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.

Limits to the strain engineering of layered square-planar nickelate thin films.

The layered square-planar nickelates, Ndn+1NinO2n+2, are an appealing system to tune the electronic properties of square-planar nickelates via dimensionality; indeed, superconductivity was recently observed in Nd6Ni5O12 thin films. Here, we investigate the role of epitaxial strain in the competing requirements for the synthesis of the n = 3 Ruddlesden-Popper compound, Nd4Ni3O10, and subsequent reduction to the square-planar phase, Nd4Ni3O8. We synthesize our highest quality Nd4Ni3O10 films under compressive strain on LaAlO3 (001), while Nd4Ni3O10 on NdGaO3 (110) exhibits tensile strain-induced rock salt faults but retains bulk-like transport properties. A high density of extended defects forms in Nd4Ni3O10 on SrTiO3 (001). Films reduced on LaAlO3 become insulating and form compressive strain-induced c-axis canting defects, while Nd4Ni3O8 films on NdGaO3 are metallic. This work provides a pathway to the synthesis of Ndn+1NinO2n+2 thin films and sets limits on the ability to strain engineer these compounds via epitaxy.

Disentangling Coexisting Structural Order Through Phase Lock-In Analysis of Atomic-Resolution STEM Data.

As a real-space technique, atomic-resolution STEM imaging contains both amplitude and geometric phase information about structural order in materials, with the latter encoding important information about local variations and heterogeneities present in crystalline lattices. Such phase information can be extracted using geometric phase analysis (GPA), a method which has generally focused on spatially mapping elastic strain. Here we demonstrate an alternative phase demodulation technique and its application to reveal complex structural phenomena in correlated quantum materials. As with other methods of image phase analysis, the phase lock-in approach can be implemented to extract detailed information about structural order and disorder, including dislocations and compound defects in crystals. Extending the application of this phase analysis to Fourier components that encode periodic modulations of the crystalline lattice, such as superlattice or secondary frequency peaks, we extract the behavior of multiple distinct order parameters within the same image, yielding insights into not only the crystalline heterogeneity but also subtle emergent order parameters such as antipolar displacements. When applied to atomic-resolution images spanning large (~0.5 × 0.5 µm2) fields of view, this approach enables vivid visualizations of the spatial interplay between various structural orders in novel 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.

Charge order textures induced by non-linear couplings in a half-doped manganite.

The self-organization of strongly interacting electrons into superlattice structures underlies the properties of many quantum materials. How these electrons arrange within the superlattice dictates what symmetries are broken and what ground states are stabilized. Here we show that cryogenic scanning transmission electron microscopy (cryo-STEM) enables direct mapping of local symmetries and order at the intra-unit-cell level in the model charge-ordered system Nd1/2Sr1/2MnO3. In addition to imaging the prototypical site-centered charge order, we discover the nanoscale coexistence of an exotic intermediate state which mixes site and bond order and breaks inversion symmetry. We further show that nonlinear coupling of distinct lattice modes controls the selection between competing ground states. The results demonstrate the importance of lattice coupling for understanding and manipulating the character of electronic self-organization and that cryo-STEM can reveal local order in strongly correlated systems at the atomic scale.

Mapping Defect Relaxation in Quantum Dot Solids upon In Situ Heating.

Epitaxially connected quantum dot solids have emerged as an interesting class of quantum confined materials with the potential for highly tunable electronic structures. Realization of the predicted emergent electronic properties has remained elusive due in part to defective interdot epitaxial connections. Thermal annealing has shown potential to eliminate such defects, but a direct understanding of this mechanism hinges on determining the nature of defects in the connections and how they respond to heating. Here, we use in situ heating in the scanning transmission electron microscope to probe the effect of heating on distinct defect types. We apply a real space, local strain mapping technique, which allows us to identify tensile and shear strain in the atomic lattice, highlighting tensile, shear, and bending defects in interdot connections. We also track the out-of-plane orientation of individual QDs and infer the prevalence of out-of-plane twisting and bending defects as a function of annealing. We find that tensile and shear defects are fully relaxed upon mild thermal annealing, while bending defects persist. Additionally, out-of-plane orientation tracking reveals an increase in correctly oriented QDs, pointing to a relaxation of either twisting defects or out-of-plane bending defects. While bending defects remain, highlighting the need for further study of orientational ordering during the preattachment phase of superlattice formation, these atomic-scale insights show that annealing can effectively eliminate tensile and shear defects, a promising step toward delocalization of charge carriers and tunable electronic properties.

Direct Visualization of Trimerized States in 1T

Transition-metal dichalcogenides containing tellurium anions show remarkable charge-lattice modulated structures and prominent interlayer character. Using cryogenic scanning transmission electron microscopy (STEM), we map the atomic-scale structures of the high temperature (HT) and low temperature (LT) modulated phases in 1T^{'}-TaTe_{2}. At HT, we directly show in-plane metal distortions which form trimerized clusters and staggered, three-layer stacking. In the LT phase at 93 K, we visualize an additional trimerization of Ta sites and subtle distortions of Te sites by extracting structural information from contrast modulations in plan-view STEM data. Coupled with density functional theory calculations and image simulations, this approach opens the door for atomic-scale visualizations of low temperature phase transitions and complex displacements in a variety of layered systems.

Tunable Magnetic Transition to a Singlet Ground State in a 2D van der Waals Layered Trimerized Kagomé Magnet.

Incorporating magnetism into two-dimensional (2D) van der Waals (vdW) heterostructures is crucial for the development of functional electronic and magnetic devices. Here, we show that Nb3X8 (X = Cl, Br) is a family of 2D layered trimerized kagomé magnets that are paramagnetic at high temperatures and undergo a first-order phase transition on cooling to a singlet magnetic state. X-ray diffraction shows that a rearrangement of the vdW stacking accompanies the magnetic transition, with high- and low-temperature phases consistent with scanning transmission electron microscopy images of the end members α-Nb3Cl8 and ß-Nb3Br8. The temperature of this transition is systematically varied across the solid solution Nb3Cl8-xBrx (x = 0-8), with x = 6 having transitions near room temperature. The solid solution also varies the optical properties, which are further modulated by the phase transition. As such, they provide a platform on which to understand and exploit the interplay between dimensionality, magnetism, and optoelectronic behavior in vdW materials.

Current-Induced Torques with Dresselhaus Symmetry Due to Resistance Anisotropy in 2D Materials.

We report measurements of current-induced torques in heterostructures of Permalloy (Py) with TaTe2, a transition-metal dichalcogenide (TMD) material possessing low crystal symmetry, and observe a torque component with Dresselhaus symmetry. We suggest that the dominant mechanism for this Dresselhaus component is not a spin-orbit torque but rather the Oersted field arising from a component of current that flows perpendicular to the applied voltage due to resistance anisotropy within the TaTe2. This type of transverse current is not present in wires made from a single uniform layer of a material with resistance anisotropy but will result whenever a material with resistance anisotropy is integrated into a heterostructure with materials having different resistivities, thereby producing a spatially nonuniform pattern of current flow. This effect will therefore influence measurements in a wide variety of heterostructures incorporating 2D TMD materials and other materials with low crystal symmetries.

Image registration of low signal-to-noise cryo-STEM data.

Combining multiple fast image acquisitions to mitigate scan noise and drift artifacts has proven essential for picometer precision, quantitative analysis of atomic resolution scanning transmission electron microscopy (STEM) data. For very low signal-to-noise ratio (SNR) image stacks - frequently required for undistorted imaging at liquid nitrogen temperatures - image registration is particularly delicate, and standard approaches may either fail, or produce subtly specious reconstructed lattice images. We present an approach which effectively registers and averages image stacks which are challenging due to their low-SNR and propensity for unit cell misalignments. Registering all possible image pairs in a multi-image stack leads to significant information surplus. In combination with a simple physical picture of stage drift, this enables identification of incorrect image registrations, and determination of the optimal image shifts from the complete set of relative shifts. We demonstrate the effectiveness of our approach on experimental, cryogenic STEM datasets, highlighting subtle artifacts endemic to low-SNR lattice images and how they can be avoided. High-SNR average images with information transfer out to 0.72 Å are achieved at 300 kV and with the sample cooled to near liquid nitrogen temperature.

Nature and evolution of incommensurate charge order in manganites visualized with cryogenic scanning transmission electron microscopy.

Incommensurate charge order in hole-doped oxides is intertwined with exotic phenomena such as colossal magnetoresistance, high-temperature superconductivity, and electronic nematicity. Here, we map, at atomic resolution, the nature of incommensurate charge-lattice order in a manganite using scanning transmission electron microscopy at room temperature and cryogenic temperature ([Formula: see text]93 K). In diffraction, the ordering wave vector changes upon cooling, a behavior typically associated with incommensurate order. However, using real space measurements, we discover that the ordered state forms lattice-locked regions over a few wavelengths interspersed with phase defects and changing periodicity. The cations undergo picometer-scale ([Formula: see text]6 pm to 11 pm) transverse displacements, suggesting that charge-lattice coupling is strong. We further unearth phase inhomogeneity in the periodic lattice displacements at room temperature, and emergent phase coherence at 93 K. Such local phase variations govern the long-range correlations of the charge-ordered state and locally change the periodicity of the modulations, resulting in wave vector shifts in reciprocal space. These atomically resolved observations underscore the importance of lattice coupling and phase inhomogeneity, and provide a microscopic explanation for putative "incommensurate" order in hole-doped oxides.

Bending and breaking of stripes in a charge ordered manganite.

In charge-ordered phases, broken translational symmetry emerges from couplings between charge, spin, lattice, or orbital degrees of freedom, giving rise to remarkable phenomena such as colossal magnetoresistance and metal-insulator transitions. The role of the lattice in charge-ordered states remains particularly enigmatic, soliciting characterization of the microscopic lattice behavior. Here we directly map picometer scale periodic lattice displacements at individual atomic columns in the room temperature charge-ordered manganite Bi0.35Sr0.18Ca0.47MnO3 using aberration-corrected scanning transmission electron microscopy. We measure transverse, displacive lattice modulations of the cations, distinct from existing manganite charge-order models. We reveal locally unidirectional striped domains as small as ~5 nm, despite apparent bidirectionality over larger length scales. Further, we observe a direct link between disorder in one lattice modulation, in the form of dislocations and shear deformations, and nascent order in the perpendicular modulation. By examining the defects and symmetries of periodic lattice displacements near the charge ordering phase transition, we directly visualize the local competition underpinning spatial heterogeneity in a complex oxide.

Atomic lattice disorder in charge-density-wave phases of exfoliated dichalcogenides (1T-TaS2).

Charge-density waves (CDWs) and their concomitant periodic lattice distortions (PLDs) govern the electronic properties in several layered transition-metal dichalcogenides. In particular, 1T-TaS2 undergoes a metal-to-insulator phase transition as the PLD becomes commensurate with the crystal lattice. Here we directly image PLDs of the nearly commensurate (NC) and commensurate (C) phases in thin, exfoliated 1T-TaS2 using atomic resolution scanning transmission electron microscopy at room and cryogenic temperature. At low temperatures, we observe commensurate PLD superstructures, suggesting ordering of the CDWs both in- and out-of-plane. In addition, we discover stacking transitions in the atomic lattice that occur via one-bond-length shifts. Interestingly, the NC PLDs exist inside both the stacking domains and their boundaries. Transitions in stacking order are expected to create fractional shifts in the CDW between layers and may be another route to manipulate electronic phases in layered dichalcogenides.