microscopy (AFM) can be considered as a unique approach to analyze phase transition materials by localized mechanical interaction. In this work, we investigate friction on the lamellar transition metal dichalcogenide 1T-TaS2, which can undergo first-order charge density wave (CDW) phase transitions. Based on temperature-dependent atomic force microscopy under ultrahigh vacuum conditions (UHV), we can characterize the general friction levels across the first-order phase transitions and for the different phases. While structural and electronic properties for different phases appear to be of minor influence on friction, a distinct peak in friction is observed during the phase transition when cooling the sample from the nearly commensurate CDW (NC-CDW) phase to the commensurate CDW (C-CDW) phase. By performing systematic measurements as a function of load, scan velocity, and scan time, a recently proposed friction mechanism can be corroborated, where the AFM tip gradually induces local transformations of the material close to the spinodal point in a thermally activated and shear-assisted process until the surface is fully "harvested". Our results demonstrate that repeated nanomechanical stress can trigger local first-order phase transitions constituting a so far little explored mechanical energy dissipation channel.

Thickness dependent charge density wave networks on thin 1T-TaS$$_2$$

We investigate mechanically exfoliated thin 1T-TaS $$_2$$ with scanning tunneling microscopy at room temperature. Sample preparation without air exposure enables access to intrinsic charge-density-wave (CDW) phases of thin 1T-TaS $$_2$$ . At room temperature, we can observe the expected nearly commensurate CDW (NCCDW) phase on thin flakes similar to bulk 1T-TaS $$_2$$ . Further analysis reveals that CDW domains in the NCCDW phase become smaller and have a more anisotropic shape with decreasing thickness in the range of 8–28 layers. Our findings demonstrate that the anisotropic CDW nature of thin 1T-TaS $$_2$$ would be crucial to understand its exotic CDW-related phenomena and demand a systematic study on its correlation between the thickness-driven CDW domain anisotropy and the intermediate CDW states in thin 1T-TaS $$_2$$ .

Evolution of static charge density wave order, amplitude mode dynamics, and suppression of Kohn anomalies at the hysteretic transition in EuTe4

Charge density wave (CDW) induces periodic spatial modulation of the charge density that is commensurate or incommensurate with the host lattice periodicity, and leads to partial or complete electronic band-gap opening at the Fermi level (${E}_{\mathrm{F}}$). The recent finding of unconventional hysteresis within the CDW phase of ${\mathrm{EuTe}}_{4}$, not observable in other rare-earth tellurides $R{\mathrm{Te}}_{n}$ ($n=2$, 3), has highlighted the role of the relative phase of CDW distortion in weakly coupled Te layers. However, detailed structural and dynamical characterization of CDW distortion on the hysteretic transition is lacking. Here we report on the static CDW order, dynamics of the amplitude mode, and their evolution on the hysteretic transition using meV resolution elastic and inelastic x-ray scattering. We discover previously unidentified multiple commensurate and incommensurate CDW wave vectors ${\mathbf{q}}_{\mathrm{CDW}}$ along all three crystallographic axes. Importantly, we find that the previously reported $b$-axis CDW peak is coupled with the interlayer CDW phase and consequently co-occurs with the doubling of the unit cell along the $c$ axis. We confirm the presence of the competing $a$-axis CDW order but found it to be four orders of magnitude weaker than the $b$-axis CDW. Furthermore, we observe multiple Kohn anomalies at ${\mathbf{q}}_{\mathrm{CDW}}$ driven by Fermi surface nesting and hidden nesting, confirming earlier reports based on electronic and lattice susceptibility simulations. The amplitude mode and Kohn anomalies are found to suppress on unconventional hysteretic transition, suggesting the presence of nondegenerate metastable states, which we identify from the x-ray scattering measurements and simulations.