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This dataset contains the raw data of "Large moiré superstructure of stacked incommensurate charge-density waves", Nature Materials, 2025
Single crystals of the quasi-skutterudite compounds Ca 3 (Ir 1-x Rh x ) 4 Sn 13 (3–4–13) were synthesized by flux growth and characterized by x-ray diffraction, energy dispersive x-ray spectroscopy, magnetization, resistivity, and radio frequency magnetic susceptibility techniques. The coexistence and competition between the charge density wave (CDW) and superconductivity was studied by varying the Rh/Ir ratio. The superconducting transition temperature, T c , varies from 7 K in pure Ir (x = 0) to 8.3 K in pure Rh (x = 1). Temperature-dependent electrical resistivity reveals monotonic suppression of the CDW transition temperature, T CDW (x). The CDW starts in pure Ir, x = 0, at T CDW ≈ 40 K and extrapolates roughly linearly to zero at x c ≈ 0.53–0.58 under the superconducting dome. Magnetization and transport measurements show a significant influence of CDW on superconducting and normal states. Meissner expulsion is substantially reduced in the CDW region, indicating competition between the CDW and superconductivity. The low-temperature resistivity is higher in the CDW part of the phase diagram, consistent with the reduced density of states due to CDW gapping. Its temperature dependence just above T c shows signs of non-Fermi liquid behavior in a cone-like composition pattern. We conclude that the Ca 3 (Ir 1-x Rh x ) 4 Sn 13 alloy is a good candidate for a composition-driven quantum critical point at ambient pressure.
Here, in this work we perform ultrafast time-resolved reflectivity measurements to study the symmetry breaking in the charge-density wave (CDW) phase of CsV 3 Sb 5 . By extracting the coherent phonon spectrum in the CDW phase of CsV 3 Sb 5 , we discover close phonon pairs near 1.3 THz and 3.1 THz, as well as a new mode at 1.84 THz. The 1.3 THz phonon pair and the 1.84 THz mode are observed up to the CDW transition temperature. Combining density-functional theory calculations, we show that these phonon pairs arise from the coexistence of Star of David and inverse Star of David distortions combined with sixfold rotational symmetry breaking. An anisotropy in the magnitude of transient reflectivity change is also revealed at the onset of CDW order. Our results thus indicate broken sixfold rotational symmetry in the charge-density wave state of CsV 3 Sb 5 , along with the absence of nematic fluctuation above 𝑇 CDW . Meanwhile, the measured coherent phonon spectrum in the CDW phase of CsV 3 Sb 5−𝑥 Sn 𝑥 with 𝑥 = 0.03–0.04 matches the staggered inverse Star of David with interlayer 𝜋 phase shift. This CDW structure contrasts with undoped CsV3Sb5 and explains the evolution from a phonon pair to a single mode at 1.3 THz by 𝑥 = 0.03–0.04 Sn doping.
The recently discovered Kagome superconductor 𝐴V 3 Sb 5 (where 𝐴 refers to K, Rb, Cs) has stimulated widespread research interest due to its interplay of nontrivial topology and unconventional correlated physics including charge-density waves (CDW) and superconductivity. The essential prerequisite to understanding the microscopic mechanisms of this complex electronic landscape is to unveil the configuration and symmetry of the charge-density wave order. As to now, little consensus has been made on what symmetry is broken. Herein, we clarify the microscopic structure and symmetry breaking of the CDW phase in RbV 3 Sb 5 and KV 3 Sb 5 by ultrafast time-resolved reflectivity. Our approach is based on extracting coherent phonon spectra induced by three-dimensional CDW and comparing them to calculated phonon frequencies via density-functional theory. The combination of these experimental results and calculations provides compelling evidence that the CDW structure of both compounds prevailing up to 𝑇 CDW is the 2 × 2 × 2 staggered inverse Star-of-David pattern with interlayer 𝜋 phase shift, in which the sixfold rotational symmetry is broken. Finally, these observations thus corroborate sixfold rotational symmetry breaking throughout the CDW phase of RbV 3 Sb 5 and KV 3 Sb 5 .
Here, the recent discovery of the AV 3 Sb 5 (A = K, Rb, Cs) kagome superconductors launched a growing field of research investigating the interplay between superconductivity and charge-density wave order in kagome metals. Specifically, the AV 3 Sb 5 family of materials naturally exhibits a Fermi level close to the Van Hove singularities associated with the saddle points formed from the prototypical kagome band structure. The charge-density wave and superconducting states that form within the kagome networks of these compounds exhibit a number of anomalous properties reminiscent of theoretical predictions of exotic states in kagome metals tuned close to their Van Hove fillings. In this Review, we discuss the key structural and electronic features of AV 3 Sb 5 compounds and survey the status of investigations of their unconventional electronic phase transitions.
Charge-density-wave implies a periodic modulation of the charge density. Typically observed in metallic systems, charge-density-wave arise from Fermi surface instabilities, resulting in the total or partial gapping of the Fermi surface. Here, we present experimental evidence for a charge-density wave state emerging in a band insulator which has no Fermi surface. The bulk and surface of our material platform, 𝛂-Bi 4 Br 4 , is gapped over the entire Brillouin zone. Through topographic and spectroscopic imaging at low temperatures, we unveil an unexpected unidirectional charge modulation in 𝛂-Bi 4 Br 4 , breaking the lattice translation symmetry. The charge-density-wave develops at temperatures below 40 K and adds an energy gap atop the existing insulating gap of 𝛂-Bi 4 Br 4 . Furthermore, our transport measurements reveal nonlinear electrical conduction, a phenomenon conventionally associated with the sliding or phason mode of incommensurate charge-density-waves. These unusual observations represent a different type of charge-density-wave
A spatially modulated superconducting state, known as pair density wave (PDW), is a tantalizing state of matter with unique properties. Recent scanning tunneling microscopy (STM) studies revealed that spin-triplet superconductor UTe 2 hosts an unprecedented spin-triplet, multi-component PDW whose three wavevectors are indistinguishable from a preceding charge-density wave (CDW) order that survives to temperatures well above the superconducting critical temperature, T c . Whether the PDW is the mother or a subordinate order remains unsettled. Here, based on a systematic search for bulk charge order above T c using resonant elastic X-ray scattering (REXS), we show that the structure factor of charge order previously identified by STM is absent in the bulk within the sensitivity of REXS. Our results invite two scenarios: either the density-wave orders condense simultaneously at T c in the bulk, in which case PDW order is likely the mother phase, or the charge modulations are restricted to the surface.
Electron correlation is a main driver of exotic quantum phases and their interplay. The 4H b-TaS 2 system, possessing an intrinsic heterostructure of 1T- and 1H -TaS 2 monolayers, offers a unique opportunity to control electron correlation by distorting the atomic lattice or tuning interlayer coupling. Here, we investigated intrinsically deformed charge-density waves (CDWs) in the 1T layer of 4H b-TaS 2 to elucidate and control their effects on flat bands using scanning tunneling microscopy and spectroscopy (STM/S) combined with first-principles calculations. We identified two types of CDW defects: Type 1 has structural distortion and locally suppressed flat bands, while Type 2 features an increased flat band filling factor of intact CDW structure. Density functional theory calculations indicate that a sulfur vacancy in the 1T layer distorts the CDW structure and gives rise to a Type 1, whereas a sulfur vacancy in the 1H layer reduces the interlayer charge transfer and leads to a Type 2. Furthermore, we demonstrated creating and erasing individual CDW defects via STM manipulation. Here, our findings provide a pathway to not only tune flat bands but also selectively manipulate the interaction between CDW, the atomic lattice, and interlayer coupling in strongly correlated systems with atomic precision.
An echo state network (ESN) is a type of reservoir computer that uses a recurrent neural network with a sparsely connected hidden layer. Compared with other recurrent neural networks, one great advantage of ESN is the simplicity of its training process. Yet, despite the seemingly restricted learnable parameters, ESN has been shown to successfully capture the spatial-temporal dynamics of complex patterns. Here we build an ESN to model the coarsening dynamics of charge-density waves (CDWs) in a semiclassical Holstein model, which exhibits a checkerboard electron density modulation at half-filling stabilized by a commensurate lattice distortion. The inputs to the ESN are local CDW order parameters in a finite neighborhood centered around a given site, while the output is the predicted CDW order of the center site at the next time step. Special care is taken in the design of couplings between hidden layer and input nodes to ensure lattice symmetries are properly incorporated into the ESN model. Since the model predictions depend only on CDW configurations of a finite domain, the ESN is scalable and transferrable in the sense that a model trained on dataset from a small system can be directly applied to dynamical simulations on larger lattices. Furthermore, our work opens avenues for efficient dynamical modeling of pattern formations in functional electron materials.
The issue of whether d-wave superconductivity (SC) occurs in the square-lattice Hubbard model with U of order of the bandwidth has been one of the most debated issues to emerge from the study of high temperature SC. Here, we report variational results on eight-leg cylinders with next-nearest-neighbor hopping in the range $-0.5t\le t^{\prime} \le 0.25t$ with U = 8t and 12t and doped hole concentrations δ = 1/12 and 1/8. For $t^{\prime} \le 0$, the ground-state appears to be a charge-density wave (CDW) of one sort or another with SC correlations that are extremely short-ranged. In contrast, in some cases, the local magnetic order has a correlation length greater than half the cylinder width - suggestive that magnetic order might also arise in the 2D limit. For $t^{\prime} \le 0$, our results depend more strongly on boundary conditions (periodic vs antiperiodic), making it still harder to correctly guess whether SC or CDW correlations dominate in the 2D limit. These results were obtained employing matrix-product states with bond dimensions large enough that energy differences as small as 10 −3 t per site can be resolved.
Electron transport driven by the phase coherence and interference of quantum many-body wavefunctions is a fascinating phenomenon with potential technological significance. Superconductivity, for example, enables dissipationless transport through macroscopic phase twisting, while charge-density waves show broadband noise and AC-DC interference once their phase is depinned. We identify an analogous phase-coherent dynamics in the intervalley-coherent (IVC) state frequently observed in rhombohedral multilayer graphene. We show that a static magnetic field drives an oscillating intervalley current, which produces an oscillating orbital magnetization and thereby a detectable AC Hall response. This mechanism is similar to the Josephson effect observed in superconductors but now happening in momentum space. In this analogy, the static magnetic field acts as the DC voltage, while the oscillating intervalley current is the AC Josephson current. We provide microscopic calculations of all the phase-number free-energy parameters in rhombohedral trilayer graphene, establishing this effect as an experimental signature of IVC order.
Among the key features for next-generation memory devices is the need for high-contrast switching between metallic and insulating states with fast switching speed and long lifetime. However, materials exhibiting such properties are rare, and their electronic structure is often poorly understood. Here, by combining state-of-the-art devices with angle-resolved photoemission spectroscopy, we study the emergence of a metastable metallic state from the insulating ground state in the charge-density wave (CDW) material 1T-TaS 2 after applying short current pulses. Analysis of the electronic structure suggests a picture in which 1T-TaS 2 transforms from a band insulator in the commensurate CDW ground state to a correlated metal in the metastable state. Moreover, the optically induced metastable state reveals a strong similarity to the current-induced one. This work provides an extensive characterization of metastable order in 1T-TaS 2 and proves how studying electronic properties under in-operando conditions is a critical step for next-generation devices.
Time-dependent density functional theory within the linear response regime provides a solid mathematical framework to capture excitations. The accuracy of the theory, however, largely depends on the approximations for the exchange–correlation (xc) kernels. Away from the long-wavelength (or q = 0 short wave-vector) and zero-frequency (ω = 0) limit, the correlation contribution to the kernel becomes more relevant and dominant over exchange. The dielectric function, in principle, can encompass xc effects relevant to describe low-density physics. Furthermore, besides collective plasmon excitations, the dielectric function can reveal collective electron–hole excitations, often dubbed “ghost excitons.” Besides collective excitons, the physics of the low-density regime is rich, as exemplified by a static charge-density wave that was recently found for r s > 69, and was shown to be associated with softening of the plasmon mode. These excitations are seen to be present in much higher density 2D homogeneous electron gases of r s ≳ 4. Here, in this work, we perform a thorough analysis with xc model kernels for excitations of various nature. The uniform electron gas, as a useful model of real metallic systems, is used as a platform for our analysis. We highlight the relevance of exact constraints as we display and explain screening and excitations in the low-density region.
The Remeika series superconductor, (Ca 𝑥 Sr 1−𝑥 ) 3 Rh 4 Sn 13 , shows a rare nonmagnetic quantum critical point (QCP) associated with the continuous charge-density wave (CDW) and structural transition under the “dome” of superconductivity achieved by tuning composition and applying pressure. Here, we use a nonmagnetic pointlike disorder induced by 2.5 MeV electron irradiation to suppress the CDW and drive the system to and even beyond the QCP. This conclusion is based on a clear evolution of temperature-dependent resistivity, 𝜌(𝑇), from the Fermi liquid to the non-Fermi liquid regime with increasing amount of disorder. Starting on the CDW side, below the suggested QCP concentration of 𝑥 𝑐 =0.9, added disorder resulted in a progressively larger linear term and a reduced quadratic term in 𝜌(𝑇). Nearly perfect 𝑇−linear dependence is observed at the dose at which long-range CDW order is suppressed to 𝑇=0, consistent with the expectations. We refine the QCP location in this system and place it in the interval between 𝑥=0.75 and 0.85. Our results strongly support the concept that the disorder can tune the system to the quantum critical regime and even beyond. It follows from the argument by Imry and Ma that any ordered phase is unstable toward quenched disorder. Introduced in a controlled way, this disorder becomes a nonthermal tuning parameter likely applicable to a variety of different systems.
The effect of pressure on the low-temperature states of the Re 3 Ge 7 is investigated by both electrical and Hall resistance and magnetization measurements. At ambient pressure, the temperature-dependent resistance of Re 3 Ge 7 behaves quasilinearly from room temperature down to 60 K, then undergoes a two-step metal-to-insulator transition (MIT) at temperatures T 1 =59.4K and T 2 =58.7K, which may be related to a structural phase transition or occurrence of charge-density wave ordering. Upon applying pressure, the two-step (T 1 ,T 2 ) MIT splits into three steps (T 1 ,T 2 . and T 3 ) above 1 GPa, and all traces of MITs are fully suppressed by ~8 GPa. Subsequently, the onset of bulk superconductivity (SC) occurs between 10.8 and 12.2 GPa and persists to our highest pressure of 26.8 GPa. At 12.2 GPa the superconducting transition temperature, T c , and upper critical field, H c 2 reach the maximum of T c (onset) ~5.9 K and H c 2 (1.8 K) ~14 kOe. Finally, our results not only present the observation of SC under high pressure in Re 3 Ge 7 but also delineate the interplay between SC and other competing electronic states by creating a T-p phase diagram for this potentially topologically nontrivial system Re 3 Ge 7 .
Multiple anomalous features in electronic spectra of metals with a kagome lattice structure—van Hove singularities, Dirac points, and flat bands—imply that materials containing this structural motif may lie at a nexus of topological and correlated electron physics. Due to the prospects of such exceptional electronic behavior, the recent discovery of superconductivity coexisting with charge-density wave (CDW) order in the layered kagome metals 𝐴V 3 Sb 5 (𝐴 = K,Rb,Cs) has attracted considerable attention. Notably, these archetypal kagome metals express unconventional magnetotransport behavior, including an unexpected linear-in-𝐻 diagonal resistivity at low fields, and an even more peculiar, nonmonotonic sign-changing behavior of the Hall resistivity, which has been speculated to arise from a chiral CDW. We argue here that this unusual magnetotransport derives not from such unconventional phenomena, but rather from the unique fermiology of the 𝐴V 3 Sb 5 materials. Specifically, it is caused by a large, concave hexagonal Fermi surface sheet formed in the close proximity to the van Hove singularities, which is backfolded into a small hexagonal sheet and two large triangular sheets in the CDW state. We introduce and analyze a model of the electronic structure of these Fermi surface sheets that allows for a full analytical treatment within Boltzmann kinetic theory and that enables semi-quantitative fits of our transport data. Specifically, we find that the anomalous magnetotransport behavior is caused by the confluence of strong reduction of the Fermi velocity near the van Hove singularities located near the vertices of the hexagonal sheet and sharp corners in Fermi surface generated by the CDW reconstruction. In conclusion, our analytical approach not only explains the anomalous magnetotransport in the kagome superconductors but also can be extended to a variety of metallic systems hosting singular features in their Fermi surfaces.
Most nonperturbative numerical studies of electron-phonon interactions focus on model Hamiltonians where the electrons interact with a phonon branch via a single type of microscopic mechanism. Two commonly explored couplings in this context are the Holstein and Su-Schrieffer-Heeger (SSH) interactions, which describe phonons modulating the on-site energy and intersite electron hopping, respectively. Many materials, however, have multiple phonon branches that can each interact with electronic degrees of freedom in different ways. We present here a determinant quantum Monte Carlo study of the half-filled two-dimensional (bond) SSH-Holstein Hamiltonian, where electrons couple to different phonon branches via either the Holstein or SSH mechanism. As a result, we map the model's phase diagram and determine the nature of the transitions between charge-density wave, bond-order wave, and antiferromagnetic order.
We demonstrate that formulating the composite-fermion theory of the fractional quantum Hall (FQH) effect in terms of quaternions greatly expands its reach and opens the door into many interesting issues that were previously not amenable to quantitative theoretical investigation. As an illustration, we explore the possibility of a nematic or a charge-density wave instability of the composite-fermion Fermi sea at half-filled Landau level and of the nearby FQH states by looking for a gap closing instability of the neutral magneto-roton excitation. As a result, our quaternion formulation of the FQH effect has been inspired by mathematical developments in the theoretical analyses of gravitational wave modes and cosmic microwave background radiation, where an important role is played by spin-weighted spherical harmonics that are nothing but monopole harmonics appearing in the spherical geometry for the FQH effect.