Incommensurate Charge Density Wave Research Articles

Atomic-scale visualization of a cascade of magnetic orders in the layered antiferromagnet GdTe3

GdTe3 is a layered antiferromagnet which has attracted attention due to its exceptionally high mobility, distinctive unidirectional incommensurate charge density wave (CDW), superconductivity under pressure, and a cascade of magnetic transitions between 7 and 12 K, with as yet unknown order parameters. Here, we use spin-polarized scanning tunneling microscopy to directly image the charge and magnetic orders in GdTe3. Below 7 K, we find a striped antiferromagnetic phase with twice the periodicity of the Gd lattice and perpendicular to the CDW. As we heat the sample, we discover a spin density wave with the same periodicity as the CDW between 7 and 12 K; the viability of this phase is supported by our Landau free energy model. Our work reveals the order parameters of the magnetic phases in GdTe3 and shows how the interplay between charge and spin can generate a cascade of magnetic orders.

Endotaxial stabilization of 2D charge density waves with long-range order

Charge density waves are emergent quantum states that spontaneously reduce crystal symmetry, drive metal-insulator transitions, and precede superconductivity. In low-dimensions, distinct quantum states arise, however, thermal fluctuations and external disorder destroy long-range order. Here we stabilize ordered two-dimensional (2D) charge density waves through endotaxial synthesis of confined monolayers of 1T-TaS2. Specifically, an ordered incommensurate charge density wave (oIC-CDW) is realized in 2D with dramatically enhanced amplitude and resistivity. By enhancing CDW order, the hexatic nature of charge density waves becomes observable. Upon heating via in-situ TEM, the CDW continuously melts in a reversible hexatic process wherein topological defects form in the charge density wave. From these results, new regimes of the CDW phase diagram for 1T-TaS2 are derived and consistent with the predicted emergence of vestigial quantum order.

An exactly solvable model of randomly pinned charge density waves in two dimensions

The nature of the interplay between fluctuations and quenched random disorder is a long-standing open problem, particularly in systems with a continuous order parameter. This lack of a full theoretical treatment has been underscored by recent advances in experiments on charge density wave materials. To address this problem, we formulate an exactly solvable model of a two-dimensional randomly pinned incommensurate charge density wave, and use the large-N technique to map out the phase diagram and order parameter correlations. Our approach captures the physics of the Berezinskii–Kosterlitz–Thouless phase transition in the clean limit at large N. We pay particular attention to the roles of thermal fluctuations and quenched random field disorder in destroying long-range order, finding a novel crossover between weakly- and strongly-disordered regimes.

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.

Endotaxial Polytype Engineering: Enhancement of Incommensurate Charge Density Waves in TaS2.

Endotaxial Polytype Engineering: Enhancement of Incommensurate Charge Density Waves in TaS2.

Discovery of charge order in a cuprate Mott insulator

Copper oxide superconductors universally exhibit multiple forms of electronically ordered phases that break the native translational symmetry of the CuO2 planes. In underdoped cuprates with correlated metallic ground states, charge/spin stripes and incommensurate charge density waves (CDWs) have been experimentally observed over the years, while early theoretical studies also predicted the emergence of a Coulomb-frustrated 'charge crystal' phase in the very lightly doped, insulating limit of CuO2 planes. Here, we search for signatures of CDW order in very lightly hole-doped cuprates from the 123 family RBa2Cu3O7 - δ (RBCO; R: Y or rare earth), by using resonant X-ray scattering, electron transport, and muon spin rotation measurements to resolve the electronic and magnetic ground states fully. Specifically, Pr is used to substitute Y at the R-site to systematically suppress the superconductivity and access the extremely low hole-doping regime of the cuprate phase diagram without changing the oxygen stoichiometry. X-ray scattering data taken on Pr-doped YBCO thin films reveal an in-plane CDW order that follows the same linear evolution of wave vector versus hole concentration as oxygen-underdoped YBCO but extends all the way to the insulating and magnetically ordered Mott limit. Combined with the recent observation of charge crystal phase on an insulating surface of Bi2Sr2CaCu2O8 + z, our results in RBCO suggest that this electronic symmetry breaking is universally present in very lightly doped CuO2 planes. These findings bridge the gap between the Mott insulating state and the underdoped metallic state and underscore the prominent role that Coulomb-frustrated electronic phase separation plays among all cuprates.

Magnetic-field-sensitive charge density waves in the superconductor UTe2.

The intense interest in triplet superconductivity partly stems from theoretical predictions of exotic excitations such as non-Abelian Majorana modes, chiral supercurrents and half-quantum vortices1-4. However, fundamentally new and unexpected states may emerge when triplet superconductivity appears in a strongly correlated system. Here we use scanning tunnelling microscopy to reveal an unusual charge-density-wave (CDW) order in the heavy-fermion triplet superconductor UTe2 (refs. 5-8). Our high-resolution maps reveal a multi-component incommensurate CDW whose intensity gets weaker with increasing field, with the CDWeventually disappearing at the superconducting critical field Hc2. To understand the phenomenology of this unusual CDW, we construct a Ginzburg-Landau theory for a uniform triplet superconductor coexisting with three triplet pair-density-wave states. This theory gives rise to daughter CDWs that would be sensitive to magnetic field owing to their origin in a pair-density-wave state and provides a possible explanation for our data. Our discovery of a CDW state that is sensitive to magnetic fields and strongly intertwined with superconductivity provides important information for understanding the order parameters of UTe2.

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.

Correlation between charge density wave phase transition and hydrogen adsorption in 1T-TaS2 thin film devices

Thin films of tantalum disulfide in the 1T-polytype structural phase (1T-TaS2), a type of metallic two-dimensional (2D) transition metal dichalcogenides (TMDs), are reactive to H2. Interestingly, in the incommensurate charge-density wave (ICCDW) phase with a metallic state, the electrical resistance of the 1T-TaS2 thin film decreases when H2 is adsorbed on it and returns to its initial value upon desorption. In contrast, the electrical resistance of the film in the nearly commensurate CDW (NCCDW) phase, which has a subtle band overlap or a small bandgap, does not change upon H2 adsorption/desorption. This difference in H2 reactivity is a result of differences in the electronic structure of the two 1T-TaS2 phases, namely, the ICCDW and NCCDW phases. Compared to other semiconductor 2D-TMDs such as MoS2 and WS2, the metallic TaS2 has been theoretically proven to capture gas molecules more easily because Ta has a stronger positive charge than Mo or W. Our experimental results provide evidence of this. Notably, this study is the first example of H2 sensing using 1T-TaS2 thin films and demonstrates the possibility of controlling the reactivity of the sensors to the gas by changing the electronic structure via CDW phase transitions.

Phonon softening and slowing-down of charge density wave fluctuations in BaNi2As2

BaNi$_2$As$_2$ is a nonmagnetic analogue of the iron pnictide superconductors, and in its tetragonal state exhibits an incommensurate charge-density-wave (IC-CDW) and a sizable elastoresistance. In this work, phonons in BaNi$_2$As$_2$ associated with the IC-CDW and uniform in-plane lattice distortions are investigated using high-resolution inelastic X-ray scattering. The in-plane transverse acoustic phonons reveal no softening at temperatures where the elastoresistance increases strongly, indicating the latter to be electronically driven. Systematic phonon measurements reveal the IC-CDW occurs in two stages upon cooling: underdamped phonons first soften to zero energy well above the IC-CDW ordering temperature, then the resulting quasielastic IC-CDW fluctuations gradually slow down and coalesce into the static IC-CDW order. A possible origin for our observations is the IC-CDW in tetragonal BaNi$_2$As$_2$ being uniaxial, which provides an additional Ising degree of freedom favorable for disordered IC-CDW modulations, and accounts for the elastoresistance through a weak coupling to the lattice.

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.

Soft-Phonon and Charge-Density-Wave Formation in Nematic BaNi2As2

We use diffuse and inelastic x-ray scattering to study the formation of an incommensurate charge-density-wave (I-CDW) in BaNi_{2}As_{2}, a candidate system for charge-driven electronic nematicity. Intense diffuse scattering is observed around the modulation vector of the I-CDW, Q_{I-CDW}. It is already visible at room temperature and collapses into superstructure reflections in the long-range ordered state where a small orthorhombic distortion occurs. A clear dip in the dispersion of a low-energy transverse optical phonon mode is observed around Q_{I-CDW}. The phonon continuously softens upon cooling, ultimately driving the transition to the I-CDW state. The transverse character of the soft-phonon branch elucidates the complex pattern of the I-CDW satellites observed in the current and earlier studies and settles the debated unidirectional nature of the I-CDW. The phonon instability and its reciprocal space position are well captured by our abinitio calculations. These, however, indicate that neither Fermi surface nesting, nor enhanced momentum-dependent electron-phonon coupling can account for the I-CDW formation, demonstrating its unconventional nature.

Elastoresistivity in the incommensurate charge density wave phase of BaNi2(As1−xPx)2

AbstractElectronic nematicity, the breaking of the crystal lattice rotational symmetry by the electronic fluid, is a fascinating quantum state of matter. In this work, using electronic transport under strain we investigate the electronic nematicity of BaNi2(As1−xPx)2, a candidate system for charge-induced nematicity. We report a large B1g elastoresistance coefficient that is maximized at the tetragonal-to-orthorhombic transition temperature, that slightly precedes the first-order triclinic transition. An hysteretic behavior is observed in the resistance versus strain sweeps and interpreted as the pinning of orthorhombic domains. Remarkably, the elastoresistance only onsets together with a strong enhancement of the incommensurate charge density wave of the material, strongly suggesting that this electronic instability is uniaxial in nature and drive the orthorhombic transition. The absence of sizeable elastoresistance above this electronic phase clearly contrasts dynamic and static electronic nematicity. Finally, the elastoresistance temperature dependence that strongly differs from the Curie-Weiss form of iron-based superconductors reveals major differences for the respective coupling of electronic nematicity to the lattice. Our results uncover an extremely strain-sensitive platform to study electronic anisotropy induced by a charge-density-wave instability.

Electron correlations rule the phonon-driven instability in single-layer TiSe2

We investigate the controversial case of charge-density-wave (CDW) order in single layer 1T-TiSe$_2$ by employing the density functional perturbation theory with on-site Hubbard interactions. The results emphasize the crucial role of electron correlations via Hubbard corrections in order to capture the accurate electronic structure, low- and high-temperature limits of the CDW phonon mode, and temperature-charge phase diagram. We show, in close agreement with the experiments, that total phase diagram consists of both commensurate and incommensurate CDW regions, where the latter coincide with the superconductive phase and might be instrumental for its formation. In addition to the established roles of quantum lattice fluctuations and excitonic interactions, our analysis emphasizes the overlooked crucial role of the momentum dependent electron-phonon coupling and electron correlations for the CDW phase transition in single layer TiSe$_2$.

Charge density wave transitions, soft phonon, and possible electronic nematicity in BaNi2(As1−xPx)2

A detailed investigation of ${\mathrm{BaNi}}_{\text{2}}{({\mathrm{As}}_{1\ensuremath{-}x}{\mathrm{P}}_{x})}_{\text{2}}$ single crystals using high-resolution thermal-expansion, heat-capacity, Young's-modulus, and resistivity measurements is presented. The phase diagram of ${\mathrm{BaNi}}_{\text{2}}{({\mathrm{As}}_{1\ensuremath{-}x}{\mathrm{P}}_{x})}_{\text{2}}$ is shown to be much richer than suggested by the original data of Kudo et al. [Phys. Rev. Lett. 109, 097002 (2012)]. The transition to the commensurate charge density wave (C-CDW) is always preceded by a fourfold symmetry-breaking transition associated with the long-range ordering of a strongly fluctuating unidirectional incommensurate charge density wave (I-CDW). Significant precursors above the I-CDW and C-CDW transitions are seen in the thermal expansion and resistivity and are particularly evident in the temperature dependence of the $c/a$ ratio of the lattice parameters. Heat-capacity measurements of the crystals with a higher P content and a higher critical temperature of 3.2 K uncover a Debye-like behavior of a soft-phonon mode with a very low ${\mathrm{\ensuremath{\Theta}}}_{\text{Debye}}$ of roughly 50 K. Associated with this soft phonon are unusually large thermal-expansion anomalies, resulting in logarithmically diverging uniaxial phonon Gr\"uneisen parameters. Young's-modulus data of these higher-${T}_{c}$ crystals exhibit a significant softening in both ${B}_{1g}$ and ${B}_{2g}$ channels, which is argued to be incompatible with nematic criticality and is rather associated with a broad phase transition to an hitherto unknown structure. Possible origins of the increase in the superconducting critical temperature with P substitution are discussed.

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.

Evidence that cuprate superconductors form an array of nanoscopic Josephson junctions

Recent measurements of charge instabilities in overdoped compounds rekindled the proposal that cuprates become superconductors by long-range order through Josephson coupling between nanoscopic charge domains. We use the theory of phase-ordering dynamics to show that incommensurate charge density waves (CDWs) are formed in the CuO planes by a series of free-energy wells separated by steep barriers. Charge oscillations in these domains give rise to a net hole-hole attraction proportional to the height of these barriers. Concomitantly, the self-consistent calculations yield localized superconducting amplitudes in the CDW domains characterizing a granular superconductor. We show that a transition by long-range phase order promoted by Josephson coupling elucidates many well-known features of cuprates like the high magnetic penetration depth anisotropy and the origin of the pseudogap, among others. Furthermore, the average Josephson energy reproduces closely the planar superfluid density temperature dependence of La-based films and the superconducting giant proximity effects of cuprates, a 20-year-old open problem.

Interplay of charge density waves, disorder, and superconductivity in 2H-TaSe2 elucidated by NMR

Single crystals of pristine and 6% Pd-intercalated 2H‐TaSe2 have been studied by means of 77Se nuclear magnetic resonance. The temperature dependence of the 77Se spectrum, with an unexpected line narrowing upon Pd intercalation, unravels the presence of correlated local lattice distortions far above the transition temperature of the charge density wave (CDW) order, thereby supporting a strong-coupling CDW mechanism in 2H‐TaSe2. While, the Knight shift data suggest that the incommensurate CDW transition involves a partial Fermi surface gap opening. As for spin dynamics, the 77Se spin-lattice relaxation rate as a function of temperature shows that a pseudogap behavior dominates the low-energy spin excitations even within the CDW phase, and gets stronger along with superconductivity in the Pd-6% sample. We discuss that CDW fluctuations may be responsible for the pseudogap as well as superconductivity, although the two phenomena are unlikely to be directly linked each other.

Observation of multiple charge density wave phases in epitaxial monolayer 1T-VSe2 film

As a special order of electronic correlation induced by spatial modulation, the charge density wave (CDW) phenomena in condensed matters attract enormous research interests. Here, using scanning–tunneling microscopy in various temperatures, we discover a hidden incommensurate stripe-like CDW order besides the () CDW phase at low-temperature of 4 K in the epitaxial monolayer 1T-VSe2 film. Combining the variable-temperature angle-resolved photoemission spectroscopic (ARPES) measurements, we discover a two-step transition of an anisotropic CDW gap structure that consists of two parts Δ 1 and Δ 2. The gap part Δ 1 that closes around ∼ 150 K is accompanied with the vanish of the () CDW phase. While another momentum-dependent gap part Δ 2 can survive up to ∼ 340 K, and is suggested to the result of the incommensurate CDW phase. This two-step transition with anisotropic gap opening and the resulted evolution in ARPES spectra are corroborated by our theoretical calculation based on a phenomenological form for the self-energy containing a two-gap structure Δ 1 + Δ 2, which suggests different forming mechanisms between the () and the incommensurate CDW phases. Our findings provide significant information and deep understandings on the CDW phases in monolayer 1T-VSe2 film as a two-dimensional (2D) material.

Unconventional Hysteretic Transition in a Charge Density Wave.

Hysteresis underlies a large number of phase transitions in solids, giving rise to exotic metastable states that are otherwise inaccessible. Here, we report an unconventional hysteretic transition in a quasi-2D material, EuTe_{4}. By combining transport, photoemission, diffraction, and x-ray absorption measurements, we observe that the hysteresis loop has a temperature width of more than 400K, setting a record among crystalline solids. The transition has an origin distinct from known mechanisms, lying entirely within the incommensurate charge density wave (CDW) phase of EuTe_{4} with no change in the CDW modulation periodicity. We interpret the hysteresis as an unusual switching of the relative CDW phases in different layers, a phenomenon unique to quasi-2D compounds that is not present in either purely 2D or strongly coupled 3D systems. Our findings challenge the established theories on metastable states in density wave systems, pushing the boundary of understanding hysteretic transitions in a broken-symmetry state.