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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Revealing the competition between charge density wave and superconductivity in CsV 3 Sb 5 through uniaxial strain

In this paper we report the effect of uniaxial strain ε applied along the crystalline a axis on the newly discovered kagome superconductor CsV 3 Sb 5 . At ambient conditions, CsV 3 Sb 5 shows a charge-density wave (CDW) transition at T CDW = 94.5K and superconducts below T c = 3.34K. In our paper, when the uniaxial strain ε is varied from –0.90% to 0.90%,T c monotonically increases by ~33% from 3.0 to 4.0 K, giving rise to the empirical relation T c (ε) = 3.4 + 0.56ε + 0.12ε 2 . On the other hand, for ε changing from –0.76% to 1.26%,TCDW decreases monotonically by ~10% from 97.5 to 87.5 K with T CDW (ε) = 94.5 – 4.72ε – 0.60ε 2 . The opposite response of T c and T CDW to the uniaxial strain suggests strong competition between these two orders. Comparison with hydrostatic pressure measurements indicate that it is the change in the c axis that is responsible for these behaviors of the CDW and superconducting transitions, and that the explicit breaking of the sixfold rotational symmetry by strain has a negligible effect. Combined with our first-principles calculations and phenomenological analysis, we conclude that the enhancement in Tc with decreasing c is caused primarily by the suppression of T CDW , rather than strain-induced modifications in the bare superconducting parameters. We propose that the sensitivity of T CDW with respect to the changes in the c axis arises from the impact of the latter on the trilinear coupling between the $M$$^{+}_{1}$ and the $L$$^{–}_{2}$ phonon modes associated with the CDW. Altogether, our paper reveals that the c-axis lattice parameter, which can be controlled by both pressure and uniaxial strain, is a powerful tuning knob for the phase diagram of CsV 3 Sb 5 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Quantum Monte Carlo and Density Functional Theory Study of Strain and Magnetism in 2D 1T-VSe 2 with Charge Density Wave States

Two-dimensional (2D) 1T-VSe 2 has prompted significant interest due to the discrepancies regarding alleged ferromagnetism (FM) at room temperature, charge density wave (CDW) states, and the interplay between the two. We employed a combined Diffusion Monte Carlo (DMC) and density functional theory (DFT) approach to accurately investigate the magnetic properties, CDW states, and their responses to strain in monolayer 1T-VSe 2 . Our calculations show the delicate competition between various phases, revealing critical insights into the relationship between their energetic and structural properties. Here, we performed classical Monte Carlo simulations informed by our DMC and DFT results and found the magnetic transition temperature (T c ) of the undistorted (non-CDW) FM phase to be 228 K and the distorted (CDW) phase to be 68 K. Additionally, we studied the response of biaxial strain on the energetic stability and magnetic properties of various phases of 2D 1T-VSe 2 and found that small amounts of strain can increase the T c , suggesting a promising route for engineering and enhancing magnetic behavior. Finally, we synthesized 1T-VSe 2 and performed Raman spectroscopy measurements, which were in close agreement with our calculated results, validating our computational approach. Our work emphasizes the role of highly accurate DMC methods in advancing the understanding of monolayer 1T-VSe 2 and provides a robust framework for future studies of 2D magnetic materials.

2D magnets↗
DOE OSTI2024

Real-space visualization of atomic displacements in a long-wavelength charge density wave using cryogenic 4D-STEM

EuA⁢l 4 , a known skyrmion magnet, represents a class of materials that show complex electronic behaviors involving long-wavelength charge density wave (CDW). Here we realize direct real-space imaging of the concomitant periodic lattice distortion (PLD) with picometer precision in EuA⁢l 4 . Simultaneous imaging of microstructure, polarization, and interatomic distance is made possible using cryogenic four-dimensional scanning transmitting electron microscopy (cryo-4DSTEM). With this approach, we determined that the PLD in EuA⁢l 4 incorporates two out-of-phase atomic displacement modes on the Eu and Al sublattices. The PLD introduces periodic local symmetry fluctuations from the average symmetry of the bulk EuA⁢l 4 crystal. This critical local structural insight helps understanding of charge-spin-lattice couplings behind the intertwined quantum order in EuA⁢l 4 . Furthermore, our results also demonstrate cryo-4DSTEM as an indispensable approach for probing CDW and related quantum materials at low temperatures.

Ni, Haoyang↗
DOE OSTI2025

Nanoscale modulation of flat bands via controllable charge density wave defects in 4⁢𝐻⁡𝑏−Ta⁢S 2

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.

Charge density waves↗
DOE OSTI2023

Spectral evidence for unidirectional charge density wave in detwinned BaNi 2 As 2

In the iron-based superconductors, unconventional superconductivity emerges in proximity to intertwined electronic orders consisting of an electronic nematic order and a spin density wave (SDW). Recently, BaNi 2 As 2 , like its well-known iron-based analog BaFe 2 As 2 , has been discovered to host a symmetry-breaking structural transition but coupled to a unidirectional charge density wave (CDW) instead of SDW, providing a novel platform to study intertwined orders. Here, in this work, through a systematic angle-resolved photoemission spectroscopy study combined with a detwinning B 1 g uniaxial strain, we identify distinct spectral evidence of band evolution due to the structural transition as well as CDW-induced band folding. In contrast to the nematicity and spin density wave in BaFe 2 As 2 , the structural and CDW order parameters in BaNi 2 As 2 are observed to be strongly coupled and do not separate in the presence of uniaxial strain. Furthermore, no nematic band splitting is resolved above the structural transition. Our measurements point to a likely lattice origin of the CDW order in BaNi 2 As 2 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Locally commensurate charge-density wave with three-unit-cell periodicity in YBa 2 Cu 3 O y

In order to identify the mechanism responsible for the formation of charge-density waves (CDW) in cuprate superconductors, it is important to understand which aspects of the CDW’s microscopic structure are generic and which are material-dependent. Here, we show that, at the local scale probed by NMR, long-range CDW order in YBa 2 Cu 3 O y is unidirectional with a commensurate period of three unit cells ( λ = 3 b ), implying that the incommensurability found in X-ray scattering is ensured by phase slips (discommensurations). Furthermore, NMR spectra reveal a predominant oxygen character of the CDW with an out-of-phase relationship between certain lattice sites but no specific signature of a secondary CDW with λ = 6 b associated with a putative pair-density wave. These results shed light on universal aspects of the cuprate CDW. In particular, its spatial profile appears to generically result from the interplay between an incommensurate tendency at long length scales, possibly related to properties of the Fermi surface, and local commensuration effects, due to electron-electron interactions or lock-in to the lattice.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Charge density wave and superconductivity in the disordered Holstein model

The interplay between electron-electron correlations and disorder has been a central theme of condensed matter physics over the past several decades, with particular interest in the possibility that interactions might cause delocalization of an Anderson insulator into a metallic state, and the disrupting effects of randomness on magnetic order and the Mott phase. In this work, we extend this physics to explore electron-phonon interactions and show, via exact quantum Monte Carlo simulations, that the suppression of the charge density wave correlations in the half-filled Holstein model by disorder can stabilize a superconducting phase. Our simulations thus capture qualitatively the suppression of charge ordered phases and emergent superconductivity recently seen experimentally.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Absence of bulk charge density wave order in the normal state of UTe 2

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.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Geometry of the charge density wave in the kagome metal A V 3 Sb 5

Kagome lattice is a fertile platform for topological and intertwined electronic excitations. Recently, experimental evidence of an unconventional charge density wave (CDW) is observed in a Z 2 kagome metal AV 3 Sb 5 (A=K, Cs, Rb). This observation triggers wide interest in the interplay between frustrated crystal structure and Fermi surface instabilities. Here, we analyze the lattice effect and its impact on CDW in AV 3 Sb 5 . Based on published experimental data, we show that the 2×2×2 CDW breaks the sixfold rotational symmetry of the crystal due to the phase shift between kagome layers and can explain the twofold symmetric CDW peak intensity observed by scanning tunneling spectroscopy. The coupling between the lattice and electronic degrees of freedom yields a weak first-order structural transition without continuous change of lattice dynamics. Our result emphasizes the fundamental role of lattice geometry in proper understanding of unconventional electronic orders in AV 3 Sb 5 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Robust superconductivity intertwined with charge density wave and disorder in Pd-intercalated ErTe 3

Pd-intercalated ErTe 3 is studied as a model system to explore the effect of "intertwined" superconducting and charge density wave (CDW) orders. Despite the common wisdom that superconductivity emerges only when CDW is suppressed, we present data from STM and AC susceptibility measurements that show no direct competition between CDW order and superconductivity. Both coexist over most of the intercalation range, with uniform superconductivity over length scales that exceed the superconducting coherence length. This is despite persisting short-range CDW order and increased scattering from the Pd intercalation. While superconductivity is insensitive to local defects in either of the bi-directional CDWs, vestiges of the Fermi-level distortions are observed in the properties of the superconducting state.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Band-Selective Spin-Charge Separation across the Charge Density Wave Transition in Quasi-1D NbSe 3

Non-Fermi liquid (non-FL) phase is a pivotal enigma in understanding intriguing quantum phases in strongly correlated systems, such as high-temperature superconductivity. Tomonaga-Luttinger liquid (TLL) theory, designed for one-dimensional (1D) systems, serves as one of the microscopic frameworks that elucidates non-FL behavior. Despite its theoretical concreteness, comprehensive experimental verification has remained incomplete. In particular, addressing the persistence of the TLL nature within ordered phases, such as charge density wave (CDW), has posed a significant challenge. We report the observation of TLL characteristics across the CDW transitions in a quasi-1D material NbSe 3 using angle-resolved photoemission spectroscopy. Spin-charge separation, a disentanglement of spin and charge degrees of freedom of electrons, is clearly observed within the band, accompanied by the suppression of spectral weight following a power-law behavior with anticipated temperature scaling. Surprisingly, the spin-charge separation persists even below the CDW transition temperatures, indicating the validity of the TLL nature in the CDW phase. In conclusion, our findings offer a unique opportunity to explore the interplay between the TLL and ordered phases, which could be connected to the interplay between non-FL and ordered phases in strongly correlated systems.

1-dimensional systems↗
DOE OSTI2024

Robust superconductivity and the suppression of charge-density wave in the quasi-skutterudites Ca 3 ( Ir 1 – x Rh x ) 4 Sn 13 single crystals at ambient pressure

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.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Echo state network for coarsening dynamics of charge density waves

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.

2-dimensional systems↗
DOE OSTI2022

Charge singlets and orbital-selective charge density wave transitions

The possibility of “orbitally selective Mott transitions” within a multiband Hubbard model, in which one orbital with large on-site electron-electron repulsion U 1 is insulating and another orbital, to which it is hybridized, with small U –1 , is metallic, is a problem of long-standing debate and investigation. In this paper we study an analogous phenomenon, the coexistence of metallic and insulating bands in a system of orbitals with different electron-phonon coupling. To this end, we examine two variants of the bilayer Holstein model: a uniform bilayer and a “Holstein-metal interface” where the electron-phonon coupling, λ, is zero in the “metallic” layer. In the uniform bilayer Holstein model, charge density wave (CDW) order dominates at small interlayer hybridization t 3 , but decreases and eventually vanishes as t 3 grows, providing a charge analog of singlet (spin liquid) physics. In the interface case, we show that CDW order penetrates into the metal layer and forms long-range CDW order at an intermediate ratio of inter- to intralayer hopping strengths, 1.4 ≲ t 3 /t ≲ 3.4. Furthermore, this is consistent with the occurrence of an “orbitally selective CDW” regime at weak t3 in which the layer with λ 1 ≠ 0 exhibits long-range charge order, but the “metallic layer” with λ –1 = 0, to which it is hybridized, does not.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Evolution of charge density wave soft phonon modes in Pd 𝑥 ⁢ErTe 3

Here, we investigated the lattice dynamics of quasi-two-dimensional Pd-intercalated ErTe 3 in relation to its charge-density-wave (CDW) transitions by means of x-ray diffuse and meV-resolution inelastic x-ray scattering. In pristine ErTe 3 , CDW order develops at orthogonal in-plane wave vectors q$^𝑐_1$ =(0,0,0.29) (the 𝑐−CDW ) and q$^𝑎_2 $= (0.31,0,0) (the 𝑎−CDW ), with transition temperatures $𝑇^𝑐_1$ = 270K and $𝑇^𝑎_2$ = 160K, respectively. Remarkably, we observe diffuse x-ray scattering already near the higher transition temperature $𝑇^𝑐_1$ along 𝑎−CDW but at a slightly different wave vector q$^𝑎_1$ = (0.29,0,0). Inelastic x-ray scattering for Pd 0.01 ⁢ErTe 3 shows that a partial phonon softening at q$^𝑎_1$, underscoring the strong competition between ordering tendencies along the nearly equivalent in-plane axes of the orthorhombic lattice. For intercalation levels 𝑥 ≥ 0.02, the 𝑎−CDW state is suppressed. Nevertheless, a similar correlation between phonon softening and diffuse scattering persists along the [100] direction, again observed at q$^𝑎_1$ = (0.29,0,0) and $𝑇^𝑐_1$. These findings suggest that the 𝑎−CDW is fully suppressed for 𝑥 ≥ 0.02, and that the residual diffuse scattering at originates from the partial phonon softening associated with the 𝑐−CDW, reflected by the near equality of the absolute size of q$^𝑐_1$ and q$^𝑎_1$.

Maity, Avishek [Technische Univ. München, Garching↗
DOE OSTI2022

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 400 K, 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. Furthermore, 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.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Emergent topological quantum orbits in the charge density wave phase of kagome metal CsV 3 Sb 5

The recently discovered kagome materials AV 3 Sb 5 (A = K, Rb, Cs) attract intense research interest in intertwined topology, superconductivity, and charge density waves (CDW). Although the in-plane 2 × 2 CDW is well studied, its out-of-plane structural correlation with the Fermi surface properties is less understood. In this work, we advance the theoretical description of quantum oscillations and investigate the Fermi surface properties in the three-dimensional CDW phase of CsV 3 Sb 5 . We derived Fermi-energy-resolved and layer-resolved quantum orbits that agree quantitatively with recent experiments in the fundamental frequency, cyclotron mass, and topology. We reveal a complex Dirac nodal network that would lead to a π Berry phase of a quantum orbit in the spinless case. However, the phase shift of topological quantum orbits is contributed by the orbital moment and Zeeman effect besides the Berry phase in the presence of spin-orbital coupling (SOC). Therefore, we can observe topological quantum orbits with a π phase shift in otherwise trivial orbits without SOC, contrary to common perception. Our work reveals the rich topological nature of kagome materials and paves a path to resolve different topological origins of quantum orbits.

36 MATERIALS SCIENCE↗