Orbital-selective time-domain signature of nematicity dynamics in the charge-density-wave phase of La1.65Eu0.2Sr0.15CuO4.

Understanding the interplay between charge, nematic, and structural ordering tendencies in cuprate superconductors is critical to unraveling their complex phase diagram. Using pump-probe time-resolved resonant X-ray scattering on the (0 0 1) Bragg peak at the Cu [Formula: see text] and O [Formula: see text] resonances, we investigate nonequilibrium dynamics of [Formula: see text] nematic order and its association with both charge density wave (CDW) order and lattice dynamics in La[Formula: see text]Eu[Formula: see text]Sr[Formula: see text]CuO[Formula: see text]. The orbital selectivity of the resonant X-ray scattering cross-section allows nematicity dynamics associated with the planar O 2[Formula: see text] and Cu 3[Formula: see text] states to be distinguished from the response of anisotropic lattice distortions. A direct time-domain comparison of CDW translational-symmetry breaking and nematic rotational-symmetry breaking reveals that these broken symmetries remain closely linked in the photoexcited state, consistent with the stability of CDW topological defects in the investigated pump fluence regime.

Real-space visualization of a defect-mediated charge density wave transition.

We study the coupled charge density wave (CDW) and insulator-to-metal transitions in the 2D quantum material 1T-TaS2. By applying in situ cryogenic 4D scanning transmission electron microscopy with in situ electrical resistance measurements, we directly visualize the CDW transition and establish that the transition is mediated by basal dislocations (stacking solitons). We find that dislocations can both nucleate and pin the transition and locally alter the transition temperature Tc by nearly ~75 K. This finding was enabled by the application of unsupervised machine learning to cluster five-dimensional, terabyte scale datasets, which demonstrate a one-to-one correlation between resistance-a global property-and local CDW domain-dislocation dynamics, thereby linking the material microstructure to device properties. This work represents a major step toward defect-engineering of quantum materials, which will become increasingly important as we aim to utilize such materials in real devices.

Direct observation of the collective modes of the charge density wave in the kagome metal CsV3Sb5.

A recently discovered group of kagome metals AV[Formula: see text]Sb[Formula: see text] (A = K, Rb, Cs) exhibit a variety of intertwined unconventional electronic phases, which emerge from a puzzling charge density wave phase. Understanding of this charge-ordered parent phase is crucial for deciphering the entire phase diagram. However, the mechanism of the charge density wave is still controversial, and its primary source of fluctuations-the collective modes-has not been experimentally observed. Here, we use ultrashort laser pulses to melt the charge order in CsV[Formula: see text]Sb[Formula: see text] and record the resulting dynamics using femtosecond angle-resolved photoemission. We resolve the melting time of the charge order and directly observe its amplitude mode, imposing a fundamental limit for the fastest possible lattice rearrangement time. These observations together with ab initio calculations provide clear evidence for a structural rather than electronic mechanism of the charge density wave. Our findings pave the way for a better understanding of the unconventional phases hosted on the kagome lattice.

Porous lanthanide metal-organic frameworks with metallic conductivity.

Metallic charge transport and porosity appear almost mutually exclusive. Whereas metals demand large numbers of free carriers and must have minimal impurities and lattice vibrations to avoid charge scattering, the voids in porous materials limit the carrier concentration, provide ample space for impurities, and create more charge-scattering vibrations due to the size and flexibility of the lattice. No microporous material has been conclusively shown to behave as a metal. Here, we demonstrate that single crystals of the porous metal-organic framework Ln1.5(2,3,6,7,10,11-hexaoxytriphenylene) (Ln = La, Nd) are metallic. The materials display the highest room-temperature conductivities of all porous materials, reaching values above 1,000 S/cm. Single crystals of the compounds additionally show clear temperature-deactivated charge transport, a hallmark of a metallic material. Lastly, a structural transition consistent with charge density wave ordering, present only in metals and rare in any materials, provides additional conclusive proof of the metallic nature of the materials. Our results provide an example of a metal with porosity intrinsic to its structure. We anticipate that the combination of porosity and chemical tunability that these materials possess will provide a unique handle toward controlling the unconventional states that lie within them, such as charge density waves that we observed, or perhaps superconductivity.

Unconventional Charge-Density-Wave Gap in Monolayer NbS2.

Using scanning tunneling microscopy and spectroscopy, for a monolayer of transition metal dichalcogenide H-NbS2 grown by molecular beam epitaxy on graphene, we provide unambiguous evidence for a charge density wave (CDW) with a 3 × 3 superstructure, which is not present in bulk NbS2. Local spectroscopy displays a pronounced gap on the order of 20 meV at the Fermi level. Within the gap, low-energy features are present. The gap structure with its low-energy features is at variance with the expectation for a gap opening in the electronic band structure due to a CDW. Instead, comparison with ab initio calculations indicates that the observed gap structure must be attributed to combined electron-phonon quasiparticles. The phonons in question are the elusive amplitude and phase collective modes of the CDW transition. Our findings advance the understanding of CDW mechanisms in 2D materials and their spectroscopic signatures.

Unconventional Spectral Gaps Induced by Charge Density Waves in the Weyl Semimetal (TaSe4)2I.

Coupling Weyl quasiparticles and charge density waves (CDWs) can lead to fascinating band renormalization and many-body effects beyond band folding and Peierls gaps. For the quasi-one-dimensional chiral compound (TaSe4)2I with an incommensurate CDW transition at TC = 263 K, photoemission mappings thus far are intriguing due to suppressed emission near the Fermi level. Models for this unconventional behavior include axion insulator phases, correlation pseudogaps, polaron subbands, bipolaron bound states, etc. Our photoemission measurements show sharp quasiparticle bands crossing the Fermi level at T > TC, but for T < TC, these bands retain their dispersions with no Peierls or axion gaps at the Weyl points. Instead, occupied band edges recede from the Fermi level, opening a spectral gap. Our results confirm localization of quasiparticles (holes created by photoemission) is the key physics, which suppresses spectral weights over an energy window governed by incommensurate modulation and inherent phase defects of CDW.

Engineering Charge Density Waves by Stackingtronics in Tantalum Disulfide.

In the realm of condensed matter physics and materials science, charge density waves (CDWs) have emerged as a captivating way to modulate correlated electronic phases and electron oscillations in quantum materials. However, collectively and efficiently tuning CDW order is a formidable challenge. Herein, we introduced a novel way to modulate the CDW order in 1T-TaS2 via stacking engineering. By introducing shear strain during the electrochemical exfoliation, the thermodynamically stable AA-stacked TaS2 consecutively transform into metastable ABC stacking, resulting in unique 3a × 1a CDW order. By decoupling atom coordinates, we atomically deciphered the 3D subtle structural variations in trilayer samples. As suggested by density functional theory (DFT) calculations, the origin of CDWs is presumably due to collective excitations and charge modulation. Therefore, our works shed light on a new avenue to collectively modulate the CDW order via stackingtronics and unveiled novel mechanisms for triggering CDW formation via charge modulation.

Temperature-Driven Rotation Symmetry-Breaking States in an Atomic Kagome Metal KV3Sb5.

Kagome lattice AV3Sb5 has attracted tremendous interest because it hosts correlated and topological physics. However, an in-depth understanding of the temperature-driven electronic states in AV3Sb5 is elusive. Here we use scanning tunneling microscopy to directly capture the rotational symmetry-breaking effect in KV3Sb5. Through both topography and spectroscopic imaging of defect-free KV3Sb5, we observe a charge density wave (CDW) phase transition from an a0 × a0 atomic lattice to a robust 2a0 × 2a0 superlattice upon cooling the sample to 60 K. An individual Sb-atom vacancy in KV3Sb5 further gives rise to the local Friedel oscillation (FO), visible as periodic charge modulations in spectroscopic maps. The rotational symmetry of the FO tends to break at the temperature lower than 40 K. Moreover, the FO intensity shows an obvious competition against the intensity of the CDW. Our results reveal a tantalizing electronic nematicity in KV3Sb5, highlighting the multiorbital correlation in the kagome lattice framework.

Controlling the Charge Density Wave Transition in Single-Layer TiTe2xSe2(1-x) Alloys by Band Gap Engineering.

Closing the band gap of a semiconductor into a semimetallic state gives a powerful potential route to tune the electronic energy gains that drive collective phases like charge density waves (CDWs) and excitonic insulator states. We explore this approach for the controversial CDW material monolayer (ML) TiSe2 by engineering its narrow band gap to the semimetallic limit of ML-TiTe2. Using molecular beam epitaxy, we demonstrate the growth of ML-TiTe2xSe2(1-x) alloys across the entire compositional range and unveil how the (2 × 2) CDW instability evolves through the normal state semiconductor-semimetal transition via in situ angle-resolved photoemission spectroscopy. Through model electronic structure calculations, we identify how this tunes the relative strength of excitonic and Peierls-like coupling, demonstrating band gap engineering as a powerful method for controlling the microscopic mechanisms underpinning the formation of collective states in two-dimensional materials.

Double Superconducting Dome of Quasi Two-Dimensional TaS2 in Non-Centrosymmetric van der Waals Heterostructure.

Two-dimensional van der Waals heterostructures (2D-vdWHs) based on transition metal dichalcogenides (TMDs) provide unparalleled control over electronic properties. However, the interlayer coupling is challenged by the interfacial misalignment and defects, which hinders a comprehensive understanding of the intertwined electronic orders, especially superconductivity and charge density wave (CDW). Here, by using pressure to regulate the interlayer coupling of non-centrosymmetric 6R-TaS2 vdWHs, we observe an unprecedented phase diagram in TMDs. This phase diagram encompasses successive suppression of the original CDW states from alternating H-layer and T-layer configurations, the emergence and disappearance of a new CDW-like state, and a double superconducting dome induced by different interlayer coupling effects. These results not only illuminate the crucial role of interlayer coupling in shaping the complex phase diagram of TMD systems but also pave a new avenue for the creation of a novel family of bulk heterostructures with customized 2D properties.

Spatially Extended Charge Density Wave Switching by Nanoscale Local Manipulation in a VTe2 Monolayer.

Monolayer transition metal dichalcogenide VTe2 exhibits multiple charge density wave (CDW) phases, mainly (4 × 4) and (4 × 1). Here we report facile dynamic and tens-of-nanometer scale switching between these CDW phases with gentle bias pulses in scanning tunneling microscopy. Bias pulses purposely stimulate a reversible random CDW symmetry change between the isotropic (4 × 4) and anisotropic (4 × 1) CDWs, as well as CDW phase slips and rotation. The switching threshold of ∼1.0 V is independent of bias polarity, and the switching rate varies linearly with the tunneling current. Density functional theory calculations indicate that a coherent CDW phase switching incurs an energy barrier of ∼2.0-3.0 eV per (4 × 4) unit cell. While there is a challenge in understanding the observed large-area CDW random fluttering, we provide some possible explanations. The ability to manipulate electronic CDW phases sheds new light on tailoring CDW properties on demand.

Intercalating Architecture for the Design of Charge Density Wave in Metallic MA2Z4 Materials.

We present a novel approach to induce charge density waves (CDWs) in metallic MA2Z4 materials, resembling the behavior observed in transition metal dichalcogenides (TMDCs). This method leverages the intercalating architecture to maintain the same crystal field and Fermi surface topologies. Our investigation reveals that CDW instability in these materials arises from electron-phonon coupling (EPC) between the d band and longitudinal acoustic (LA) phonons, mirroring TMDC's behavior. By combining α-MA2Z4 with 1H-MX2 materials in a predictive CDW phase diagram using critical EPC constants, we demonstrate the feasibility of extending CDW across material families with comparable crystal fields and reveal the crucial role in CDW instability of the competition between ionic charge transfer and electron correlation. We further uncover a strain-induced Mott transition in ß2-NbGe2N4 monolayer featuring star-of-David patterns. This work highlights the potential of intercalating architecture to engineer CDW materials, expanding our understanding of CDW instability and correlation physics.

Charge density waves in two-dimensional transition metal dichalcogenides.

Charge density wave (CDW is one of the most ubiquitous electronic orders in quantum materials. While the essential ingredients of CDW order have been extensively studied, a comprehensive microscopic understanding is yet to be reached. Recent research efforts on the CDW phenomena in two-dimensional (2D) materials provide a new pathway toward a deeper understanding of its complexity. This review provides an overview of the CDW orders in 2D with atomically thin transition metal dichalcogenides (TMDCs) as the materials platform. We mainly focus on the electronic structure investigations on the epitaxially grown TMDC samples with angle-resolved photoemission spectroscopy and scanning tunneling microscopy/spectroscopy as complementary experimental tools. We discuss the possible origins of the 2D CDW, novel quantum states coexisting with them, and exotic types of charge orders that can only be realized in the 2D limit.

Non-Fermi liquid behavior below the Néel temperature in the frustrated heavy fermion magnet UAu2.

The term Fermi liquid is almost synonymous with the metallic state. The association is known to break down at quantum critical points (QCPs), but these require precise values of tuning parameters, such as pressure and applied magnetic field, to exactly suppress a continuous phase transition temperature to the absolute zero. Three-dimensional non-Fermi liquid states, apart from superconductivity, that are unshackled from a QCP are much rarer and are not currently well understood. Here, we report that the triangular lattice system uranium diauride (UAu2) forms such a state with a non-Fermi liquid low-temperature heat capacity [Formula: see text] and electrical resistivity [Formula: see text] far below its Néel temperature. The magnetic order itself has a novel structure and is accompanied by weak charge modulation that is not simply due to magnetostriction. The charge modulation continues to grow in amplitude with decreasing temperature, suggesting that charge degrees of freedom play an important role in the non-Fermi liquid behavior. In contrast with QCPs, the heat capacity and resistivity we find are unusually resilient in magnetic field. Our results suggest that a combination of magnetic frustration and Kondo physics may result in the emergence of this novel state.

Modulating Charge-Density Wave Order and Superconductivity from Two Alternative Stacked Monolayers in a Bulk 4Hb-TaSe2 Heterostructure via Pressure.

Two-dimensional (2D) van der Waals heterostructures (VDWHs) containing a charge-density wave (CDW) and superconductivity (SC) have revealed rich tunability in their properties, which provide a new route for optimizing their novel exotic states. The interaction between SC and CDW is critical to its properties; however, understanding this interaction within VDWHs is very limited. A comprehensive in situ study and theoretical calculation on bulk 4Hb-TaSe2 VDWHs consisting of alternately stacking 1T-TaSe2 and 1H-TaSe2 monolayers are investigated under high pressure. Surprisingly, the superconductivity competes with the intralayer and adjacent-layer CDW order in 4Hb-TaSe2, which results in substantially and continually boosted superconductivity under compression. Upon total suppression of the CDW, the superconductivity in the individual layers responds differently to the charge transfer. Our results provide an excellent method to efficiently tune the interplay between SC and CDW in VDWHs and a new avenue for designing materials with tailored properties.

Chiral Charge Density Wave and Backscattering-Immune Orbital Texture in Monolayer 1T-TiTe2.

Nontrivial electronic states are attracting intense attention in low-dimensional physics. Though chirality has been identified in charge states with a scalar order parameter, its intertwining with charge density waves (CDW), film thickness, and the impact on the electronic behaviors remain less well understood. Here, using scanning tunneling microscopy, we report a 2 × 2 chiral CDW as well as a strong suppression of the Te-5p hole-band backscattering in monolayer 1T-TiTe2. These exotic characters vanish in bilayer TiTe2 in a non-CDW state. Theoretical calculations prove that chirality comes from a helical stacking of the triple-q CDW components and, therefore, can persist at the two-dimensional limit. Furthermore, the chirality renders the Te-5p bands with an unconventional orbital texture that prohibits electron backscattering. Our study establishes TiTe2 as a promising playground for manipulating the chiral ground states at the monolayer limit and provides a novel path to engineer electronic properties from an orbital degree.

Large-Area Epitaxial Mott Insulating 1T-TaSe2 Monolayer on GaP(111)B.

Two-dimensional Mott materials have recently been reported in the dichalcogenide family with high potential for Mottronic applications. Nevertheless, their widespread use as a single or few layers is hampered by their limited device integration resulting from their growth on graphene, a metallic substrate. Here, we report on the fabrication of 1T-TaSe2 monolayers grown by molecular beam epitaxy on semiconducting gallium phosphide substrates. At the nanoscale, the charge density wave reconstruction and a moiré pattern resulting from the monolayer interaction with the substrate are observed by scanning tunneling microscopy. The fully open gap unveiled by tunneling spectroscopy, which can be further manipulated by the proximity of a metal tip, is confirmed by transport measurements from micrometric to millimetric scales, demonstrating a robust Mott insulating phase at up to 400 K.

Optically Induced Symmetry Breaking Due to Nonequilibrium Steady State Formation in Charge Density Wave Material 1T-TiSe2.

The strongly correlated charge density wave (CDW) phase of 1T-TiSe2 is of interest to verify the claims of a chiral order parameter. Characterization of the symmetries of 1T-TiSe2 is critical to understand the origin of its intriguing properties. Here we use very low-power, continuous wave laser excitation to probe the symmetries of 1T-TiSe2 by using the circular photogalvanic effect. We observe that the ground state of the CDW phase (D3d) is achiral. However, laser excitation above a threshold intensity transforms 1T-TiSe2 into a nonequilibrium chiral phase (C3), which changes the electronic correlations in the material. The inherent sensitivity of the photogalvanic technique to structural symmetries provides evidence of the different optically driven phase of 1T-TiSe2, which allows us to assign symmetry groups to these states. Our work demonstrates that optically induced phase change can occur at extremely low optical intensities in strongly correlated materials, providing a pathway to engineer new phases using light.

Influence of Light Atoms on Quantification of Atomic Column Positions in Distorted Perovskites with HAADF-STEM.

Measurement of picometer-scale atomic displacements by aberration-corrected STEM has become invaluable in the study of crystalline materials, where it can elucidate ordering mechanisms and local heterogeneities. HAADF-STEM imaging, often used for such measurements due to its atomic number contrast, is generally considered insensitive to light atoms such as oxygen. Light atoms, however, still affect the propagation of the electron beam in the sample and, therefore, the collected signal. Here, we demonstrate experimentally and through simulations that cation sites in distorted perovskites can appear to be displaced by several picometers from their true positions in shared cation-anion columns. The effect can be decreased through careful choice of sample thickness and beam voltage or can be entirely avoided if the experiment allows reorientation of the crystal along a more favorable zone axis. Therefore, it is crucial to consider the possible effects of light atoms and crystal symmetry and orientation when measuring atomic positions.

Real-Space Observation of Unidirectional Charge Density Wave and Complex Structural Modulation in the Pnictide Superconductor Ba1-xSrxNi2As2.

Here we use low-temperature and variable-temperature scanning tunneling microscopy to study the pnictide superconductor, Ba1-xSrxNi2As2. In the low-temperature phase (triclinic phase) of BaNi2As2, we observe the unidirectional charge density wave (CDW) with Q = 1/3 on both the Ba and NiAs surfaces. On the NiAs surface of the triclinic BaNi2As2, there are structural-modulation-induced chain-like superstructures with distinct periodicities. In the high-temperature phase (tetragonal phase) of BaNi2As2, the NiAs surface appears as the periodic 1 × 2 superstructure. Interestingly, in the triclinic phase of Ba0.5Sr0.5Ni2As2, the unidirectional CDW is suppressed on both the Ba/Sr and NiAs surfaces, and the Sr substitution stabilizes the periodic 1 × 2 superstructure on the NiAs surface, which enhance the superconductivity in Ba0.5Sr0.5Ni2As2. Our results provide important microscopic insights for the interplay among the unidirectional CDW, structural modulation, and superconductivity in this class of pnictide superconductors.