Generic character of charge and spin density waves in superconducting cuprates.

Charge density waves (CDWs) have been observed in nearly all families of copper-oxide superconductors. But the behavior of these phases across different families has been perplexing. In La-based cuprates, the CDW wavevector is an increasing function of doping, exhibiting the so-called Yamada behavior, while in Y- and Bi-based materials the behavior is the opposite. Here, we report a combined resonant soft X-ray scattering (RSXS) and neutron scattering study of charge and spin density waves in isotopically enriched La1.8−xEu0.2SrxCuO4 over a range of doping 0.07≤x≤0.20. We find that the CDW amplitude is temperature independent and develops well above experimentally accessible temperatures. Further, the CDW wavevector shows a nonmonotonic temperature dependence, exhibiting Yamada behavior at low temperature with a sudden change occurring near the spin ordering temperature. We describe these observations using a Landau­Ginzburg theory for an incommensurate CDW in a metallic system with a finite charge compressibility and spin-CDW coupling. Extrapolating to high temperature, where the CDW amplitude is small and spin order is absent, our analysis predicts a decreasing wavevector with doping, similar to Y and Bi cuprates. Our study suggests that CDW order in all families of cuprates forms by a common mechanism.

Coexisting Charge Density Waves in Twisted Bilayer NbSe2.

Twisted bilayers of 2D materials have emerged as a tunable platform for studying broken symmetry phases. While most interest has been focused toward emergent states in systems whose constituent monolayers do not feature broken symmetry states, assembling monolayers that exhibit ordered states into twisted bilayers can also give rise to interesting phenomena. Here, we use first-principles density-functional theory calculations to study the atomic structure of twisted bilayer NbSe2 whose constituent monolayers feature a charge density wave. We find that different charge density wave states coexist in the ground state of the twisted bilayer: monolayer-like 3 × 3 triangular and hexagonal charge density waves are observed in low-energy stacking regions, while stripe charge density waves are found in the domain walls surrounding the low-energy stacking regions. These predictions, which can be tested by scanning tunneling microscopy experiments, highlight the potential to create complex charge density wave ground states in twisted bilayer systems.

Nanoscale Operando Imaging of Electrically Driven Charge-Density Wave Phase Transitions.

Structural transformations in strongly correlated materials promise efficient and fast control of materials' properties via electrical or optical stimulation. The desired functionality of devices operating based on phase transitions, however, will also be influenced by nanoscale heterogeneity. Experimentally characterizing the relationship between microstructure and phase switching remains challenging, as nanometer resolution and high sensitivity to subtle structural modifications are required. Here, we demonstrate nanoimaging of a current-induced phase transformation in the charge-density wave (CDW) material 1T-TaS2. Combining electrical characterizations with tailored contrast enhancement, we correlate macroscopic resistance changes with the nanoscale nucleation and growth of CDW phase domains. In particular, we locally determine the transformation barrier in the presence of dislocations and strain, underlining their non-negligible impact on future functional devices. Thereby, our results demonstrate the merit of tailored contrast enhancement and beam shaping for advanced operando microscopy of quantum materials and devices.

Structural approach to charge density waves in low-dimensional systems: electronic instability and chemical bonding.

The charge density wave (CDW) instability, usually occurring in low-dimensional metals, has been a topic of interest for longtime. However, some very fundamental aspects of the mechanism remain unclear. Recently, a plethora of new CDW materials, a substantial fraction of which is two-dimensional or even three-dimensional, has been prepared and characterised as bulk and/or single-layers. As a result, the need for revisiting the primary mechanism of the instability, based on the electron-hole instability established more than 50 years ago for quasi-one-dimensional (quasi-1D) conductors, has clearly emerged. In this work, we consider a large number of CDW materials to revisit the main concepts used in understanding the CDW instability, and emphasise the key role of the momentum dependent electron-phonon coupling in linking electronic and structural degrees of freedom. We argue that for quasi-1D systems, earlier weak coupling theories work appropriately and the energy gain due to the CDW and the concomitant periodic lattice distortion (PLD) remains primarily due to a Fermi surface nesting mechanism. However, for materials with higher dimensionality, intermediate and strong coupling regimes are generally at work and the modification of the chemical bonding network by the PLD is at the heart of the instability. We emphasise the need for a microscopic approach blending condensed matter physics concepts and state-of-the-art first-principles calculations with quite fundamental chemical bonding ideas in understanding the CDW phenomenon in these materials.

Observation of Electronic Nematicity Driven by the Three-Dimensional Charge Density Wave in Kagome Lattice KV3Sb5.

Kagome superconductors AV3Sb5 (A = K, Rb, Cs) provide a fertile playground for studying intriguing phenomena, including nontrivial band topology, superconductivity, giant anomalous Hall effect, and charge density wave (CDW). Recently, a C2 symmetric nematic phase prior to the superconducting state in AV3Sb5 drew enormous attention due to its potential inheritance of the symmetry of the unusual superconductivity. However, direct evidence of the rotation symmetry breaking of the electronic structure in the CDW state from the reciprocal space is still rare, and the underlying mechanism remains ambiguous. The observation shows unconventional unidirectionality, indicative of rotation symmetry breaking from six-fold to two-fold. The interlayer coupling between adjacent planes with π-phase offset in the 2 × 2 × 2 CDW phase leads to the preferred two-fold symmetric electronic structure. These rarely observed unidirectional back-folded bands in KV3Sb5 may provide important insights into its peculiar charge order and superconductivity.

Melting of Unidirectional Charge Density Waves across Twin Domain Boundaries in GdTe3.

Solids undergoing a transition from order to disorder experience a proliferation of topological defects. The melting process generates transient quantum states. However, their dynamic nature with a femtosecond lifetime hinders exploration with atomic precision. Here, we suggest an alternative approach to the dynamic melting process by focusing on the interface created by competing degenerate quantum states. We use a scanning tunneling microscope (STM) to visualize the unidirectional charge density wave (CDW) and its spatial progression ("static melting") across a twin domain boundary (TDB) in the layered material GdTe3. Combining the STM with a spatial lock-in technique, we reveal that the order parameter amplitude attenuates with the formation of dislocations and thus two different unidirectional CDWs coexist near the TDB, reducing the CDW anisotropy. Notably, we discovered a correlation between this anisotropy and the CDW gap. Our study provides valuable insight into the behavior of topological defects and transient quantum states.

Realization of Multiple Charge-Density Waves in NbTe2 at the Monolayer Limit.

Layered transition-metal dichalcogenides down to the monolayer (ML) limit provide a fertile platform for exploring charge-density waves (CDWs). Here, we experimentally unveil the richness of the CDW phases in ML-NbTe2 for the first time. Not only the theoretically predicted 4 × 4 and 4 × 1 phases but also two unexpected 28×28 and 19×19 phases are realized. For such a complex CDW system, we establish an exhaustive growth phase diagram via systematic efforts in the material synthesis and scanning tunneling microscope characterization. Moreover, the energetically stable phase is the larger-scale order (19×19), which is surprisingly in contradiction to the prior prediction (4 × 4). These findings are confirmed using two different kinetic pathways: i.e., direct growth at proper growth temperatures (T) and low-T growth followed by high-T annealing. Our results provide a comprehensive diagram of the "zoo" of CDW orders in ML-NbTe2.

Robust Behavior of Charge Density Wave Quantum Motif Star-of-David in 2D NbSe2 Nanocrystals.

Charge density wave (CDW) is a typical collective phenomenon, and the phase change is generally accompanied by electronic transition with potential device applications. For the continuous miniaturization of devices, it is important to investigate the size effect down to the nanoscale. In this work, single-layer (SL) 1T-NbSe2 islands provide an ideal research platform to investigate the size effect on CDW arrangement and electronic states. The CDW motifs (Star-of-David [SOD]) at the island border are along the edge, and those at the interior tend to arrange in a triangular lattice for islands as small as 5 nm. Interestingly, in some small islands, the SOD clusters rearrange into a square-like lattice, and each SOD cluster remains robust as a quantum motif, both in the sense of geometry and electronic structures. Moreover, the electronic structure at the center of the small islands is downwards shifted compared to the big islands, explained by the spatial extension of the band bending originating from the edge of the islands. These findings reveal the robust behavior of CDW motifs down to the nanoscale and provide new insights into the size-limiting effect on 2D2D CDW ordering and electronic states down to a few nanometer extremes.

Multiorbital charge-density wave excitations and concomitant phonon anomalies in Bi2Sr2LaCuO6+δ.

Charge-density waves (CDWs) are ubiquitous in underdoped cuprate superconductors. As a modulation of the valence electron density, CDWs in hole-doped cuprates possess both Cu-3d and O-2p orbital character owing to the strong hybridization of these orbitals near the Fermi level. Here, we investigate underdoped Bi2Sr1.4La0.6CuO6+δ using resonant inelastic X-ray scattering (RIXS) and find that a short-range CDW exists at both Cu and O sublattices in the copper-oxide (CuO2) planes with a comparable periodicity and correlation length. Furthermore, we uncover bond-stretching and bond-buckling phonon anomalies concomitant to the CDWs. Comparing to slightly overdoped Bi2Sr1.8La0.2CuO6+δ, where neither CDWs nor phonon anomalies appear, we highlight that a sharp intensity anomaly is induced in the proximity of the CDW wavevector (QCDW) for the bond-buckling phonon, in concert with the diffused intensity enhancement of the bond-stretching phonon at wavevectors much greater than QCDW Our results provide a comprehensive picture of the quasistatic CDWs, their dispersive excitations, and associated electron-phonon anomalies, which are key for understanding the competing electronic instabilities in cuprates.

Axial-Bonding-Driven Dimensionality Effect on the Charge-Density Wave in NbSe2.

2H-NbSe2 is a prototypical charge-density-wave (CDW) system, exhibiting such a symmetry-breaking quantum ground state in its bulk and down to a single-atomic-layer limit. However, how this state depends on dimensionality and what governs the dimensionality effect remain controversial. Here, we experimentally demonstrate a robust 3 × 3 CDW phase in both freestanding and substrate-supported bilayer NbSe2, far above the bulk transition temperature. We exclude environmental effects and reveal a strong temperature and thickness dependence of Raman intensity from an axially vibrating A1g phonon mode, involving Se ions. Using first-principles calculations, we show that these result from a delicate but profound competition between the intra- and interlayer bonding formed between Se-pz orbitals. Our results suggest the crucial role of Se out-of-plane displacement in driving the CDW distortion, revealing the Se-dominated dimensionality effect and establishing a new perspective on the chemical bonding and mechanical stability in layered CDW materials.

Raman Optical Activity of 1T-TaS2.

Measurements of optical activity can be readily performed in transparent matter by means of a rotation of transmitted light polarization. In the case of opaque bulk materials, such measurements cannot be performed, making it difficult to assess possible chiral properties. In this work, we present full angular polarization dependencies of the Raman modes of bulk 1T-TaS2, which has recently been suggested to have chiral properties after pulsed laser excitation. We found that a mechanical rotation of the sample does not alter polarization-resolved Raman spectra, which can only be explained by introducing an antisymmetric Raman tensor, frequently used to describe Raman optical activity (ROA). Raman spectra obtained under circularly polarized excitation demonstrate that 1T-TaS2 indeed shows ROA, providing strong evidence that 1T-TaS2 is chiral under the used conditions of laser excitation. Our results suggest that ROA may be used as a universal tool to study chiral properties of quantum materials.

Alternating Superconducting and Charge Density Wave Monolayers within Bulk 6R-TaS2.

Van der Waals (vdW) heterostructures continue to attract intense interest as a route of designing materials with novel properties that cannot be found in nature. Unfortunately, this approach is currently limited to only a few layers that can be stacked on top of each other. Here, we report a bulk vdW material consisting of superconducting 1H TaS2 monolayers interlayered with 1T TaS2 monolayers displaying charge density waves (CDW). This bulk vdW heterostructure is created by phase transition of 1T-TaS2 to 6R at 800 °C in an inert atmosphere. Its superconducting transition (Tc) is found at 2.6 K, exceeding the Tc of the bulk 2H phase. Using first-principles calculations, we argue that the coexistence of superconductivity and CDW within 6R-TaS2 stems from amalgamation of the properties of adjacent 1H and 1T monolayers, where the former dominates the superconducting state and the latter the CDW behavior.

Probing the Origin of Chiral Charge Density Waves in the Two-Dimensional Limits.

Chirality generates spontaneous symmetry breaking and profoundly influences the topology, charge, and spin orders of materials. The chiral charge density wave (CDW) exhibits macroscopic chirality in the achiral crystal during the spontaneous electronic phase transitions. However, the mechanism of chiral CDW formation is shrouded in controversy. In this work, we report that two-dimensional H-phase TaS2 synthesized by molecular-beam epitaxy (MBE) shows a predominantly chiral CDW phase. Scanning tunneling microscopy (STM) imaging of the CDW reconstruction spots reveals a clockwise or anticlockwise intensity variation along the STM-imaged spots. First-principles calculations further show that the rotational symmetry of the momentum-dependent electron-phonon coupling is broken, giving rise to chirality. Our work provides new insights into the physical origin of the chiral charge-ordered states, shedding light on a general ordering rule in chiral CDWs.

Layered Monophosphate Tungsten Bronzes [Ba(PO4 )2 ]Wm O3m-3 : 2D Metals with Locked Charge-Density-Wave Instabilities.

Phosphate tungsten and molybenum bronzes represent an outstanding class of materials displaying textbook examples of charge-density-wave (CDW) physics among other fundamental properties. Here we report on the existence of a novel structural branch with the general formula [Ba(PO4 )2 ][Wm O3m-3 ] (m=3, 4 and 5) denominated 'layered monophosphate tungsten bronzes' (L-MPTB). It results from thick [Ba(PO4 )2 ]4- spacer layers disrupting the cationic metal-oxide 2D units and enforcing an overall trigonal structure. Their symmetries are preserved down to 1.8 K and the compounds show metallic behaviour with no clear anomaly as a function of temperature. However, their electronic structure displays the characteristic Fermi surface of previous bronzes derived from 5d W states with hidden nesting properties. By analogy with previous bronzes, such a Fermi surface should result into CDW order. Evidence of CDW order was only indirectly observed in the low-temperature specific heat, giving an exotic context at the crossover between stable 2D metals and CDW order.

Metal chalcogenides for neuromorphic computing: emerging materials and mechanisms.

The approaching end of Moore's law scaling has significantly accelerated multiple fields of research including neuromorphic-, quantum-, and photonic computing, each of which possesses unique benefits unobtained through conventional binary computers. One of the most compelling arguments for neuromorphic computing systems is power consumption, noting that computations made in the human brain are approximately 106times more efficient than conventional CMOS logic. This review article focuses on the materials science and physical mechanisms found in metal chalcogenides that are currently being explored for use in neuromorphic applications. We begin by reviewing the key biological signal generation and transduction mechanisms within neuronal components of mammalian brains and subsequently compare with observed experimental measurements in chalcogenides. With robustness and energy efficiency in mind, we will focus on short-range mechanisms such as structural phase changes and correlated electron systems that can be driven by low-energy stimuli, such as temperature or electric field. We aim to highlight fundamental materials research and existing gaps that need to be overcome to enable further integration or advancement of metal chalcogenides for neuromorphic systems.

Atomic-scale strain manipulation of a charge density wave.

A charge density wave (CDW) is one of the fundamental instabilities of the Fermi surface occurring in a wide range of quantum materials. In dimensions higher than one, where Fermi surface nesting can play only a limited role, the selection of the particular wavevector and geometry of an emerging CDW should in principle be susceptible to controllable manipulation. In this work, we implement a simple method for straining materials compatible with low-temperature scanning tunneling microscopy/spectroscopy (STM/S), and use it to strain-engineer CDWs in 2H-NbSe2 Our STM/S measurements, combined with theory, reveal how small strain-induced changes in the electronic band structure and phonon dispersion lead to dramatic changes in the CDW ordering wavevector and geometry. Our work unveils the microscopic mechanism of a CDW formation in this system, and can serve as a general tool compatible with a range of spectroscopic techniques to engineer electronic states in any material where local strain or lattice symmetry breaking plays a role.

Anharmonicity and Doping Melt the Charge Density Wave in Single-Layer TiSe2.

Low-dimensional systems with a vanishing band gap and a large electron-hole interaction have been proposed to be unstable toward exciton formation. As the exciton binding energy increases in low dimension, conventional wisdom suggests that excitonic insulators should be more stable in 2D than in 3D. Here we study the effects of the electron-hole interaction and anharmonicity in single-layer TiSe2. We find that, contrary to the bulk case and to the generally accepted picture, in single-layer TiSe2, the electron-hole exchange interaction is much smaller in 2D than in 3D and it has weak effects on phonon spectra. By calculating anharmonic phonon spectra within the stochastic self-consistent harmonic approximation, we obtain TCDW ≈ 440 K for an isolated and undoped single layer and TCDW ≈ 364 K for an electron-doping n = 4.6 × 1013 cm-2, close to the experimental result of 200-280 K on supported samples. Our work demonstrates that anharmonicity and doping melt the charge density wave in single-layer TiSe2.

Photocurrent Imaging of Multi-Memristive Charge Density Wave Switching in Two-Dimensional 1T-TaS2.

Transport studies of atomically thin 1T-TaS2 have demonstrated the presence of intermediate resistance states across the nearly commensurate (NC) to commensurate (C) charge density wave (CDW) transition, which can be further switched electrically. While this presents exciting opportunities for memristor applications, the switching mechanism could be potentially attributed to the formation of inhomogeneous C and NC domains. Here, we present combined electrical driving and photocurrent imaging of ultrathin 1T-TaS2 in a heterostructure geometry. While micron-sized CDW domains are seen upon cooling, electrically driven transitions are largely uniform, indicating that the latter likely induces true metastable CDW states, which we then explain by a free energy analysis. Additionally, we are able to perform repeatable and bidirectional switching across the intermediate states without changing sample temperature, demonstrating that atomically thin 1T-TaS2 can be further used as a robust and reversible multimemristor material for the first time.

Large Optical Tunability from Charge Density Waves in 1T-TaS2 under Incoherent Illumination.

Strongly correlated materials possess a complex energy landscape and host many interesting physical phenomena, including charge density waves (CDWs). CDWs have been observed and extensively studied in many materials since their first discovery in 1972. Yet they present ample opportunities for discovery. Here, we report a large tunability in the optical response of a quasi-2D CDW material, 1T-TaS2, upon incoherent light illumination at room temperature. We hypothesize that the observed tunability is a consequence of light-induced rearrangement of CDW stacking across the layers of 1T-TaS2. Our model, based on this hypothesis, agrees reasonably well with experiments suggesting that the interdomain CDW interaction is a vital potentially knob to control the phase of strongly correlated materials.

Anomalous relaxation kinetics and charge-density-wave correlations in underdoped BaPb1-x Bi x O3.

Superconductivity often emerges in proximity of other symmetry-breaking ground states, such as antiferromagnetism or charge-density-wave (CDW) order. However, the subtle interrelation of these phases remains poorly understood, and in some cases even the existence of short-range correlations for superconducting compositions is uncertain. In such circumstances, ultrafast experiments can provide new insights by tracking the relaxation kinetics following excitation at frequencies related to the broken-symmetry state. Here, we investigate the transient terahertz conductivity of BaPb1-x Bi x O3--a material for which superconductivity is "adjacent" to a competing CDW phase--after optical excitation tuned to the CDW absorption band. In insulating BaBiO3 we observed an increase in conductivity and a subsequent relaxation, which are consistent with quasiparticles injection across a rigid semiconducting gap. In the doped compound BaPb0.72Bi0.28O3 (superconducting below TC = 7 K), a similar response was also found immediately above TC This observation evidences the presence of a robust gap up to T [Formula: see text] 40 K, which is presumably associated with short-range CDW correlations. A qualitatively different behavior was observed in the same material for [Formula: see text] 40 K. Here, the photoconductivity was dominated by an enhancement in carrier mobility at constant density, suggestive of melting of the CDW correlations rather than excitation across an optical gap. The relaxation displayed a temperature-dependent, Arrhenius-like kinetics, suggestive of the crossing of a free-energy barrier between two phases. These results support the existence of short-range CDW correlations above TC in underdoped BaPb1-x Bi x O3, and provide information on the dynamical interplay between superconductivity and charge order.