Fast electronic resistance switching involving hidden charge density wave states

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.

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.

Resolving length-scale-dependent transient disorder through an ultrafast phase transition

Material functionality can be strongly determined by structure extending only over nanoscale distances. The pair distribution function presents an opportunity for structural studies beyond idealized crystal models and to investigate structure over varying length scales. Applying this method with ultrafast time resolution has the potential to similarly disrupt the study of structural dynamics and phase transitions. Here we demonstrate such a measurement of CuIr2S4 optically pumped from its low-temperature Ir-dimerized phase. Dimers are optically suppressed without spatial correlation, generating a structure whose level of disorder strongly depends on the length scale. The redevelopment of structural ordering over tens of picoseconds is directly tracked over both space and time as a transient state is approached. This measurement demonstrates the crucial role of local structure and disorder in non-equilibrium processes as well as the feasibility of accessing this information with state-of-the-art XFEL facilities.

Non-equilibrium quantum domain reconfiguration dynamics in a two-dimensional electronic crystal and a quantum annealer

Relaxation dynamics of complex many-body quantum systems trapped into metastable states is a very active field of research from both the theoretical and experimental point of view with implications in a wide array of topics from macroscopic quantum tunnelling and nucleosynthesis to non-equilibrium superconductivity and energy-efficient memory devices. In this work, we investigate quantum domain reconfiguration dynamics in the electronic superlattice of a quantum material using time-resolved scanning tunneling microscopy and unveil a crossover from temperature to noisy quantum fluctuation dominated dynamics. The process is modeled using a programmable superconducting quantum annealer in which qubit interconnections correspond directly to the microscopic interactions between electrons in the quantum material. Crucially, the dynamics of both the experiment and quantum simulation is driven by spectrally similar pink noise. We find that the simulations reproduce the emergent time evolution and temperature dependence of the experimentally observed electronic domain dynamics.

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.

Three-dimensional ultrafast charge-density-wave dynamics in CuTe

Charge density waves (CDWs) involved with electronic and phononic subsystems simultaneously are a common quantum state in solid-state physics, especially in low-dimensional materials. However, CDW phase dynamics in various dimensions are yet to be studied, and their phase transition mechanism is currently moot. Here we show that using the distinct temperature evolution of orientation-dependent ultrafast electron and phonon dynamics, different dimensional CDW phases are verified in CuTe. When the temperature decreases, the shrinking of c-axis length accompanied with the appearance of interchain and interlayer interactions causes the quantum fluctuations (QF) of the CDW phase until 220 K. At T < 220 K, the CDWs on the different ab-planes are finally locked with each other in anti-phase to form a CDW phase along the c-axis. This study shows the dimension evolution of CDW phases in one CDW system and their stabilized mechanisms in different temperature regimes.

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.

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.

Encoding multistate charge order and chirality in endotaxial heterostructures

High-density phase change memory (PCM) storage is proposed for materials with multiple intermediate resistance states, which have been observed in 1T-TaS2 due to charge density wave (CDW) phase transitions. However, the metastability responsible for this behavior makes the presence of multistate switching unpredictable in TaS2 devices. Here, we demonstrate the fabrication of nanothick verti-lateral H-TaS2/1T-TaS2 heterostructures in which the number of endotaxial metallic H-TaS2 monolayers dictates the number of resistance transitions in 1T-TaS2 lamellae near room temperature. Further, we also observe optically active heterochirality in the CDW superlattice structure, which is modulated in concert with the resistivity steps, and we show how strain engineering can be used to nucleate these polytype conversions. This work positions the principle of endotaxial heterostructures as a promising conceptual framework for reliable, non-volatile, and multi-level switching of structure, chirality, and resistance.

Electrical switching of ferro-rotational order in nanometre-thick 1T-TaS2 crystals

Hysteretic switching of domain states is a salient characteristic of all ferroic materials and the foundation for their multifunctional applications. Ferro-rotational order is emerging as a type of ferroic order that features structural rotations, but control over state switching remains elusive due to its invariance under both time reversal and spatial inversion. Here we demonstrate electrical switching of ferro-rotational domain states in the charge-density-wave phases of nanometre-thick 1T-TaS2 crystals. Cooling from the high-symmetry phase to the ferro-rotational phase under an external electric field induces domain state switching and domain wall formation, which is realized in a simple two-terminal configuration using a volt-scale bias. Although the electric field does not couple with the order due to symmetry mismatch, it drives domain wall propagation to give rise to reversible, durable and non-volatile isothermal state switching at room temperature. These results offer a route to the manipulation of ferro-rotational order and its nanoelectronic applications.

Controllable Synthesis and Charge Density Wave Phase Transitions of Two-Dimensional 1T-TaS2 Crystals

1T-TaS₂ has attracted much attention recently due to its abundant charge density wave phases. In this work, high-quality two-dimensional 1T-TaS₂ crystals were successfully synthesized by a chemical vapor deposition method with controllable layer numbers, confirmed by the structural characterization. Based on the as-grown samples, their thickness-dependency nearly commensurate charge density wave/commensurate charge density wave phase transitions was revealed by the combination of the temperature-dependent resistance measurements and Raman spectra. The phase transition temperature increased with increasing thickness, but no apparent phase transition was found on the 2~3 nm thick crystals from temperature-dependent Raman spectra. The transition hysteresis loops due to temperature-dependent resistance changes of 1T-TaS₂ can be used for memory devices and oscillators, making 1T-TaS₂ a promising material for various electronic applications.

Quantum Composites with Charge-Density-Wave Fillers

A unique class of advanced materials-quantum composites based on polymers with fillers composed of a van der Waals quantum material that reveals multiple charge-density-wave quantum condensate phases-is demonstrated. Materials that exhibit quantum phenomena are typically crystalline, pure, and have few defects because disorder destroys the coherence of the electrons and phonons, leading to collapse of the quantum states. The macroscopic charge-density-wave phases of filler particles after multiple composite processing steps are successfully preserved in this work. The prepared composites display strong charge-density-wave phenomena even above room temperature. The dielectric constant experiences more than two orders of magnitude enhancement while the material maintains its electrically insulating properties, opening a venue for advanced applications in energy storage and electronics. The results present a conceptually different approach for engineering the properties of materials, extending the application domain for van der Waals materials.

Spectroscopic visualization and phase manipulation of chiral charge density waves in 1T-TaS2

The chiral charge density wave is a many-body collective phenomenon in condensed matter that may play a role in unconventional superconductivity and topological physics. Two-dimensional chiral charge density waves provide the building blocks for the fabrication of various stacking structures and chiral homostructures, in which physical properties such as chiral currents and the anomalous Hall effect may emerge. Here, we demonstrate the phase manipulation of two-dimensional chiral charge density waves and the design of in-plane chiral homostructures in 1T-TaS₂. We use chiral Raman spectroscopy to directly monitor the chirality switching of the charge density wave-revealing a temperature-mediated reversible chirality switching. We find that interlayer stacking favours homochirality configurations, which is confirmed by first-principles calculations. By exploiting the interlayer chirality-locking effect, we realise in-plane chiral homostructures in 1T-TaS₂. Our results provide a versatile way to manipulate chiral collective phases by interlayer coupling in layered van der Waals semiconductors.

Unveiling Electronic Behaviors in Heterochiral Charge-Density-Wave Twisted Stacking Materials with 1.25 nm Unit Dependence

Layered charge-density-wave (CDW) materials have gained increasing interest due to their CDW stacking-dependent electronic properties for practical applications. Among the large family of CDW materials, those with star of David (SOD) patterns are very important due to the potentials for quantum spin liquid and related device applications. However, the spatial extension and the spin coupling information down to the nanoscale remain elusive. Here, we report the study of heterochiral CDW stackings in bilayer (BL) NbSe₂ with high spatial resolution. We reveal that there exist well-defined heterochiral stackings, which have inhomogeneous electronic states among neighboring CDW units (star of David, SOD), significantly different from the homogeneous electronic states in the homochiral stackings. Intriguingly, the different electronic behaviors are spatially localized within each SOD with a unit size of 1.25 nm, and the gap sizes are determined by the different types of SOD stackings. Density functional theory (DFT) calculations match the experimental measurements well and reveal the SOD-stacking-dependent correlated electronic states and antiferromagnetic/ferromagnetic couplings. Our findings give a deep understanding of the spatial distribution of interlayer stacking and the delicate modulation of the spintronic states, which is very helpful for CDW-based nanoelectronic devices.

Electrical Gating of the Charge-Density-Wave Phases in Two-Dimensional h-BN/1T-TaS2 Devices

We report on the electrical gating of the charge-density-wave phases and current in h-BN-capped three-terminal 1T-TaS₂ heterostructure devices. It is demonstrated that the application of a gate bias can shift the source-drain current-voltage hysteresis associated with the transition between the nearly commensurate and incommensurate charge-density-wave phases. The evolution of the hysteresis and the presence of abrupt spikes in the current while sweeping the gate voltage suggest that the effect is electrical rather than self-heating. We attribute the gating to an electric-field effect on the commensurate charge-density-wave domains in the atomic planes near the gate dielectric. The transition between the nearly commensurate and incommensurate charge-density-wave phases can be induced by both the source-drain current and the electrostatic gate. Since the charge-density-wave phases are persistent in 1T-TaS₂ at room temperature, one can envision memory applications of such devices when scaled down to the dimensions of individual commensurate domains and few-atomic plane thicknesses.

Atomic-scale thermopower in charge density wave states

The microscopic origins of thermopower have been investigated to design efficient thermoelectric devices, but strongly correlated quantum states such as charge density waves and Mott insulating phase remain to be explored for atomic-scale thermopower engineering. Here, we report on thermopower and phonon puddles in the charge density wave states in 1T-TaS₂, probed by scanning thermoelectric microscopy. The Star-of-David clusters of atoms in 1T-TaS₂ exhibit counterintuitive variations in thermopower with broken three-fold symmetry at the atomic scale, originating from the localized nature of valence electrons and their interlayer coupling in the Mott insulating charge density waves phase of 1T-TaS₂. Additionally, phonon puddles are observed with a spatial range shorter than the conventional mean free path of phonons, revealing the phonon propagation and scattering in the subsurface structures of 1T-TaS₂.

Snapshots of a light-induced metastable hidden phase driven by the collapse of charge order

Nonequilibrium hidden states provide a unique window into thermally inaccessible regimes of strong coupling between microscopic degrees of freedom in quantum materials. Understanding the origin of these states allows the exploration of far-from-equilibrium thermodynamics and the development of optoelectronic devices with on-demand photoresponses. However, mapping the ultrafast formation of a long-lived hidden phase remains a longstanding challenge since the initial state is not recovered rapidly. Here, using state-of-the-art single-shot spectroscopy techniques, we present a direct ultrafast visualization of the photoinduced phase transition to both transient and long-lived hidden states in an electronic crystal, 1T-TaS₂, and demonstrate a commonality in their microscopic pathways, driven by the collapse of charge order. We present a theory of fluctuation-dominated process that helps explain the nature of the metastable state. Our results shed light on the origin of this elusive state and pave the way for the discovery of other exotic phases of matter.

Mott versus Hybridization Gap in the Low-Temperature Phase of 1T-TaS_{2}

We address the long-standing problem of the ground state of 1T-TaS_{2} by computing the correlated electronic structure of stacked bilayers using the GW+EDMFT method. Depending on the surface termination, the semi-infinite uncorrelated system is either band insulating or exhibits a metallic surface state. For realistic values of the on-site and inter-site interactions, a Mott gap opens in the surface state, but it is smaller than the gap originating from the bilayer structure. Our results are consistent with recent scanning tunneling spectroscopy measurements for different terminating layers, and with our own photoemission measurements, which indicate the coexistence of spatial regions with different gaps in the electronic spectrum. By comparison to exact diagonalization data, we clarify the interplay between Mott insulating and band insulating behavior in this archetypal layered system.

Charge Configuration Memory Devices: Energy Efficiency and Switching Speed

Current trends in data processing have given impetus for an intense search of new concepts of memory devices with emphasis on efficiency, speed, and scalability. A promising new approach to memory storage is based on resistance switching between charge-ordered domain states in the layered dichalcogenide 1T-TaS2. Here we investigate the energy efficiency scaling of such charge configuration memory (CCM) devices as a function of device size and data write time τW as well as other parameters that have bearing on efficient device operation. We find that switching energy efficiency scales approximately linearly with both quantities over multiple decades, departing from linearity only when τW approaches the ∼0.5 ps intrinsic switching limit. Compared to current state of the art memory devices, CCM devices are found to be much faster and significantly more energy efficient, demonstrated here with two-terminal switching using 2.2 fJ, 16 ps electrical pulses.

Electronic Dislocation Dynamics in Metastable Wigner Crystal States

Metastable states appear in many areas of physics as a result of symmetry-breaking phase transitions. An important challenge is to understand the microscopic mechanisms which lead to the formation of the energy barrier separating a metastable state from the ground state. In this paper, we describe an experimental example of the hidden metastable domain state in 1T-TaS2, created by photoexcitation or carrier injection. The system is an example of a charge density wave superlattice in the Wigner crystal limit displaying discommensurations and domain formation when additional charge is injected either through contacts or by photoexcitation. The domain walls and their crossings in particular display interesting, topologically entangled structures, which have a crucial role in the metastability of the system. We model the properties of experimentally observed thermally activated dynamics of topologically protected defects—dislocations—whose annihilation dynamics can be observed experimentally by scanning tunnelling microscopy as emergent phenomena described by a doped Wigner crystal. The different dynamics of trivial and non-trivial topological defects are quite striking. Trivial defects appear to annihilate quite rapidly at low temperatures on the timescale of the experiments, while non-trivial defects annihilate rarely, if at all.

Observation and Manipulation of a Phase Separated State in a Charge Density Wave Material

The 1T polytype of TaS₂ has been studied extensively as a strongly correlated system. As 1T-TaS₂ is thinned toward the 2D limit, its phase diagram shows significant deviations from that of the bulk material. Optoelectronic maps of ultrathin 1T-TaS₂ have indicated the presence of nonequilibrium charge density wave phases within the hysteresis region of the nearly commensurate (NC) to commensurate (C) transition. We perform scanning tunneling microscopy on exfoliated ultrathin flakes of 1T-TaS₂ within the NC-C hysteresis window, finding evidence that the observed nonequilibrium phases consist of intertwined, irregularly shaped NC-like and C-like domains. After applying lateral electrical signals to the sample, we image changes in the geometric arrangement of the different regions. We use a phase separation model to explore the relationship between electronic inhomogeneity present in ultrathin 1T-TaS₂ and its bulk resistivity. These results demonstrate the role of phase competition morphologies in determining the properties of 2D materials.

Size Dependence of Charge-Density-Wave Orders in Single-Layer NbSe2 Hetero/Homophase Junctions

Controlling charge-density-wave (CDW) orders in two-dimensional (2D) crystals has attracted a great deal of interest because of their fundamental physics and their demand inse in miniaturized devices. In this work, we systematically studied the size-dependent CDW orders in single-layer hetero/homo-NbSe₂ stacking junctions. We found that the CDW orders in the top 1T-NbSe₂ layer of the junctions are highly dependent on its lateral size. For the 1T/2H-NbSe₂ heterojunction, the critical lateral size of 1T-NbSe₂ islands for the formation of well-defined CDW orders is ∼26 nm, whereas below 15 nm, the CDW orders melt. However, for the 1T/1T-NbSe₂ homojunction, the CDW orders in the islands can persist even with a lateral size of <11 nm. Our findings illuminate the fresh phenomenon of size-dependent CDW orders existing in 2D van der Waals hetero/homojunctions and provide useful information for the control of CDW orders.

Two-dimensional charge order stabilized in clean polytype heterostructures

Compelling evidence suggests distinct correlated electron behavior may exist only in clean 2D materials such as 1T-TaS2. Unfortunately, experiment and theory suggest that extrinsic disorder in free standing 2D layers disrupts correlation-driven quantum behavior. Here we demonstrate a route to realizing fragile 2D quantum states through endotaxial polytype engineering of van der Waals materials. The true isolation of 2D charge density waves (CDWs) between metallic layers stabilizes commensurate long-range order and lifts the coupling between neighboring CDW layers to restore mirror symmetries via interlayer CDW twinning. The twinned-commensurate charge density wave (tC-CDW) reported herein has a single metal-insulator phase transition at ~350 K as measured structurally and electronically. Fast in-situ transmission electron microscopy and scanned nanobeam diffraction map the formation of tC-CDWs. This work introduces endotaxial polytype engineering of van der Waals materials to access latent 2D ground states distinct from conventional 2D fabrication.

Engineering Domain Wall Electronic States in Strongly Correlated van der Waals Material of 1T-TaS2

Although a few physical methods were demonstrated for domain wall engineering in various electronic or ferroic materials with broken discrete symmetries, the direct control over the electronic properties of individual domain walls has been extremely limited. Here, we introduce a chemical method to tune the electronic property of domain walls in 1T tantalum disulfide. By using scanning tunneling microscopy and spectroscopy techniques, we find that indium adatoms on 1T-TaS₂ have distinct behaviors on the domains with different bulk terminations. Moreover, the adatoms form their own chains along the edges of neighboring domains. The density functional theory calculations reveal a 1D Mott insulating state on a modified domain wall, resulting from the degenerated spin-polarized bands with electron doping from adsorbates and charge transfer from neighboring domains. This work suggests that chemical decoration by adsorbates can be widely used to tune local electronic states of domain walls and various 2D materials.

Exploring the growth and oxidation of 2D-TaS2on Cu(111)

In this work, the growth and stability towards O₂exposure of two dimensional (2D) TaS₂on a Cu(111) substrate is investigated. Large area (∼1 cm²) crystalline 2D-TaS₂films with a metallic character are prepared on a single crystal Cu(111) substrate via a multistep approach based on physical vapor deposition. Analytical techniques such as Auger electron spectroscopy, low energy electron diffraction, and photoemission spectroscopy are used to characterize the composition, crystallinity, and electronic structure of the surface. At coverages below one monolayer equivalent (ML), misoriented TaS₂domains are formed, which are rotated up to±13orelative to the Cu(111) crystallographic directions. The TaS₂domains misorientation decreases as the film thickness approaches 1 ML, at which the crystallographic directions of TaS₂and Cu(111) are aligned. The TaS₂film is found to grow epitaxially on Cu(111). As revealed by low energy electron diffraction in conjunction with an atomic model simulation, the (3 × 3) unit cells of TaS₂match the (4 × 4) supercell of Cu(111). Furthermore, the exposure of TaS₂to O₂, does not lead to the formation of a robust tantalum oxide film, only minor amounts of stable oxides being detected on the surface. Instead, the exposure of TaS₂films to O₂leads predominantly to a reduction of the film thickness, evidenced by a decrease in the content of both Ta and S atoms of the film. This is attributed to the formation of oxide species that are unstable and mainly desorb from the surface below room temperature. Temperature programmed desorption spectroscopy confirms the formation of SO₂, which desorbs from the surface between 100 and500 K.These results provide new insights into the oxidative degradation of 2D-TaS₂on Cu(111).

Micromask Lithography for Cheap and Fast 2D Materials Microstructures Fabrication

The fast and precise fabrication of micro-devices based on single flakes of novel 2D materials and stacked heterostructures is vital for exploration of novel functionalities. In this paper, we demonstrate a fast high-resolution contact mask lithography through a simple upgrade of metallographic optical microscope. Suggested kit for the micromask lithography is compact and easily compatible with a glove box, thus being suitable for a wide range of air-unstable materials. The shadow masks could be either ordered commercially or fabricated in a laboratory using a beam lithography. The processes of the mask alignment and the resist exposure take a few minutes and provide a micrometer resolution. With the total price of the kit components around USD 200, our approach would be convenient for laboratories with the limited access to commercial lithographic systems.

Universal phase dynamics in VO2 switches revealed by ultrafast operando diffraction

Understanding the pathways and time scales underlying electrically driven insulator-metal transitions is crucial for uncovering the fundamental limits of device operation. Using stroboscopic electron diffraction, we perform synchronized time-resolved measurements of atomic motions and electronic transport in operating vanadium dioxide (VO₂) switches. We discover an electrically triggered, isostructural state that forms transiently on microsecond time scales, which is shown by phase-field simulations to be stabilized by local heterogeneities and interfacial interactions between the equilibrium phases. This metastable phase is similar to that formed under photoexcitation within picoseconds, suggesting a universal transformation pathway. Our results establish electrical excitation as a route for uncovering nonequilibrium and metastable phases in correlated materials, opening avenues for engineering dynamical behavior in nanoelectronics.

Coherent Phonon Disruption and Lock-In during a Photoinduced Charge-Density-Wave Phase Transition

Ultrafast manipulation of phase domains in quantum materials is a promising approach to unraveling and harnessing interwoven charge and lattice degrees of freedom. Here we find evidence for coupling of displacively excited coherent acoustic phonons (CAPs) and periodic lattice distortions (PLDs) in the intensely studied charge-density-wave material, 1T-TaS₂, using 4D ultrafast electron microscopy (UEM). Initial photoinduced Bragg-peak dynamics reveal partial CAP coherence and localized c-axis dilations. Weak, partially coherent dynamics give way to higher-amplitude, increasingly coherent oscillations, the transition period of which matches that of photoinduced incommensurate domain growth and stabilization from the nearly-commensurate phase. With UEM imaging, it is found that phonon wave trains emerge from linear defects 100 ps after photoexcitation. The CAPs consist of coupled longitudinal and transverse character and propagate at anomalously high velocities along wave vectors independent from PLDs, instead being dictated by defect orientation. Such behaviors illustrate a means to control phases in quantum materials using defect-engineered coherent-phonon seeding.

Femtosecond control of phonon dynamics near a magnetic order critical point

The spin-phonon interaction in spin density wave (SDW) systems often determines the free energy landscape that drives the evolution of the system. When a passing energy flux, such as photoexcitation, drives a crystalline system far from equilibrium, the resulting lattice displacement generates transient vibrational states. Manipulating intermediate vibrational states in the vicinity of the critical point, where the SDW order parameter changes dramatically, would then allow dynamical control over functional properties. Here we combine double photoexcitation with an X-ray free-electron laser (XFEL) probe to control and detect the lifetime and magnitude of the intermediate vibrational state near the critical point of the SDW in chromium. We apply Landau theory to identify the mechanism of control as a repeated partial quench and sub picosecond recovery of the SDW. Our results showcase the capabilities to influence and monitor quantum states by combining multiple optical photoexcitations with an XFEL probe. They open new avenues for manipulating and researching the behaviour of photoexcited states in charge and spin order systems near the critical point.

Precise control of vibrational states coupled to electronic degrees of freedom could enable control over charge or magnetic order in a material. Here, the authors use a double-pulse photoexcitation combined with an X-ray probe to control vibrational states near the critical point of spin density wave in Cr films.

A time-domain phase diagram of metastable states in a charge ordered quantum material

Metastable self-organized electronic states in quantum materials are of fundamental importance, displaying emergent dynamical properties that may be used in new generations of sensors and memory devices. Such states are typically formed through phase transitions under non-equilibrium conditions and the final state is reached through processes that span a large range of timescales. Conventionally, phase diagrams of materials are thought of as static, without temporal evolution. However, many functional properties of materials arise as a result of complex temporal changes in the material occurring on different timescales. Hitherto, such properties were not considered within the context of a temporally-evolving phase diagram, even though, under non-equilibrium conditions, different phases typically evolve on different timescales. Here, by using time-resolved optical techniques and femtosecond-pulse-excited scanning tunneling microscopy (STM), we track the evolution of the metastable states in a material that has been of wide recent interest, the quasi-two-dimensional dichalcogenide 1T-TaS₂. We map out its temporal phase diagram using the photon density and temperature as control parameters on timescales ranging from 10⁻¹² to 10³ s. The introduction of a time-domain axis in the phase diagram enables us to follow the evolution of metastable emergent states created by different phase transition mechanisms on different timescales, thus enabling comparison with theoretical predictions of the phase diagram, and opening the way to understanding of the complex ordering processes in metastable materials.

Tracking the evolution of non-equilibrium phases requires measurements over a wide range of timescales. Here, using a combination of femtosecond spectroscopy and scanning tunneling microscopy, the authors map out a temporal phase diagram of metastable states in a charge-ordered material 1T-TaS₂.

Tuning Molecular Superlattice by Charge-Density-Wave Patterns in Two-Dimensional Monolayer Crystals

Charge density wave (CDW) in two-dimensional (2D) crystals plays a vital role in tuning the interface structures and properties. However, how the CDW tunes the self-assembled molecular superlattice still remains unclear. In this study, we investigated the self-assembled manganese phthalocyanine (MnPc) molecular superlattice on single-layered 1T- and 2H-NbSe₂ crystals under regulation by distinct CDW patterns. We observe that, in low coverage, MnPc molecules preferentially adsorb on 2H-NbSe₂ compared to 1T-NbSe₂. With increasing coverage, MnPc can form a highly ordered superlattice on 2H-NbSe₂; however, it is randomly distributed on 1T-NbSe₂. We reveal a perfect geometric commensurability between the molecular superlattice and intrinsic CDW pattern in 2H-NbSe₂ and a poor commensurability for that of 1T-NbSe₂. We believe that the subtly different geometric commensurability dominates the different adsorption and arrangement of the molecular superlattices on 2D CDW patterns. Our study provides a pioneering approach for tuning the molecular superlattices using the CDW patterns.

Direct identification of Mott Hubbard band pattern beyond charge density wave superlattice in monolayer 1T-NbSe2

Understanding Mott insulators and charge density waves (CDW) is critical for both fundamental physics and future device applications. However, the relationship between these two phenomena remains unclear, particularly in systems close to two-dimensional (2D) limit. In this study, we utilize scanning tunneling microscopy/spectroscopy to investigate monolayer 1T-NbSe2 to elucidate the energy of the Mott upper Hubbard band (UHB), and reveal that the spin-polarized UHB is spatially distributed away from the dz2 orbital at the center of the CDW unit. Moreover, the UHB shows a √3 × √3 R30° periodicity in addition to the typically observed CDW pattern. Furthermore, a pattern similar to the CDW order is visible deep in the Mott gap, exhibiting CDW without contribution of the Mott Hubbard band. Based on these findings in monolayer 1T-NbSe2, we provide novel insights into the relation between the correlated and collective electronic structures in monolayer 2D systems.

Ultrafast Neuromorphic Dynamics Using Hidden Phases in the Prototype of Relaxor Ferroelectrics

Materials possessing multiple states are promising to emulate synaptic and neuronic behaviors. Their operation frequency, typically in or below the GHz range, however, limits the speed of neuromorphic computing. Ultrafast THz electric field excitation has been employed to induce nonequilibrium states of matter, called hidden phases in oxides. One may wonder if there are systems for which THz pulses can generate neuronic and synaptic behavior, via the creation of hidden phases. Using atomistic simulations, we discover that relaxor ferroelectrics can emulate all the key neuronic and memristive synaptic features. Their occurrence originates from the activation of many hidden phases of polarization order, resulting from the response of nanoregions to THz pulses. Such phases further possess different dielectric constants, which is also promising for memcapacitor devices.

Chemical vapor deposition and temperature-dependent Raman characterization of two-dimensional vanadium ditelluride

Recently, ultrathin two-dimensional (2D) metallic vanadium dichalcogenides have attracted widespread attention because of the charge density wave (CDW) phase transition and possible ferromagnetism. Herein, we report the synthesis and temperature-dependent Raman characterization of the 2D vanadium ditelluride (VTe₂). The synthesis is done by atmospheric pressure chemical vapor deposition (APCVD) using vanadium chloride (VCl₃) precursor on fluorphlogopite mica, sapphire, and h-BN substrates. A large area of the thin film with thickness ∼10 nm is grown on the hexagonal boron nitride (h-BN) substrate. Temperature-dependent Raman characterization of VTe₂ is conducted from room temperature to 513 K. Remarkable changes of Raman modes at around 413 K are observed, indicating the structural phase transition.

Two-dimensional vanadium ditelluride has been synthesized on mica, sapphire, and h-BN substrates by atmospheric pressure chemical vapor deposition.

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.

Phase Transition Photodetection in Charge Density Wave Tantalum Disulfide

The charge density wave (CDW) phase is a macroscopic quantum state with periodic charge density modulation accompanied by periodic lattice distortion in low-dimensional metals. External fields, such as an electric field and optical excitation, can trigger the transitions among different CDW states, leaving an under-explored mechanism and attracting great interest toward optoelectronic applications. Here, we explore a photoinduced phase transition in 1T-TaS₂ under an electrical field. By analyzing the phase transition probability, we obtained a linear dependence of the phase transition barrier on the electric field and laser energy density. Additionally, the threshold laser energy for the phase transition decreases linearly with an increasing applied electrical field. Finally, picojoule photodetection was realized in the visible and near-infrared ranges near the CDW transition edge. Our work will promote the understanding of the CDW phase transition mechanism as well as open pathways for optoelectronic applications.

Pseudogap and Weak Multifractality in 2D Disordered Mott Charge-Density-Wave Insulator

We investigate electronic states of Se-substituted 1T-TaS₂ by scanning tunneling microscopy/spectroscopy (STM/STS), where superconductivity emerges from the unique Mott-charge-density-wave (Mott-CDW) state. Spatially resolved STS measurements reveal that a pseudogap replaces the Mott gap with the CDW gaps intact. The pseudogap has little correlation with the unit-cell-to-unit-cell variation in the local Se concentration but appears globally. The correlation length of the local density of states (LDOS) is substantially enhanced at the Fermi energy and decays rapidly at high energies. Furthermore, the statistical analysis of LDOS indicates the weak multifractal behavior of the wave functions. These findings suggest a correlated metallic state induced by disorder and provide a new insight into the emerging superconductivity in two-dimensional materials.

Charge doping induced reversible multistep structural phase transitions and electromechanical actuation in two-dimensional 1T'-MoS2

The 1T' phase of transition metal dichalcogenides (TMDs) is a low symmetry charge density wave (CDW) phase, which can be viewed as a periodically distorted structure (Peierls distortion) of the high symmetry 1T phase. In this paper, using density functional theory (DFT) calculations, we report that the positive charge (hole) injection is an effective method to modulate the Peierls distortion of MoS2 1T' for a new CDW phase and superior electromechanical properties. A new stable CDW phase is discovered at a hole doping level of 0.10 h+ per atom, named 1T't. Hole charging and discharging can induce a reversible phase transition of MoS2 among the three phases, 1T, 1T' and 1T't. Such a reversible phase transition leads to superior electromechanical properties including a strain output as high as -5.8% with a small hysteresis loop, multi-step super-elasticity, and multi-shape memory effect, which are valuable in active electromechanical device designs at the nanoscale. In-depth analysis of the change of the electronic structure under hole doping was performed to understand the new CDW phase and the observed phase transition. Using charge doping to modulate the Peierls distortion in two-dimensional materials can serve as a general concept for nano-active material designs.

Mottness versus unit-cell doubling as the driver of the insulating state in 1T-TaS2

If a material with an odd number of electrons per unit-cell is insulating, Mott localisation may be invoked as an explanation. This is widely accepted for the layered compound 1T-TaS₂, which has a low-temperature insulating phase comprising charge order clusters with 13 unpaired orbitals each. But if the stacking of layers doubles the unit-cell to include an even number of orbitals, the nature of the insulating state is ambiguous. Here, scanning tunnelling microscopy reveals two distinct terminations of the charge order in 1T-TaS₂, the sign of such a double-layer stacking pattern. However, spectroscopy at both terminations allows us to disentangle unit-cell doubling effects and determine that Mott localisation alone can drive gap formation. We also observe the collapse of Mottness at an extrinsically re-stacked termination, demonstrating that the microscopic mechanism of insulator-metal transitions lies in degrees of freedom of inter-layer stacking.

In many strongly correlated systems the coupling of electronic and lattice degrees of freedom leads to ambiguity over the mechanism driving electronic phase transitions. Here the authors show that inter-layer effects play an important role in the charge ordering transition of 1T-TaS₂.

Realization of a Metallic State in 1T-TaS_{2} with Persisting Long-Range Order of a Charge Density Wave

Metallization of 1T-TaS_{2} is generally initiated at the domain boundary of a charge density wave (CDW), at the expense of its long-range order. However, we demonstrate in this study that the metallization of 1T-TaS_{2} can be also realized without breaking the long-range CDW order upon surface alkali doping. By using scanning tunneling microscopy, we find the long-range CDW order is always persisting, and the metallization is instead associated with additional in-gap excitations. Interestingly, the in-gap excitation is near the top of the lower Hubbard band, in contrast to a conventional electron-doped Mott insulator where it is beneath the upper Hubbard band. In combination with the numerical calculations, we suggest that the appearance of the in-gap excitations near the lower Hubbard band is mainly due to the effectively reduced on-site Coulomb energy by the adsorbed alkali ions.

Potential 2D Materials with Phase Transitions: Structure, Synthesis, and Device Applications

Layered materials with phase transitions, such as charge density wave (CDW) and magnetic and dipole ordering, have potential to be exfoliated into monolayers and few-layers and then become a large and important subfamily of two-dimensional (2D) materials. Benefitting from enriched physical properties from the collective interactions, long-range ordering, and related phase transitions, as well as the atomic thickness yet having nondangling bonds on the surface, 2D phase-transition materials have vast potential for use in new-concept and functional devices. Here, potential 2D phase-transition materials with CDWs and magnetic and dipole ordering, including transition metal dichalcogenides, transition metal halides, metal thio/selenophosphates, chromium silicon/germanium tellurides, and more, are introduced. The structures and experimental phase-transition properties are summarized for the bulk materials and some of the obtained monolayers. In addition, recent experimental progress on the synthesis and measurement of monolayers, such as 1T-TaS₂ , CrI₃ , and Cr₂ Ge₂ Te₆ , is reviewed.

Emergent honeycomb network of topological excitations in correlated charge density wave

When two periodic potentials compete in materials, one may adopt the other, which straightforwardly generates topological defects. Of particular interest are domain walls in charge-, dipole-, and spin-ordered systems, which govern macroscopic properties and important functionality. However, detailed atomic and electronic structures of domain walls have often been uncertain and the microscopic mechanism of their functionality has been elusive. Here, we clarify the complete atomic and electronic structures of the domain wall network, a honeycomb network connected by Z3 vortices, in the nearly commensurate Mott charge-density wave (CDW) phase of 1T-TaS2. Scanning tunneling microscopy resolves characteristic charge orders within domain walls and their vortices. Density functional theory calculations disclose their unique atomic relaxations and the metallic in-gap states confined tightly therein. A generic theory is constructed, which connects this emergent honeycomb network of conducting electrons to the enhanced superconductivity.

Dynamical Metal to Charge-Density-Wave Junctions in an Atomic Wire Array

We investigated the atomic scale electronic phase separation emerging from a quasi-1D charge-density-wave (CDW) state of the In atomic wire array on a Si(111) surface. Spatial variations of the CDW gap and amplitude are quantified for various interfaces of metallic and insulating CDW domains by scanning tunneling microscopy and spectroscopy (STS). The strong anisotropy in the metal-insulator junctions is revealed with an order of magnitude difference in the interwire and intrawire junction lengths of 0.4 and 7 nm, respectively. The intrawire junction length is reduced dramatically by an atomic scale impurity, indicating the tunability of the metal-insulator junction in an atomic scale. Density functional theory calculations disclose the dynamical nature of the intrawire junction formation and tunability.

Strongly Compressed Few-Layered SnSe2 Films Grown on a SrTiO3 Substrate: The Coexistence of Charge Ordering and Enhanced Interfacial Superconductivity

High pressure has been demonstrated to be a powerful approach of producing novel condensed-matter states, particularly in tuning the superconducting transition temperature (T_c) of the superconductivity in a clean fashion without involving the complexity of chemical doping. However, the challenge of high-pressure experiment hinders further in-depth research for underlying mechanisms. Here, we have successfully synthesized continuous layer-controllable SnSe₂ films on SrTiO₃ substrate using molecular beam epitaxy. By means of scanning tunneling microscopy/spectroscopy (STM/S) and Raman spectroscopy, we found that the strong compressive strain is intrinsically built in few-layers films, with a largest equivalent pressure up to 23 GPa in the monolayer. Upon this, unusual 2 × 2 charge ordering is induced at the occupied states in the monolayer, accompanied by prominent decrease in the density of states (DOS) near the Fermi energy (E_F), resembling the gap states of CDW reported in transition metal dichalcogenide (TMD) materials. Subsequently, the coexistence of charge ordering and the interfacial superconductivity is observed in bilayer films as a result of releasing the compressive strain. In conjunction with spatially resolved spectroscopic study and first-principles calculation, we find that the enhanced interfacial superconductivity with an estimated T_c of 8.3 K is observed only in the 1 × 1 region. Such superconductivity can be ascribed to a combined effect of interfacial charge transfer and compressive strain, which leads to a considerable downshift of the conduction band minimum and an increase in the DOS at E_F. Our results provide an attractive platform for further in-depth investigation of compression-induced charge ordering (monolayer) and the interplay between charge ordering and superconductivity (bilayer). Meanwhile, it has opened up a pathway to prepare strongly compressed two-dimensional materials by growing onto a SrTiO₃ substrate, which is promising to induce superconductivity with a higher T_c.

Strain-Induced Metastable Topological Networks in Laser-Fabricated TaS2 Polytype Heterostructures for Nanoscale Devices

The stacking of layered materials into heterostructures offers diverse possibilities for generating deformed moiré states arising from their mutual interaction. Here we report self-assembled two-dimensional nanoscale strain networks formed within a single prismatic (H) polytype monolayer of TaS₂ created in situ on the surface of an orthorhombic 1T-TaS₂ single crystal by a low-temperature laser-induced polytype transformation. The networks revealed by scanning tunneling microscopy (STM) take on diverse configurations at different temperatures, including extensive double stripes and a twisted 3-gonal mesh of connected 6-pronged vertices. The resulting phase diagram can be understood to be a consequence of thermally driven minimization of discommensurations between the H and 1T layers. Nontrivial dislocation defects of embedded 2- and 4-gonal structures are shown to be associated with local inhomogeneous strains. The creation of metastable heterostructures by laser quench at cryogenic temperatures in combination with STM manipulation of local strain demonstrates nanoscale control of topological defects in transition metal dichalcogenide heterostructures may be utilized in the fabrication of nanoscale electronic devices and neural networks.

Bias-Voltage Driven Switching of the Charge-Density-Wave and Normal Metallic Phases in 1T-TaS2 Thin-Film Devices

We report on switching among three charge-density-wave phases, commensurate, nearly commensurate, incommensurate, and the high-temperature normal metallic phase in thin-film 1T-TaS₂ devices induced by application of an in-plane bias voltage. The switching among all phases has been achieved over a wide temperature range, from 77 to 400 K. The low-frequency electronic noise spectroscopy has been used as an effective tool for monitoring the transitions, particularly the switching from the incommensurate charge-density-wave phase to the normal metal phase. The noise spectral density exhibits sharp increases at the phase transition points, which correspond to the step-like changes in resistivity. Assignment of the phases is consistent with low-field resistivity measurements over the temperature range from 77 to 600 K. Analysis of the experimental data and calculations of heat dissipation indicate that Joule heating plays a dominant role in the voltage induced transitions in the 1T-TaS₂ devices on Si/SiO₂ substrates, contrary to some recent claims. The possibility of the bias-voltage switching among four different phases of 1T-TaS₂ is a promising step toward nanoscale device applications. The results also demonstrate the potential of noise spectroscopy for investigating and identifying phase transitions in the materials.

Modulating Charge Density Wave Order in a 1T-TaS2/Black Phosphorus Heterostructure

Controllability of collective electron states has been a long-sought scientific and technological goal and promises development of new devices. Herein, we investigate the tuning of charge density wave (CDW) in 1T-TaS₂ via a two-dimensional (2D) van der Waals heterostructure of 1T-TaS₂/BP. Unusual gate-dependent conductance oscillations were observed in 1T-TaS₂ nanoflake supported on BP in transport measurements. Scanning tunneling microscopy study shows that the nearly commensurate (NC) CDW phase survived to 4.5 K in this system, which is substantially lower than the NC to commensurate CDW phase transition temperature of 180 K. A Coulomb blockade model was invoked to explain the conductance oscillations, where the domain walls and domains in NC phase serve as series of quantum dot arrays and tunnelling barriers, respectively. Density functional theory calculations show that a range of interfacial interactions, including strain and charge transfer, influences the CDW stabilities. Our work sheds light on tuning CDW orders via 2D heterostructure stacking and provides new insights on the CDW phase transition and sliding mechanism.

Phase transitions and pattern formation in ensembles of phase-amplitude solitons in quasi-one-dimensional electronic systems

Most common types of symmetry breaking in quasi-one-dimensional electronic systems possess a combined manifold of states degenerate with respect to both the phase θ and the amplitude A sign of the order parameter Aexp(iθ). These degrees of freedom can be controlled or accessed independently via either the spin polarization or the charge densities. To understand statistical properties and the phase diagram in the course of cooling under the controlled parameters, we present here an analytical treatment supported by Monte Carlo simulations for a generic coarse-grained two-field model of XY-Ising type. The degeneracies give rise to two coexisting types of topologically nontrivial configurations: phase vortices and amplitude kinks, i.e., the solitons. In two- and three-dimensional states with long-range (or Berezinskii--Kosterlitz--Thouless-type) orders, the topological confinement sets in at a temperature T=T_{1} which binds together the kinks and unusual half-integer vortices. At a lower T=T_{2}, the solitons start to aggregate into walls formed as rods of amplitude kinks which are ultimately terminated by half-integer vortices. With lowering T, the walls multiply, passing sequentially across the sample. The presented results indicate a possible physical realization of a peculiar system of half-integer vortices with rods of amplitude kinks connecting their cores. Its experimental realization becomes feasible in view of recent successes in real-space observations and even manipulations of domain walls in correlated electronic systems.