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The field of two-dimensional (2D) materials has expanded to multilayered systems where electronic, optical, and mechanical properties change-often dramatically-with stacking order, thickness, twist, and interlayer spacing [1-5]. For transition metal dichalcogenides (TMDs), bond coordination within a single van der Waals layer changes the out-of-plane symmetry that can cause metal-insulator transitions [1, 6] or emergent quantum behavior [7]. Discerning these structural order parameters is often difficult using real-space measurements, however, we show 2D materials have distinct, conspicuous three-dimensional (3D) structure in reciprocal space described by near infinite oscillating Bragg rods. Combining electron diffraction and specimen tilt we probe Bragg rods in all three dimensions to identify multilayer structure with sub-Angstrom precision across several 2D materials-including TMDs (MoS2, TaSe2, TaS2) and multilayer graphene. We demonstrate quantitative determination of key structural parameters such as surface roughness, inter- & intra-layer spacings, stacking order, and interlayer twist using a rudimentary transmission electron microscope (TEM). We accurately characterize the full interlayer stacking order of multilayer graphene (1-, 2-, 6-, 12-layers) as well the intralayer structure of MoS2 and extract a chalcogen-chalcogen layer spacing of 3.07 +/- 0.11 Angstrom. Furthermore, we demonstrate quick identification of multilayer rhombohedral graphene., 9 pages, 6 figures

Relativistic Dirac fermions can be locally confirmed in nanoscale graphene quantum dots using electrostatic gating, and directly imaged using scanning tunnelling microscopy before escaping via Klein tunnelling.

Chirality—or ‘handedness’—is a symmetry property crucial to fields as diverse as biology, chemistry and high-energy physics. In graphene, chiral symmetry emerges naturally as a consequence of the carbon honeycomb lattice. This symmetry can be broken by interactions that couple electrons with opposite momenta in graphene. Here we directly visualize the formation of Kekule bond order, one such phase of broken chiral symmetry, in an ultraflat graphene sheet grown epitaxially on a copper substrate. We show that its origin lies in the interactions between individual vacancies in the copper substrate that are mediated electronically by the graphene. We show that this interaction causes the bonds in graphene to distort, creating a phase with broken chiral symmetry. The Kekule ordering is robust at ambient temperature and atmospheric conditions, indicating that intercalated atoms may be harnessed to drive graphene and other two-dimensional materials towards electronically desirable and exotic collective phases. Scanning tunnelling microscopy shows how the interaction between electrons in graphene and atomic vacancies in a copper substrate produces Kekule ordering — an electronic phase that breaks chiral symmetry.

When two sheets of graphene stack in a twisted bilayer graphene (tBLG) configuration, the resulting constrained overlap between interplanar 2p orbitals produce angle-tunable electronic absorption resonances. By applying a novel combination of multiphoton transient absorption (TA) microscopy and TEM, we resolve the electronic structure and ensuing relaxation by probing resonant excitations of single tBLG domains. Strikingly, we find that the transient electronic population in resonantly excited tBLG domains is enhanced many fold, forming a major electronic relaxation bottleneck. Two-photon TA microscopy shows this bottleneck effect originates from a strongly bound, dark exciton state lying ∼0.37 eV below the 1-photon absorption resonance. This stable coexistence of strongly bound excitons alongside free-electron continuum states has not been previously observed in a metallic, 2D material.

We report the scalable growth of aligned graphene and hexagonal boron nitride on commercial copper foils, where each film originates from multiple nucleations yet exhibits a single orientation. Thorough characterization of our graphene reveals uniform crystallographic and electronic structures on length scales ranging from nanometers to tens of centimeters. As we demonstrate with artificial twisted graphene bilayers, these inexpensive and versatile films are ideal building blocks for large-scale layered heterostructures with angle-tunable optoelectronic properties.

Precise vertical stacking and lateral stitching of two-dimensional (2D) materials, such as graphene and hexagonal boron nitride (h-BN), can be used to create ultrathin heterostructures with complex functionalities, but this diversity of behaviors also makes these new materials difficult to characterize. We report a DUV-vis-NIR hyperspectral microscope that provides imaging and spectroscopy at energies of up to 6.2 eV, allowing comprehensive, all-optical mapping of chemical composition in graphene/h-BN lateral heterojunctions and interlayer rotations in twisted bilayer graphene (tBLG). With the addition of transmission electron microscopy, we obtain quantitative structure-property relationships, confirming the formation of interfaces in graphene/h-BN lateral heterojunctions that are abrupt on a micrometer scale, and a one-to-one relationship between twist angle and interlayer optical resonances in tBLG. Furthermore, we perform similar hyperspectral imaging of samples that are supported on a nontransparent silicon/SiO2 substrate, enabling facile fabrication of atomically thin heterostructure devices with known composition and structure.

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.

The electronic, optical, and mechanical properties of bilayer and trilayer graphene vary with their structure, including the stacking order and relative twist, providing novel ways to realize useful characteristics not available to single layer graphene. However, developing controlled growth of bilayer and trilayer graphene requires efficient large-scale characterization of multilayer graphene structures. Here, we use dark-field transmission electron microscopy for rapid and accurate determination of key structural parameters (twist angle, stacking order, and interlayer spacing) of few-layer CVD graphene. We image the long-range atomic registry for oriented bilayer and trilayer graphene, find that it conforms exclusively to either Bernal or rhombohedral stacking, and determine their relative abundances. In contrast, our data on twisted multilayers suggest the absence of such long-range atomic registry. The atomic registry and its absence are consistent with the two different strain-induced deformations we observe; by tilting the samples to break mirror symmetry, we find a high density of twinned domains in oriented multilayer graphene, where multiple domains of two different stacking configurations coexist, connected by discrete twin boundaries. In contrast, individual layers in twisted regions continuously stretch and shear independently, forming elaborate Moiré patterns. These results, and the twist angle distribution in our CVD graphene, can be understood in terms of an angle-dependent interlayer potential model.

Parenting style and its impact on student achievement in a multidimensional society continues to pose significant challenges to clinicians, researchers, educators, and parents alike. This literature review summarizes the research surrounding five domains: (1) parental control; (2) gender and parenting style; (3) parental education; (4) perceptual differences between parents and their children; and (5) ethnicity and diversity. Behavioral control and psychological control were found to be two inherent features of parental style that have a direct affect on student achievement. Adolescents' perceived level of independence when interacting with their parents also seemed to have a direct relationship on their academic achievement. Research concerning children's progress in mathematics as related to parenting style and gender stereotype was also uncovered. Evidence was found to support the notion that parental education can have an indirect impact on children's academic achievement in various cultures....

The ability to control the stacking structure in layered materials could provide an exciting approach to tuning their optical and electronic properties. Because of the lower symmetry of each constituent monolayer, hexagonal boron nitride (h-BN) allows more structural variations in multiple layers than graphene; however, the structure-property relationships in this system remain largely unexplored. Here, we report a strong correlation between the interlayer stacking structures and optical and topological properties in chemically grown h-BN bilayers, measured mainly by using dark-field transmission electron microscopy (DF-TEM) and optical second harmonic generation (SHG) mapping. Our data show that there exist two distinct h-BN bilayer structures with different interlayer symmetries that give rise to a distinct difference in their SHG intensities. In particular, the SHG signal in h-BN bilayers is observed only for structures with broken inversion symmetry, with an intensity much larger than that of single layer h-BN. In addition, our DF-TEM data identify the formation of interlayer topological defects in h-BN bilayers, likely induced by local strain, whose properties are determined by the interlayer symmetry and the different interlayer potential landscapes.

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.

We report a systematic study of the optical conductivity of twisted bilayer graphene (tBLG) across a large energy range (1.2 eV to 5.6 eV) for various twist angles, combined with first-principles calculations. At previously unexplored high energies, our data show signatures of multiple van Hove singularities (vHSs) in the tBLG bands, as well as the nonlinearity of the single layer graphene bands and their electron-hole asymmetry. Our data also suggest that excitonic effects play a vital role in the optical spectra of tBLG. Including electron-hole interactions in first-principles calculations is essential to reproduce the shape of the conductivity spectra, and we find evidence of coherent interactions between the states associated with the multiple vHSs in tBLG.

Graphene, a truly two-dimensional hexagonal lattice of carbon atoms, possesses remarkable properties not seen in any other material, including ultrahigh electron mobility, high tensile strength, and uniform broadband optical absorption. While scientists initially studied its intrinsic properties with small, mechanically exfoliated graphene crystals found randomly, applying this knowledge would require growing large-area films with uniform structural and physical properties. The science of graphene has recently experienced revolutionary change, mainly due to the development of several large-scale growth methods. In particular, graphene synthesis by chemical vapor deposition (CVD) on copper is a reliable method to obtain films with mostly monolayer coverage. These films are also polycrystalline, consisting of multiple graphene crystals joined by grain boundaries. In addition, portions of these graphene films contain more than one layer, and each layer can possess a different crystal orientation and stacking order. In this Account, we review the structural and physical properties that originate from polycrystallinity and stacking in CVD graphene. To begin, we introduce dark-field transmission electron microscopy (DF-TEM), a technique which allows rapid and accurate imaging of key structural properties, including the orientation of individual domains and relative stacking configurations. Using DF-TEM, one can easily identify "lateral junctions," or grain boundaries between adjacent domains, as well as "vertical junctions" from the stacking of graphene multilayers. With this technique, we can distinguish between oriented (Bernal or rhombohedral) and misoriented (twisted) configurations. The structure of lateral junctions in CVD graphene is sensitive to growth conditions and is reflected in the material's electrical and mechanical properties. In particular, grain boundaries in graphene grown under faster reactant flow conditions have no gaps or overlaps, unlike more slowly grown films. These structural differences can affect the material's electrical properties: for example, better-connected grain boundaries are more electrically conductive. However, grain boundaries in general are mechanically weaker than pristine graphene, which is an order of magnitude stronger than CVD graphene based on indentation measurements performed with an atomic force microscope. Vertical junctions in multilayer CVD graphene have two key structural features. First, bilayer graphene (BLG) with Bernal stacking exists in two mirrored configurations (AB or AC) that also form isolated domains. Similarly, oriented trilayer graphene also has alternating ABA and ABC stacked layers. Second, in twisted multilayer graphene, stacked layers lack long-range atomic registry and can move freely relative to each other, which generates unique optical properties. In particular, an interlayer optical excitation produces strong Raman and absorption peaks, dependent on the twist angle. A better understanding of the structural and physical properties of grain boundaries and multilayers in CVD graphene is central to realizing the full potential of graphene in large-scale applications. In addition, these studies provide a model for characterizing other layered materials, such as hexagonal boron nitride and MoS2, where similar polycrystallinity and stacking are expected when grown in large areas.

Few-layer graphene is a prototypical layered material, whose properties are determined by the relative orientations and interactions between layers. Exciting electrical and optical phenomena have been observed for the special case of Bernal-stacked few-layer graphene, but structure-property correlations in graphene which deviates from this structure are not well understood. Here, we combine two direct imaging techniques, dark-field transmission electron microscopy (DF-TEM) and widefield Raman imaging, to establish a robust, one-to-one correlation between twist angle and Raman intensity in twisted bilayer graphene (tBLG). The Raman G band intensity is strongly enhanced due to a previously unreported singularity in the joint density of states of tBLG, whose energy is exclusively a function of twist angle and whose optical transition strength is governed by interlayer interactions, enabling direct optical imaging of these parameters. Furthermore, our findings suggest future potential for novel optical and optoelectronic tBLG devices with angle-dependent, tunable characteristics.

Raman spectroscopy has been used extensively to study graphene and other sp(2)-bonded carbon materials, but the imaging capability of conventional micro-Raman spectroscopy is limited by the technique's low throughput. In this work, we apply an existing alternative imaging mode, widefield Raman imaging (WRI), to image and characterize graphene films on arbitrary substrates with high throughput. We show that WRI can be used to image graphene orders of magnitude faster than micro-Raman imaging allows, while still obtaining detailed spectral information about the sample. The advantages of WRI allow characterization of graphene under conditions that would be impossible or prohibitively time-consuming with other techniques, such as micro-Raman imaging or reflected optical microscopy. To demonstrate these advantages, we show that WRI enables graphene imaging on a large variety of substrates (copper, unoxidized silicon, suspended), large-scale studies of defect distribution in CVD graphene samples, and real-time imaging of dynamic processes.

The ability to protect refined metals from reactive environments is vital to many industrial and academic applications. Current solutions, however, typically introduce several negative effects, including increased thickness and changes in the metal physical properties. In this paper, we demonstrate for the first time the ability of graphene films grown by chemical vapor deposition to protect the surface of the metallic growth substrates of Cu and Cu/Ni alloy from air oxidation. In particular, graphene prevents the formation of any oxide on the protected metal surfaces, thus allowing pure metal surfaces only one atom away from reactive environments. SEM, Raman spectroscopy, and XPS studies show that the metal surface is well protected from oxidation even after heating at 200 °C in air for up to 4 h. Our work further shows that graphene provides effective resistance against hydrogen peroxide. This protection method offers significant advantages and can be used on any metal that catalyzes graphene growth.

Extended abstract of a paper presented at Microscopy and Microanalysis 2012 in Phoenix, Arizona, USA, July 29 – August 2, 2012.

Extended abstract of a paper presented at Microscopy and Microanalysis 2012 in Phoenix, Arizona, USA, July 29 – August 2, 2012.

Extended abstract of a paper presented at Microscopy and Microanalysis 2009 in Richmond, Virginia, USA, July 26 – July 30, 2009