Spontaneous Supercrystal Formation During a Strain-Engineered Metal-Insulator Transition.

Mott metal-insulator transitions possess electronic, magnetic, and structural degrees of freedom promising next-generation energy-efficient electronics. A previously unknown, hierarchically ordered, and anisotropic supercrystal state is reported and its intrinsic formation characterized in-situ during a Mott transition in a Ca2RuO4 thin film. Machine learning-assisted X-ray nanodiffraction together with cryogenic electron microscopy reveal multi-scale periodic domain formation at and below the film transition temperature (TFilm ≈ 200-250 K) and a separate anisotropic spatial structure at and above TFilm. Local resistivity measurements imply an intrinsic coupling of the supercrystal orientation to the material's anisotropic conductivity. These findings add a new degree of complexity to the physical understanding of Mott transitions, opening opportunities for designing materials with tunable electronic properties.

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.

In operando cryo-STEM of pulse-induced charge density wave switching in TaS2.

The charge density wave material 1T-TaS2 exhibits a pulse-induced insulator-to-metal transition, which shows promise for next-generation electronics such as memristive memory and neuromorphic hardware. However, the rational design of TaS2 devices is hindered by a poor understanding of the switching mechanism, the pulse-induced phase, and the influence of material defects. Here, we operate a 2-terminal TaS2 device within a scanning transmission electron microscope at cryogenic temperature, and directly visualize the changing charge density wave structure with nanoscale spatial resolution and down to 300 µs temporal resolution. We show that the pulse-induced transition is driven by Joule heating, and that the pulse-induced state corresponds to the nearly commensurate and incommensurate charge density wave phases, depending on the applied voltage amplitude. With our in operando cryogenic electron microscopy experiments, we directly correlate the charge density wave structure with the device resistance, and show that dislocations significantly impact device performance. This work resolves fundamental questions of resistive switching in TaS2 devices, critical for engineering reliable and scalable TaS2 electronics.

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 imaging of periodic nanotextures in thin films via phasing of diffraction data.

New properties and exotic quantum phenomena can form due to periodic nanotextures, including Moire patterns, ferroic domains, and topologically protected magnetization and polarization textures. Despite the availability of powerful tools to characterize the atomic crystal structure, the visualization of nanoscale strain-modulated structural motifs remains challenging. Here, we develop nondestructive real-space imaging of periodic lattice distortions in thin epitaxial films and report an emergent periodic nanotexture in a Mott insulator. Specifically, we combine iterative phase retrieval with unsupervised machine learning to invert the diffuse scattering pattern from conventional X-ray reciprocal-space maps into real-space images of crystalline displacements. Our imaging in PbTiO3/SrTiO3 superlattices exhibiting checkerboard strain modulation substantiates published phase-field model calculations. Furthermore, the imaging of biaxially strained Mott insulator Ca2RuO4 reveals a strain-induced nanotexture comprised of nanometer-thin metallic-structure wires separated by nanometer-thin Mott-insulating-structure walls, as confirmed by cryogenic scanning transmission electron microscopy (cryo-STEM). The nanotexture in Ca2RuO4 film is induced by the metal-to-insulator transition and has not been reported in bulk crystals. We expect the phasing of diffuse X-ray scattering from thin crystalline films in combination with cryo-STEM to open a powerful avenue for discovering, visualizing, and quantifying the periodic strain-modulated structures in quantum materials.

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.

Ultrafast Modulations and Detection of a Ferro-Rotational Charge Density Wave Using Time-Resolved Electric Quadrupole Second Harmonic Generation.

We show the ferro-rotational nature of the commensurate charge density wave (CCDW) in 1T-TaS_{2} and track its dynamic modulations by temperature-dependent and time-resolved electric quadrupole rotation anisotropy-second harmonic generation (EQ RA-SHG), respectively. The ultrafast modulations manifest as the breathing and the rotation of the EQ RA-SHG patterns at three frequencies around the reported single CCDW amplitude mode frequency. A sudden shift of the triplet frequencies and a dramatic increase in the breathing and rotation magnitude further reveal a photoinduced transient CDW phase across a critical pump fluence of ∼0.5 mJ/cm^{2}.

Optimal STEM Convergence Angle Selection Using a Convolutional Neural Network and the Strehl Ratio.

The selection of the correct convergence angle is essential for achieving the highest resolution imaging in scanning transmission electron microscopy (STEM). The use of poor heuristics, such as Rayleigh's quarter-phase rule, to assess probe quality and uncertainties in the measurement of the aberration function results in the incorrect selection of convergence angles and lower resolution. Here, we show that the Strehl ratio provides an accurate and efficient way to calculate criteria for evaluating the probe size for STEM. A convolutional neural network trained on the Strehl ratio is shown to outperform experienced microscopists at selecting a convergence angle from a single electron Ronchigram using simulated datasets. Generating tens of thousands of simulated Ronchigram examples, the network is trained to select convergence angles yielding probes on average 85% nearer to optimal size at millisecond speeds (0.02% of human assessment time). Qualitative assessment on experimental Ronchigrams with intentionally introduced aberrations suggests that trends in the optimal convergence angle size are well modeled but high accuracy requires a high number of training datasets. This near-immediate assessment of Ronchigrams using the Strehl ratio and machine learning highlights a viable path toward the rapid, automated alignment of aberration-corrected electron microscopes.

Atomic-Resolution Cryo-STEM Across Continuously Variable Temperatures.

Atomic-resolution cryogenic scanning transmission electron microscopy (cryo-STEM) has provided a path to probing the microscopic nature of select low-temperature phases in quantum materials. Expanding cryo-STEM techniques to broadly tunable temperatures will give access to the rich temperature-dependent phase diagrams of these materials. With existing cryo-holders, however, variations in sample temperature significantly disrupt the thermal equilibrium of the system, resulting in large-scale sample drift. The ability to tune the temperature without negative impact on the overall instrument stability is crucial, particularly for high-resolution experiments. Here, we test a new side-entry continuously variable temperature dual-tilt cryo-holder which integrates liquid nitrogen cooling with a 6-pin micro-electromechanical system (MEMS) sample heater to overcome some of these experimental challenges. We measure consistently low drift rates of 0.3-0.4 Å/s and demonstrate atomic-resolution cryo-STEM imaging across a continuously variable temperature range from ~100 K to well above room temperature. We conduct additional drift stability measurements across several commercial sample stages and discuss implications for further developments of ultra-stable, flexible cryo-stages.

Nanoscale deformation mechanics reveal resilience in nacre of Pinna nobilis shell.

The combination of soft nanoscale organic components with inorganic nanograins hierarchically designed by natural organisms results in highly ductile structural materials that can withstand mechanical impact and exhibit high resilience on the macro- and nano-scale. Our investigation of nacre deformation reveals the underlying nanomechanics that govern the structural resilience and absorption of mechanical energy. Using high-resolution scanning/transmission electron microscopy (S/TEM) combined with in situ indentation, we observe nanoscale recovery of heavily deformed nacre that restores its mechanical strength on external stimuli up to 80% of its yield strength. Under compression, nacre undergoes deformation of nanograins and non-destructive locking across organic interfaces such that adjacent inorganic tablets structurally join. The locked tablets respond to strain as a continuous material, yet the organic boundaries between them still restrict crack propagation. Remarkably, the completely locked interface recovers its original morphology without any noticeable deformation after compressive contact stresses as large as 1.2 GPa.

Thickness and Stacking Sequence Determination of Exfoliated Dichalcogenides (1T-TaS2, 2H-MoS2) Using Scanning Transmission Electron Microscopy.

Layered transition metal dichalcogenides (TMDs) have attracted interest due to their promise for future electronic and optoelectronic technologies. As one approaches the two-dimensional (2D) limit, thickness and local topology can greatly influence the macroscopic properties of a material. To understand the unique behavior of TMDs it is therefore important to identify the number of atomic layers and their stacking in a sample. The goal of this work is to extract the thickness and stacking sequence of TMDs directly by matching experimentally recorded high-angle annular dark-field scanning transmission electron microscope images and convergent-beam electron diffraction (CBED) patterns to quantum mechanical, multislice scattering simulations. Advantageously, CBED approaches do not require a resolved lattice in real space and are capable of neglecting the thickness contribution of amorphous surface layers. Here we demonstrate the crystal thickness can be determined from CBED in exfoliated 1T-TaS2 and 2H-MoS2 to within a single layer for ultrathin ≲9 layers and ±1 atomic layer (or better) in thicker specimens while also revealing information about stacking order-even when the crystal structure is unresolved in real space.