Evolution of the flat band and the role of lattice relaxations in twisted bilayer graphene.

Magic-angle twisted bilayer graphene exhibits correlated phenomena such as superconductivity and Mott insulating states related to the weakly dispersing flat band near the Fermi energy. Such a flat band is expected to be sensitive to both the moiré period and lattice relaxations. Thus, clarifying the evolution of the electronic structure with the twist angle is critical for understanding the physics of magic-angle twisted bilayer graphene. Here we combine nano-spot angle-resolved photoemission spectroscopy and atomic force microscopy to resolve the fine electronic structure of the flat band and remote bands, as well as their evolution with twist angle from 1.07° to 2.60°. Near the magic angle, the dispersion is characterized by a flat band near the Fermi energy with a strongly reduced band width. Moreover, we observe a spectral weight transfer between remote bands at higher binding energy, which allows to extract the modulated interlayer spacing near the magic angle. Our work provides direct spectroscopic information on flat band physics and highlights the important role of lattice relaxations.

Epitaxial growth of a 100-square-centimetre single-crystal hexagonal boron nitride monolayer on copper.

The development of two-dimensional (2D) materials has opened up possibilities for their application in electronics, optoelectronics and photovoltaics, because they can provide devices with smaller size, higher speed and additional functionalities compared with conventional silicon-based devices1. The ability to grow large, high-quality single crystals for 2D components-that is, conductors, semiconductors and insulators-is essential for the industrial application of 2D devices2-4. Atom-layered hexagonal boron nitride (hBN), with its excellent stability, flat surface and large bandgap, has been reported to be the best 2D insulator5-12. However, the size of 2D hBN single crystals is typically limited to less than one millimetre13-18, mainly because of difficulties in the growth of such crystals; these include excessive nucleation, which precludes growth from a single nucleus to large single crystals, and the threefold symmetry of the hBN lattice, which leads to antiparallel domains and twin boundaries on most substrates19. Here we report the epitaxial growth of a 100-square-centimetre single-crystal hBN monolayer on a low-symmetry Cu (110) vicinal surface, obtained by annealing an industrial copper foil. Structural characterizations and theoretical calculations indicate that epitaxial growth was achieved by the coupling of Cu <211> step edges with hBN zigzag edges, which breaks the equivalence of antiparallel hBN domains, enabling unidirectional domain alignment better than 99 per cent. The growth kinetics, unidirectional alignment and seamless stitching of the hBN domains are unambiguously demonstrated using centimetre- to atomic-scale characterization techniques. Our findings are expected to facilitate the wide application of 2D devices and lead to the epitaxial growth of broad non-centrosymmetric 2D materials, such as various transition-metal dichalcogenides20-23, to produce large single crystals.

Domino-like stacking order switching in twisted monolayer-multilayer graphene.

Atomic reconstruction has been widely observed in two-dimensional van der Waals structures with small twist angles1-7. This unusual behaviour leads to many novel phenomena, including strong electronic correlation, spontaneous ferromagnetism and topologically protected states1,5,8-14. Nevertheless, atomic reconstruction typically occurs spontaneously, exhibiting only one single stable state. Using conductive atomic force microscopy, here we show that, for small-angle twisted monolayer-multilayer graphene, there exist two metastable reconstruction states with distinct stacking orders and strain soliton structures. More importantly, we demonstrate that these two reconstruction states can be reversibly switched, and the switching can propagate spontaneously in an unusual domino-like fashion. Assisted by lattice-resolved conductive atomic force microscopy imaging and atomistic simulations, the detailed structure of the strain soliton networks has been identified and the associated propagation mechanism is attributed to the strong mechanical coupling among solitons. The fine structure of the bistable states is critical for understanding the unique properties of van der Waals structures with tiny twists, and the switching mechanism offers a viable means for manipulating their stacking states.

Visualizing the Anomalous Catalysis in Two-Dimensional Confined Space.

Confined nanospaces provide a new platform to promote catalytic reactions. However, the mechanism of catalytic enhancement in the nanospace still requires insightful exploration due to the lack of direct visualization. Here, we report operando investigations on the etching and growth of graphene in a two-dimensional (2D) confined space between graphene and a Cu substrate. We observed that the graphene layer between the Cu and top graphene layer was surprisingly very active in etching (more than 10 times faster than the etching of the top graphene layer). More strikingly, at a relatively low temperature (∼530 °C), the etched carbon radicals dissociated from the bottom layer, in turn feeding the growth of the top graphene layer with a very high efficiency. Our findings reveal the in situ dynamics of the anomalous confined catalytic processes in 2D confined spaces and thus pave the way for the design of high-efficiency catalysts.

Dual-Scale Stick-Slip Friction on Graphene/h-BN Moiré Superlattice Structure.

Using atomic force microscopy, we have shown that friction on graphene/h-BN superlattice structures may exhibit unusual moiré-scale stick slip in addition to the regular ones observed at the atomic scale. Such dual-scale slip instability will lead to unique length-scale dependent energy dissipation when the different slip mechanisms are sequentially activated. Assisted by an improved theoretical model and comparative experiments, we find that accumulation and unstable release of the in-plane strain of the graphene layer is the key mechanism underlying the moiré-scale behavior. This work highlights the distinct role of the internal state of the van der Waals interfaces in determining the rich dynamics and energy dissipation of layer-structured materials.

The evolving quality of frictional contact with graphene.

Graphite and other lamellar materials are used as dry lubricants for macroscale metallic sliding components and high-pressure contacts. It has been shown experimentally that monolayer graphene exhibits higher friction than multilayer graphene and graphite, and that this friction increases with continued sliding, but the mechanism behind this remains subject to debate. It has long been conjectured that the true contact area between two rough bodies controls interfacial friction. The true contact area, defined for example by the number of atoms within the range of interatomic forces, is difficult to visualize directly but characterizes the quantity of contact. However, there is emerging evidence that, for a given pair of materials, the quality of the contact can change, and that this can also strongly affect interfacial friction. Recently, it has been found that the frictional behaviour of two-dimensional materials exhibits traits unlike those of conventional bulk materials. This includes the abovementioned finding that for few-layer two-dimensional materials the static friction force gradually strengthens for a few initial atomic periods before reaching a constant value. Such transient behaviour, and the associated enhancement of steady-state friction, diminishes as the number of two-dimensional layers increases, and was observed only when the two-dimensional material was loosely adhering to a substrate. This layer-dependent transient phenomenon has not been captured by any simulations. Here, using atomistic simulations, we reproduce the experimental observations of layer-dependent friction and transient frictional strengthening on graphene. Atomic force analysis reveals that the evolution of static friction is a manifestation of the natural tendency for thinner and less-constrained graphene to re-adjust its configuration as a direct consequence of its greater flexibility. That is, the tip atoms become more strongly pinned, and show greater synchrony in their stick-slip behaviour. While the quantity of atomic-scale contacts (true contact area) evolves, the quality (in this case, the local pinning state of individual atoms and the overall commensurability) also evolves in frictional sliding on graphene. Moreover, the effects can be tuned by pre-wrinkling. The evolving contact quality is critical for explaining the time-dependent friction of configurationally flexible interfaces.

Tuning friction to a superlubric state via in-plane straining.

Controlling, and in many cases minimizing, friction is a goal that has long been pursued in history. From the classic Amontons-Coulomb law to the recent nanoscale experiments, the steady-state friction is found to be an inherent property of a sliding interface, which typically cannot be altered on demand. In this work, we show that the friction on a graphene sheet can be tuned reversibly by simple mechanical straining. In particular, by applying a tensile strain (up to 0.60%), we are able to achieve a superlubric state (coefficient of friction nearly 0.001) on a suspended graphene. Our atomistic simulations together with atomically resolved friction images reveal that the in-plane strain effectively modulates the flexibility of graphene. Consequently, the local pinning capability of the contact interface is changed, resulting in the unusual strain-dependent frictional behavior. This work demonstrates that the deformability of atomic-scale structures can provide an additional channel of regulating the friction of contact interfaces involving configurationally flexible materials.

Length Scale Effect in Frictional Aging of Silica Contacts.

Friction between two solid surfaces often exhibits strong rate and slip-history dependence, which critically determines the dynamic stability of frictional sliding. Empirically, such an evolutional effect has been captured by the rate-and-state friction (RSF) law based on laboratory-scale experiments; but its applicability for generic sliding interfaces under different length scales remains unclear. In this Letter, frictional aging, the key manifestation of the evolutional behavior, of silica-silica contacts is studied via slide-hold-slide tests with apparent contact size spanning across 3 orders of magnitude. The experimental results demonstrate a clear and strong length scale dependency in frictional aging characteristics. Assisted by a multiasperity RSF model, we attribute the length scale effect to roughness-dependent true contact area evolution as well as scale-dependent friction stress due to nonconcurrent slip.

Modeling Atomic-Scale Electrical Contact Quality Across Two-Dimensional Interfaces.

Contacting interfaces with physical isolation and weak interactions usually act as barriers for electrical conduction. The electrical contact conductance across interfaces has long been correlated with the true contact area or the "contact quantity". Much of the physical understanding of the interfacial electrical contact quality was primarily based on Landauer's theory or Richardson formulation. However, a quantitative model directly connecting contact conductance to interfacial atomistic structures still remains absent. Here, we measure the atomic-scale local electrical contact conductance instead of local electronic surface states in graphene/Ru(0001) superstructure, via atomically resolved conductive atomic force microscopy. By defining the "quality" of individual atom-atom contact as the carrier tunneling probability along the interatomic electron transport pathways, we establish a relationship between the atomic-scale contact quality and local interfacial atomistic structure. This real-space model unravels the atomic-level spatial modulation of contact conductance, and the twist angle-dependent interlayer conductance between misoriented graphene layers.

Droplet Precise Self-Splitting on Patterned Adhesive Surfaces for Simultaneous Multidetection.

Precise separation and localization of microdroplets are fundamental for various fields, such as high-throughput screening, combinatorial chemistry, and the recognition of complex analytes. We have developed a droplet self-splitting strategy to divide an impacting droplet into predictable microdroplets and deposit them at preset spots for simultaneous multidetection. No matter exchange was observed between these microdroplets, so they could be manipulated independently. Droplet self-splitting was attributed to anisotropic liquid recoiling on the patterned adhesive surface, as influenced by the droplet Weber number and the width of the low-adhesive stripe. A quantitative criterion was also developed to judge the droplet self-splitting capability. The precise separation and distribution of microdroplets enabled simultaneous arrayed reactions and multiple analyte detection using one droplet of sample.

Tuning Local Electrical Conductivity via Fine Atomic Scale Structures of Two-Dimensional Interfaces.

Two-dimensional (2D) materials have seen a broad range of applications in electronic and optoelectronic applications; however, full realization of this potential hitherto largely hinges on the quality and performance of the electrical contacts formed between 2D materials and their surrounding metals/semiconductors. Despite the progress in revealing the charge injecting mechanisms and enhancing electrical conductance using various interfacial treatments, how the microstructure of contact interfaces affects local electrical conductivity is still very limited. Here, using conductive atomic force microscopy (c-AFM), for the first time, we directly confirm the conjecture that the electrical conductivity of physisorbed 2D material-metal/semiconductor interfaces is determined by the local electronic charge transfer. Using lattice-resolved conductivity mapping and first-principles calculations, we demonstrate that the electronic charge transfer, thereby electrical conductivity, can be fine-tuned by the topological defects of 2D materials and the atomic stacking with respect to the substrate. Our finding provides a novel route to engineer the electrical contact properties by exploiting fine atomic interactions; in the meantime, it also suggests a convenient and nondestructive means of probing subtle interactions along 2D heterogeneous interfaces.

Revisiting the Critical Condition for the Cassie-Wenzel Transition on Micropillar-Structured Surfaces.

Biological and engineering applications of superhydrophobic surfaces are limited by the stability of the wetting state determined by the transition from the Cassie-Baxter state to the Wenzel state (C-W transition). In this paper, we performed water droplet squeeze tests to investigate the critical conditions for the C-W transition for solid surfaces with periodic micropillar arrays. The experimental results indicate that the critical transition pressures for the samples with varying micropillar dimensions are all significantly higher than the theoretical predictions. Through independent measurements, we attributed the disparity to the incorrect assessment of the contact angle on the sidewall surfaces of the micropillars. We also showed that the theoretical models are still applicable when the correct contact angle of the sidewall surfaces is adopted. Our work directly validates and improves the theoretical models regarding the C-W transition and suggests a potential route of tuning superhydrophobicity using finer scale surface features.

Sliding friction and contact angle hysteresis of droplets on microhole-structured surfaces.

Microstructured surfaces with continuous solid topography have many potential applications in biology and industry. To understand the liquid transport property of microstructured surfaces with continuous solid topography, we studied the sliding behavior of a droplet on microhole-structured surfaces. We found that the sliding friction of the droplet increased with increasing solid area fraction due to enlarged apparent contact area and enhanced contact angle hysteresis. By introducing a correction factor to the modified Cassie-Baxter relation, we proposed an improved theoretical model to better predict the apparent receding contact angle. Our experimental data also revealed that the geometric topology of surface microstructures could affect the sliding friction with microhole-decorated surfaces, exhibiting a larger resistance than that for micropillar-decorated surfaces. Assisted by optical microscopy, we attributed this topology effect to the continuity and the true total length of the three-phase contact line at the receding edge during the sliding. Our study provides new insights into the liquid sliding behavior on microstructured surfaces with different topologies, which may help better design functional surfaces with special liquid transport properties.

Ice Melting to Release Reactants in Solution Syntheses.

Aqueous solution syntheses are mostly based on mixing two solutions with different reactants. It is shown that freezing one solution and melting it in another solution provides a new interesting strategy to mix chemicals and to significantly change the reaction kinetics and thermodynamics. For example, a precursor solution containing a certain concentration of AgNO3 was frozen and dropped into a reductive NaBH4 solution at about 0 °C. The ultra-slow release of reactants was successfully achieved. An ice-melting process can be used to synthesize atomically dispersed metals, including cobalt, nickel, copper, rhodium, ruthenium, palladium, silver, osmium, iridium, platinum, and gold, which can be easily extended to other solution syntheses (such as precipitation, hydrolysis, and displacement reactions) and provide a generalized method to redesign the interphase reaction kinetics and ion diffusion in wet chemistry.

Friction of Droplets Sliding on Microstructured Superhydrophobic Surfaces.

Liquid transport is a fundamental process relevant to a wide range of applications, for example, heat transfer, anti-icing, self-cleaning, drag reduction, and microfluidic systems. For these applications, a deeper understanding of the sliding behavior of water droplets on solid surfaces is of particular importance. In this study, the frictional behavior of water droplets sliding on superhydrophobic surfaces decorated with micropillar arrays was studied using a nanotribometer. Our experiments show that surfaces with a higher solid area fraction generally exhibited larger friction, although friction might drop when the solid area fraction was close to unity. More interestingly, we found that the sliding friction of droplets was enhanced when the dimension of the microstructures increased, showing a distinct size effect. The nonmonotonic dependence of friction force on solid area fraction and the apparent size effect can be qualitatively explained by the evolution of two governing factors, that is, the true length of the contact line and the coordination degree of the depinning events. The mechanisms are expected to be generally applicable for other liquid transport processes involving the dynamic motion of a three-phase contact line, which may provide a new means of tuning liquid-transfer behavior through surface microstructures.

Frictional ageing from interfacial bonding and the origins of rate and state friction.

Earthquakes have long been recognized as being the result of stick-slip frictional instabilities. Over the past few decades, laboratory studies of rock friction have elucidated many aspects of tectonic fault zone processes and earthquake phenomena. Typically, the static friction of rocks grows logarithmically with time when they are held in stationary contact, but the mechanism responsible for this strengthening is not understood. This time-dependent increase of frictional strength, or frictional ageing, is one manifestation of the 'evolution effect' in rate and state friction theory. A prevailing view is that the time dependence of rock friction results from increases in contact area caused by creep of contacting asperities. Here we present the results of atomic force microscopy experiments that instead show that frictional ageing arises from the formation of interfacial chemical bonds, and the large magnitude of ageing at the nanometre scale is quantitatively consistent with what is required to explain observations in macroscopic rock friction experiments. The relative magnitude of the evolution effect compared with that of the 'direct effect'--the dependence of friction on instantaneous changes in slip velocity--determine whether unstable slip, leading to earthquakes, is possible. Understanding the mechanism underlying the evolution effect would enable us to formulate physically based frictional constitutive laws, rather than the current empirically based 'laws', allowing more confident extrapolation to natural faults.

Guided Self-Propelled Leaping of Droplets on a Micro-Anisotropic Superhydrophobic Surface.

By introducing anisotropic micropatterns on a superhydrophobic surface, we demonstrate that water microdroplets can coalesce and leap over the surface spontaneously along a prescribed direction. This controlled behavior is attributed to anisotropic liquid-solid adhesion. An analysis relating the preferential leaping probability to the geometrical parameters of the system is presented with consistent experimental results. Surfaces with this rare quality demonstrate many unique characteristics, such as self-powered, and relatively long-distance transport of microdroplets by "relay" coalescence-induced leaping.

Fluorination of graphene enhances friction due to increased corrugation.

The addition of a single sheet of carbon atoms in the form of graphene can drastically alter friction between a nanoscale probe tip and a surface. Here, for the first time we show that friction can be altered over a wide range by fluorination. Specifically, the friction force between silicon atomic force microscopy tips and monolayer fluorinated graphene can range from 5-9 times higher than for graphene. While consistent with previous reports, the combined interpretation from our experiments and molecular dynamics simulations allows us to propose a novel mechanism: that the dramatic friction enhancement results from increased corrugation of the interfacial potential due to the strong local charge concentrated at fluorine sites, consistent with the Prandtl-Tomlinson model. The monotonic increase of friction with fluorination in experiments also demonstrates that friction force measurements provide a sensitive local probe of the degree of fluorination. Additionally, we found a transition from ordered to disordered atomic stick-slip upon fluorination, suggesting that fluorination proceeds in a spatially random manner.

WS2 ribbon arrays with defined chirality and coherent polarity.

One-dimensional transition metal dichalcogenides exhibiting an enhanced bulk photovoltaic effect have the potential to exceed the Shockley-Queisser limit efficiency in solar energy harvest within p-n junction architectures. However, the collective output of these prototype devices remains a challenge. We report on the synthesis of single-crystalline WS2 ribbon arrays with defined chirality and coherent polarity through an atomic manufacturing strategy. The chirality of WS2 ribbon was defined by substrate couplings into tunable armchair, zigzag, and chiral species, and the polarity direction was determined by the ribbon-precursor interfacial energy along a coherent direction. A single armchair ribbon showed strong bulk photovoltaic effect and the further integration of ~1000 aligned ribbons with coherent polarity enabled upscaling of the photocurrent.