Thermally induced atomic reconstruction into fully commensurate structures of transition metal dichalcogenide layers.

Twist angle between two-dimensional layers is a critical parameter that determines their interfacial properties, such as moiré excitons and interfacial ferro-electricity. To achieve better control over these properties for fundamental studies and various applications, considerable efforts have been made to manipulate twist angle. However, due to mechanical limitations and the inevitable formation of incommensurate regions, there remains a challenge in attaining perfect alignment of crystalline orientation. Here we report a thermally induced atomic reconstruction of randomly stacked transition metal dichalcogenide multilayers into fully commensurate heterostructures with zero twist angle by encapsulation annealing, regardless of twist angles of as-stacked samples and lattice mismatches. We also demonstrate the selective formation of R- and H-type fully commensurate phases with a seamless lateral junction using chemical vapour-deposited transition metal dichalcogenides. The resulting fully commensurate phases exhibit strong photoluminescence enhancement of the interlayer excitons, even at room temperature, due to their commensurate structure with aligned momentum coordinates. Our work not only demonstrates a way to fabricate zero-twisted, two-dimensional bilayers with R- and H-type configurations, but also provides a platform for studying their unexplored properties.

In Situ Imaging of an Anisotropic Layer-by-Layer Phase Transition in Few-Layer MoTe2.

Understanding the phase transition mechanisms in two-dimensional (2D) materials is a key to precisely tailor their properties at the nanoscale. Molybdenum ditelluride (MoTe2) exhibits multiple phases at room temperature, making it a promising candidate for phase-change applications. Here, we fabricate lateral 2H-Td interfaces with laser irradiation and probe their phase transitions from micro- to atomic scales with in situ heating in the transmission electron microscope (TEM). By encapsulating the MoTe2 with graphene protection layers, we create an in situ reaction cell compatible with atomic resolution imaging. We find that the Td-to-2H phase transition initiates at phase boundaries at low temperatures (200-225 °C) and propagates anisotropically along the b-axis in a layer-by-layer fashion. We also demonstrate a fully reversible 2H-Td-2H phase transition cycle, which generates a coherent 2H lattice containing inversion domain boundaries. Our results provide insights on fabricating 2D heterophase devices with atomically sharp and coherent interfaces.

Atomic-Resolution Imaging of Small Organic Molecules on Graphene.

Here, we demonstrate atomic-resolution scanning transmission electron microscopy (STEM) imaging of light elements in small organic molecules on graphene. We use low-dose, room-temperature, aberration-corrected STEM to image 2D monolayer and bilayer molecular crystals, followed by advanced image processing methods to create high-quality composite images from ∼102-104 individual molecules. In metalated porphyrin and phthalocyanine derivatives, these images contain an elementally sensitive contrast with up to 1.3 Å resolution─sufficient to distinguish individual carbon and nitrogen atoms. Importantly, our methods can be applied to molecules with low masses (∼0.6 kDa) and nanocrystalline domains containing just a few hundred molecules, making it possible to study systems for which large crystals cannot easily be grown. Our approach is enabled by low-background graphene substrates, which we show increase the molecules' critical dose by 2-7×. These results indicate a new route for low-dose, atomic-resolution electron microscopy imaging to solve the structures of small organic molecules.

Wafer-Scale Programmed Assembly of One-Atom-Thick Crystals.

Crystalline films offer various physical properties based on the modulation of their thicknesses and atomic structures. The layer-by-layer assembly of atomically thin crystals provides a powerful means to arbitrarily design films at the atomic level, which are unattainable with existing growth technologies. However, atomically clean assembly of the materials with high scalability and reproducibility remains challenging. We report programmed crystal assembly of graphene and monolayer hexagonal boron nitride, assisted by van der Waals interactions, to form wafer-scale films of pristine interfaces with near-unity yield. The atomic configurations of the films are tailored with layer-resolved compositions and in-plane crystalline orientations. We demonstrate batch-fabricated tunnel device arrays with modulation of the resistance over orders of magnitude by thickness control of the hexagonal boron nitride barrier with single-atom precision and large-scale, twisted multilayer graphene with programmable electronic band structures and crystal symmetries. Our results constitute an important development in the artificial design of large-scale films.

Author Correction: Ultrasoft slip-mediated bending in few-layer graphene.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Ultrasoft slip-mediated bending in few-layer graphene.

Continuum scaling laws often break down when materials approach atomic length scales, reflecting changes in their underlying physics and the opportunities to access unconventional properties. These continuum limits are evident in two-dimensional materials, where there is no consensus on their bending stiffnesses or how they scale with thickness. Through combined computational and electron microscopy experiments, we measure the bending stiffness of graphene, obtaining 1.2-1.7 eV for a monolayer. Moreover, we find that the bending stiffness of few-layer graphene decreases sharply as a function of bending angle, tuning by almost 400% for trilayer graphene. This softening results from shear, slip and the onset of superlubricity between the atomic layers and corresponds with a gradual change in scaling power from cubic to linear. Our results provide a unified model for bending in two-dimensional materials and show that their multilayers can be orders of magnitude softer than previously thought, among the most flexible electronic materials currently known.

High-mobility three-atom-thick semiconducting films with wafer-scale homogeneity.

The large-scale growth of semiconducting thin films forms the basis of modern electronics and optoelectronics. A decrease in film thickness to the ultimate limit of the atomic, sub-nanometre length scale, a difficult limit for traditional semiconductors (such as Si and GaAs), would bring wide benefits for applications in ultrathin and flexible electronics, photovoltaics and display technology. For this, transition-metal dichalcogenides (TMDs), which can form stable three-atom-thick monolayers, provide ideal semiconducting materials with high electrical carrier mobility, and their large-scale growth on insulating substrates would enable the batch fabrication of atomically thin high-performance transistors and photodetectors on a technologically relevant scale without film transfer. In addition, their unique electronic band structures provide novel ways of enhancing the functionalities of such devices, including the large excitonic effect, bandgap modulation, indirect-to-direct bandgap transition, piezoelectricity and valleytronics. However, the large-scale growth of monolayer TMD films with spatial homogeneity and high electrical performance remains an unsolved challenge. Here we report the preparation of high-mobility 4-inch wafer-scale films of monolayer molybdenum disulphide (MoS2) and tungsten disulphide, grown directly on insulating SiO2 substrates, with excellent spatial homogeneity over the entire films. They are grown with a newly developed, metal-organic chemical vapour deposition technique, and show high electrical performance, including an electron mobility of 30 cm(2) V(-1) s(-1) at room temperature and 114 cm(2) V(-1) s(-1) at 90 K for MoS2, with little dependence on position or channel length. With the use of these films we successfully demonstrate the wafer-scale batch fabrication of high-performance monolayer MoS2 field-effect transistors with a 99% device yield and the multi-level fabrication of vertically stacked transistor devices for three-dimensional circuitry. Our work is a step towards the realization of atomically thin integrated circuitry.

Graphene kirigami.

For centuries, practitioners of origami ('ori', fold; 'kami', paper) and kirigami ('kiru', cut) have fashioned sheets of paper into beautiful and complex three-dimensional structures. Both techniques are scalable, and scientists and engineers are adapting them to different two-dimensional starting materials to create structures from the macro- to the microscale. Here we show that graphene is well suited for kirigami, allowing us to build robust microscale structures with tunable mechanical properties. The material parameter crucial for kirigami is the Föppl-von Kármán number γ: an indication of the ratio between in-plane stiffness and out-of-plane bending stiffness, with high numbers corresponding to membranes that more easily bend and crumple than they stretch and shear. To determine γ, we measure the bending stiffness of graphene monolayers that are 10-100 micrometres in size and obtain a value that is thousands of times higher than the predicted atomic-scale bending stiffness. Interferometric imaging attributes this finding to ripples in the membrane that stiffen the graphene sheets considerably, to the extent that γ is comparable to that of a standard piece of paper. We may therefore apply ideas from kirigami to graphene sheets to build mechanical metamaterials such as stretchable electrodes, springs, and hinges. These results establish graphene kirigami as a simple yet powerful and customizable approach for fashioning one-atom-thick graphene sheets into resilient and movable parts with microscale dimensions.

Stochastic Stress Jumps Due to Soliton Dynamics in Two-Dimensional van der Waals Interfaces.

The creation and movement of dislocations determine the nonlinear mechanics of materials. At the nanoscale, the number of dislocations in structures become countable, and even single defects impact material properties. While the impact of solitons on electronic properties is well studied, the impact of solitons on mechanics is less understood. In this study, we construct nanoelectromechanical drumhead resonators from Bernal stacked bilayer graphene and observe stochastic jumps in frequency. Similar frequency jumps occur in few-layer but not twisted bilayer or monolayer graphene. Using atomistic simulations, we show that the measured shifts are a result of changes in stress due to the creation and annihilation of individual solitons. We develop a simple model relating the magnitude of the stress induced by soliton dynamics across length scales, ranging from <0.01 N/m for the measured 5 µm diameter to ∼1.2 N/m for the 38.7 nm simulations. These results demonstrate the sensitivity of 2D resonators are sufficient to probe the nonlinear mechanics of single dislocations in an atomic membrane and provide a model to understand the interfacial mechanics of different kinds of van der Waals structures under stress, which is important to many emerging applications such as engineering quantum states through electromechanical manipulation and mechanical devices like highly tunable nanoelectromechanical systems, stretchable electronics, and origami nanomachines.

Deep Learning Enabled Strain Mapping of Single-Atom Defects in Two-Dimensional Transition Metal Dichalcogenides with Sub-Picometer Precision.

Two-dimensional (2D) materials offer an ideal platform to study the strain fields induced by individual atomic defects, yet challenges associated with radiation damage have so far limited electron microscopy methods to probe these atomic-scale strain fields. Here, we demonstrate an approach to probe single-atom defects with sub-picometer precision in a monolayer 2D transition metal dichalcogenide, WSe2-2xTe2x. We utilize deep learning to mine large data sets of aberration-corrected scanning transmission electron microscopy images to locate and classify point defects. By combining hundreds of images of nominally identical defects, we generate high signal-to-noise class averages which allow us to measure 2D atomic spacings with up to 0.2 pm precision. Our methods reveal that Se vacancies introduce complex, oscillating strain fields in the WSe2-2xTe2x lattice that correspond to alternating rings of lattice expansion and contraction. These results indicate the potential impact of computer vision for the development of high-precision electron microscopy methods for beam-sensitive materials.

Ultrasonic Nebulization for TEM Sample Preparation on Single-Layer Graphene Grids.

Spray-coating using ultrasonic nebulization is reported for depositing nanoparticles on a TEM grid without many of the drying artifacts that are often associated with drop-casting. Spray-coating is suitable for preparing TEM samples on fragile support materials, such as suspended single-layer graphene, that rupture when samples are prepared by drop-casting. Additionally, because ultrasonic nebulization produces uniform droplets, nanoparticles deposited by spray-coating occur on the TEM grid in clusters, whose size is dependent on the concentration of the nanoparticle dispersion, which may allow the concentration of nanoparticle dispersions to be estimated using TEM.

Quantitative Imaging of Organic Ligand Density on Anisotropic Inorganic Nanocrystals.

A longstanding challenge in nanoparticle characterization is to understand anisotropic distributions of organic ligands at the surface of inorganic nanoparticles. Here, we show that using electron energy loss spectroscopy in an aberration-corrected scanning transmission electron microscope we can directly visualize and quantify ligand distributions on gold nanorods (AuNRs). These experiments analyze dozens of particles on graphene substrates, providing insight into how ligand binding densities vary within and between individual nanoparticles. We demonstrate that the distribution of cetyltrimethylammonium bromide (CTAB) on AuNRs is anisotropic, with a 30% decrease in ligand density at the poles of the nanoparticles. In contrast, the distribution of (16-mercaptohexadecyl)trimethylammonium bromide (MTAB) is more uniform. These results are consistent with literature reported higher reactivity at the ends of CTAB-coated AuNRs. Our results demonstrate the impact of electron spectroscopy to probe molecular distributions at soft-hard interfaces and how they produce spatially heterogeneous properties in colloidal nanoparticles.

Selective-Area Superconductor Epitaxy to Ballistic Semiconductor Nanowires.

Semiconductor nanowires such as InAs and InSb are promising materials for studying Majorana zero modes and demonstrating non-Abelian particle exchange relevant for topological quantum computing. While evidence for Majorana bound states in nanowires has been shown, the majority of these experiments are marked by significant disorder. In particular, the interfacial inhomogeneity between the superconductor and nanowire is strongly believed to be the main culprit for disorder and the resulting "soft superconducting gap" ubiquitous in tunneling studies of hybrid semiconductor-superconductor systems. Additionally, a lack of ballistic transport in nanowire systems can create bound states that mimic Majorana signatures. We resolve these problems through the development of selective-area epitaxy of Al to InSb nanowires, a technique applicable to other nanowires and superconductors. Epitaxial InSb-Al devices generically possess a hard superconducting gap and demonstrate ballistic 1D superconductivity and near-perfect transmission of supercurrents in the single mode regime, requisites for engineering and controlling 1D topological superconductivity. Additionally, we demonstrate that epitaxial InSb-Al superconducting island devices, the building blocks for Majorana-based quantum computing applications, prepared using selective-area epitaxy can achieve micron-scale ballistic 1D transport. Our results pave the way for the development of networks of ballistic superconducting electronics for quantum device applications.

Strain Modulation of Graphene by Nanoscale Substrate Curvatures: A Molecular View.

Spatially nonuniform strain is important for engineering the pseudomagnetic field and band structure of graphene. Despite the wide interest in strain engineering, there is still a lack of control on device-compatible strain patterns due to the limited understanding of the structure-strain relationship. Here, we study the effect of substrate corrugation and curvature on the strain profiles of graphene via combined experimental and theoretical studies of a model system: graphene on closely packed SiO2 nanospheres with different diameters (20-200 nm). Experimentally, via quantitative Raman analysis, we observe partial adhesion and wrinkle features and find that smaller nanospheres induce larger tensile strain in graphene; theoretically, molecular dynamics simulations confirm the same microscopic structure and size dependence of strain and reveal that a larger strain is caused by a stronger, inhomogeneous interaction force between smaller nanospheres and graphene. This molecular-level understanding of the strain mechanism is important for strain engineering of graphene and other two-dimensional materials.

Graphene and boron nitride lateral heterostructures for atomically thin circuitry.

Precise spatial control over the electrical properties of thin films is the key capability enabling the production of modern integrated circuitry. Although recent advances in chemical vapour deposition methods have enabled the large-scale production of both intrinsic and doped graphene, as well as hexagonal boron nitride (h-BN), controlled fabrication of lateral heterostructures in these truly atomically thin systems has not been achieved. Graphene/h-BN interfaces are of particular interest, because it is known that areas of different atomic compositions may coexist within continuous atomically thin films and that, with proper control, the bandgap and magnetic properties can be precisely engineered. However, previously reported approaches for controlling these interfaces have fundamental limitations and cannot be easily integrated with conventional lithography. Here we report a versatile and scalable process, which we call 'patterned regrowth', that allows for the spatially controlled synthesis of lateral junctions between electrically conductive graphene and insulating h-BN, as well as between intrinsic and substitutionally doped graphene. We demonstrate that the resulting films form mechanically continuous sheets across these heterojunctions. Conductance measurements confirm laterally insulating behaviour for h-BN regions, while the electrical behaviour of both doped and undoped graphene sheets maintain excellent properties, with low sheet resistances and high carrier mobilities. Our results represent an important step towards developing atomically thin integrated circuitry and enable the fabrication of electrically isolated active and passive elements embedded in continuous, one-atom-thick sheets, which could be manipulated and stacked to form complex devices at the ultimate thickness limit.

Grains and grain boundaries in single-layer graphene atomic patchwork quilts.

The properties of polycrystalline materials are often dominated by the size of their grains and by the atomic structure of their grain boundaries. These effects should be especially pronounced in two-dimensional materials, where even a line defect can divide and disrupt a crystal. These issues take on practical significance in graphene, which is a hexagonal, two-dimensional crystal of carbon atoms. Single-atom-thick graphene sheets can now be produced by chemical vapour deposition on scales of up to metres, making their polycrystallinity almost unavoidable. Theoretically, graphene grain boundaries are predicted to have distinct electronic, magnetic, chemical and mechanical properties that strongly depend on their atomic arrangement. Yet because of the five-order-of-magnitude size difference between grains and the atoms at grain boundaries, few experiments have fully explored the graphene grain structure. Here we use a combination of old and new transmission electron microscopy techniques to bridge these length scales. Using atomic-resolution imaging, we determine the location and identity of every atom at a grain boundary and find that different grains stitch together predominantly through pentagon-heptagon pairs. Rather than individually imaging the several billion atoms in each grain, we use diffraction-filtered imaging to rapidly map the location, orientation and shape of several hundred grains and boundaries, where only a handful have been previously reported. The resulting images reveal an unexpectedly small and intricate patchwork of grains connected by tilt boundaries. By correlating grain imaging with scanning probe and transport measurements, we show that these grain boundaries severely weaken the mechanical strength of graphene membranes but do not as drastically alter their electrical properties. These techniques open a new window for studies on the structure, properties and control of grains and grain boundaries in graphene and other two-dimensional materials.

Strain solitons and topological defects in bilayer graphene.

Bilayer graphene has been a subject of intense study in recent years. The interlayer registry between the layers can have dramatic effects on the electronic properties: for example, in the presence of a perpendicular electric field, a band gap appears in the electronic spectrum of so-called Bernal-stacked graphene [Oostinga JB, et al. (2007) Nature Materials 7:151-157]. This band gap is intimately tied to a structural spontaneous symmetry breaking in bilayer graphene, where one of the graphene layers shifts by an atomic spacing with respect to the other. This shift can happen in multiple directions, resulting in multiple stacking domains with soliton-like structural boundaries between them. Theorists have recently proposed that novel electronic states exist at these boundaries [Vaezi A, et al. (2013) arXiv:1301.1690; Zhang F, et al. (2013) arXiv:1301.4205], but very little is known about their structural properties. Here we use electron microscopy to measure with nanoscale and atomic resolution the widths, motion, and topological structure of soliton boundaries and related topological defects in bilayer graphene. We find that each soliton consists of an atomic-scale registry shift between the two graphene layers occurring over 6-11 nm. We infer the minimal energy barrier to interlayer translation and observe soliton motion during in situ heating above 1,000 °C. The abundance of these structures across a variety of samples, as well as their unusual properties, suggests that they will have substantial effects on the electronic and mechanical properties of bilayer graphene.

In-Plane Anisotropy in Mono- and Few-Layer ReS2 Probed by Raman Spectroscopy and Scanning Transmission Electron Microscopy.

Rhenium disulfide (ReS2) is a semiconducting layered transition metal dichalcogenide that exhibits a stable distorted 1T phase. The reduced symmetry of this system leads to in-plane anisotropy in various material properties. Here, we demonstrate the strong anisotropy in the Raman scattering response for linearly polarized excitation. Polarized Raman scattering is shown to permit a determination of the crystallographic orientation of ReS2 through comparison with direct structural analysis by scanning transmission electron microscopy (STEM). Analysis of the frequency difference of appropriate Raman modes is also shown to provide a means of precisely determining layer thickness up to four layers.

Tailoring the electronic structure in bilayer molybdenum disulfide via interlayer twist.

Molybdenum disulfide bilayers with well-defined interlayer twist angle were constructed by stacking single-crystal monolayers. Varying interlayer twist angle results in strong tuning of the indirect optical transition energy and second-harmonic generation and weak tuning of direct optical transition energies and Raman mode frequencies. Electronic structure calculations show the interlayer separation changes with twist due to repulsion between sulfur atoms, resulting in shifts of the indirect optical transition energies. These results show that interlayer alignment is a crucial variable in tailoring the properties of two-dimensional heterostructures.