Van der Waals interaction affects wrinkle formation in two-dimensional materials.

Nonlinear mechanics of solids is an exciting field that encompasses both beautiful mathematics, such as the emergence of instabilities and the formation of complex patterns, as well as multiple applications. Two-dimensional crystals and van der Waals (vdW) heterostructures allow revisiting this field on the atomic level, allowing much finer control over the parameters and offering atomistic interpretation of experimental observations. In this work, we consider the formation of instabilities consisting of radially oriented wrinkles around mono- and few-layer "bubbles" in two-dimensional vdW heterostructures. Interestingly, the shape and wavelength of the wrinkles depend not only on the thickness of the two-dimensional crystal forming the bubble, but also on the atomistic structure of the interface between the bubble and the substrate, which can be controlled by their relative orientation. We argue that the periodic nature of these patterns emanates from an energetic balance between the resistance of the top membrane to bending, which favors large wavelength of wrinkles, and the membrane-substrate vdW attraction, which favors small wrinkle amplitude. Employing the classical "Winkler foundation" model of elasticity theory, we show that the number of radial wrinkles conveys a valuable relationship between the bending rigidity of the top membrane and the strength of the vdW interaction. Armed with this relationship, we use our data to demonstrate a nontrivial dependence of the bending rigidity on the number of layers in the top membrane, which shows two different regimes driven by slippage between the layers, and a high sensitivity of the vdW force to the alignment between the substrate and the membrane.

Stacking Order in Graphite Films Controlled by van der Waals Technology.

In graphite crystals, layers of graphene reside in three equivalent, but distinct, stacking positions typically referred to as A, B, and C projections. The order in which the layers are stacked defines the electronic structure of the crystal, providing an exciting degree of freedom which can be exploited for designing graphitic materials with unusual properties including predicted high-temperature superconductivity and ferromagnetism. However, the lack of control of the stacking sequence limits most research to the stable ABA form of graphite. Here, we demonstrate a strategy to control the stacking order using van der Waals technology. To this end, we first visualize the distribution of stacking domains in graphite films and then perform directional encapsulation of ABC-rich graphite crystallites with hexagonal boron nitride (hBN). We found that hBN encapsulation, which is introduced parallel to the graphite zigzag edges, preserves ABC stacking, while encapsulation along the armchair edges transforms the stacking to ABA. The technique presented here should facilitate new research on the important properties of ABC graphite.

Tuning the Pseudospin Polarization of Graphene by a Pseudomagnetic Field.

One of the intriguing characteristics of honeycomb lattices is the appearance of a pseudomagnetic field as a result of mechanical deformation. In the case of graphene, the Landau quantization resulting from this pseudomagnetic field has been measured using scanning tunneling microscopy. Here we show that a signature of the pseudomagnetic field is a local sublattice symmetry breaking observable as a redistribution of the local density of states. This can be interpreted as a polarization of graphene's pseudospin due to a strain induced pseudomagnetic field, in analogy to the alignment of a real spin in a magnetic field. We reveal this sublattice symmetry breaking by tunably straining graphene using the tip of a scanning tunneling microscope. The tip locally lifts the graphene membrane from a SiO2 support, as visible by an increased slope of the I(z) curves. The amount of lifting is consistent with molecular dynamics calculations, which reveal a deformed graphene area under the tip in the shape of a Gaussian. The pseudomagnetic field induced by the deformation becomes visible as a sublattice symmetry breaking which scales with the lifting height of the strained deformation and therefore with the pseudomagnetic field strength. Its magnitude is quantitatively reproduced by analytic and tight-binding models, revealing fields of 1000 T. These results might be the starting point for an effective THz valley filter, as a basic element of valleytronics.

Photoelectrochemistry of Pristine Mono- and Few-Layer MoS2.

Two-dimensional crystals are promising building blocks for the new generation of energy materials due to their low volume, high surface area, and high transparency. Electrochemical behavior of these crystals determines their performance in applications such as energy storage/conversion, sensing, and catalysis. Nevertheless, the electrochemistry of an isolated monolayer of molybdenum disulfide, which is one of the most promising semiconducting crystals, has not been achieved to date. We report here on photoelectrochemical properties of pristine monolayer and few-layer basal plane MoS2, namely the electron transfer kinetics and electric double-layer capacitance, supported by an extensive physical and chemical characterization. This enables a comparative qualitative correlation among the electrochemical data, MoS2 structure, and external illumination, although the absolute magnitudes of the electron transfer and capacitance are specific to the redox mediator and electrolyte used in these measurements ([Ru(NH3)6](3+/2+) and LiCl, respectively). Our work shows a strong dependence of the electrochemical properties on the number of MoS2 layers and illumination intensity and proves that an effective interlayer charge transport occurs in bulk MoS2. This highlights the exciting opportunities for tuning of the electrochemical performance of MoS2 through modification of its structure, external environment, and illumination.

Electrostatically Confined Monolayer Graphene Quantum Dots with Orbital and Valley Splittings.

The electrostatic confinement of massless charge carriers is hampered by Klein tunneling. Circumventing this problem in graphene mainly relies on carving out nanostructures or applying electric displacement fields to open a band gap in bilayer graphene. So far, these approaches suffer from edge disorder or insufficiently controlled localization of electrons. Here we realize an alternative strategy in monolayer graphene, by combining a homogeneous magnetic field and electrostatic confinement. Using the tip of a scanning tunneling microscope, we induce a confining potential in the Landau gaps of bulk graphene without the need for physical edges. Gating the localized states toward the Fermi energy leads to regular charging sequences with more than 40 Coulomb peaks exhibiting typical addition energies of 7-20 meV. Orbital splittings of 4-10 meV and a valley splitting of about 3 meV for the first orbital state can be deduced. These experimental observations are quantitatively reproduced by tight binding calculations, which include the interactions of the graphene with the aligned hexagonal boron nitride substrate. The demonstrated confinement approach appears suitable to create quantum dots with well-defined wave function properties beyond the reach of traditional techniques.

Graphene oxide-DNA/graphene oxide-PDDA sandwiched membranes with neuromorphic function.

The behavior of polyelectrolytes in confined spaces has direct relevance to the protein mediated ion transport in living organisms. In this paper, we govern lithium chloride transport by the interface provided by polyelectrolytes, polycation, poly(diallyldimethylammonium chloride) (PDDA) and, polyanion, double stranded deoxyribonucleic acid (dsDNA), in confined graphene oxide (GO) membranes. Polyelectrolyte-GO interfaces demonstrate neuromorphic functions that were successfully applied with nanochannel ion interactions contributed, resulting in ion memory effects. Excitatory and inhibitory post-synaptic currents were tuned continuously as the number of pulses applied increased accordingly, increasing decay times. Furthermore, we demonstrated the short-term memory of a trained vs untrained device in computation. On account of its simple and safe production along with its robustness and stability, we anticipate our device to be a low dimensional building block for arrays to embed artificial neural networks in hardware for neuromorphic computing. Additionally, incorporating such devices with sensing and actuating parts for a complete feedback loop produces robotics with its own ability to learn by modifying actuation based on sensing data.

Piezoelectricity in Monolayer Hexagonal Boron Nitride.

2D hexagonal boron nitride (hBN) is a wide-bandgap van der Waals crystal with a unique combination of properties, including exceptional strength, large oxidation resistance at high temperatures, and optical functionalities. Furthermore, in recent years hBN crystals have become the material of choice for encapsulating other 2D crystals in a variety of technological applications, from optoelectronic and tunneling devices to composites. Monolayer hBN, which has no center of symmetry, is predicted to exhibit piezoelectric properties, yet experimental evidence is lacking. Here, by using electrostatic force microscopy, this effect is observed as a strain-induced change in the local electric field around bubbles and creases, in agreement with theoretical calculations. No piezoelectricity is found in bilayer and bulk hBN, where the center of symmetry is restored. These results add piezoelectricity to the known properties of monolayer hBN, which makes it a desirable candidate for novel electromechanical and stretchable optoelectronic devices, and pave a way to control the local electric field and carrier concentration in van der Waals heterostructures via strain. The experimental approach used here also shows a way to investigate the piezoelectric properties of other materials on the nanoscale by using electrostatic scanning probe techniques.

Electron Tunneling through Boron Nitride Confirms Marcus-Hush Theory Predictions for Ultramicroelectrodes.

Marcus-Hush theory of electron transfer is one of the pillars of modern electrochemistry with a large body of supporting experimental evidence presented to date. However, some predictions, such as the electrochemical behavior at disk ultramicroelectrodes, remain unverified. Herein, we present a study of electron tunneling across a hexagonal boron nitride acting as a barrier between a graphite electrode and redox mediators in a liquid solution. This was achieved by the fabrication of disk ultramicroelectrodes with a typical diameter of 5 µm. Analysis of voltammetric measurements, using two common outer-sphere redox mediators, yielded several electrochemical parameters, including the electron transfer rate constant, limiting current, and transfer coefficient. They depart significantly from the Butler-Volmer kinetics and instead show behavior previously predicted by the Marcus-Hush theory of electron transfer. In addition, our system provides a noteworthy experimental platform, which could be applied to address a number of scientific problems such as identification of reaction mechanisms, surface modification, or long-range electron transfer.

Large tunable valley splitting in edge-free graphene quantum dots on boron nitride.

Coherent manipulation of the binary degrees of freedom is at the heart of modern quantum technologies. Graphene offers two binary degrees: the electron spin and the valley. Efficient spin control has been demonstrated in many solid-state systems, whereas exploitation of the valley has only recently been started, albeit without control at the single-electron level. Here, we show that van der Waals stacking of graphene onto hexagonal boron nitride offers a natural platform for valley control. We use a graphene quantum dot induced by the tip of a scanning tunnelling microscope and demonstrate valley splitting that is tunable from -5 to +10 meV (including valley inversion) by sub-10-nm displacements of the quantum dot position. This boosts the range of controlled valley splitting by about one order of magnitude. The tunable inversion of spin and valley states should enable coherent superposition of these degrees of freedom as a first step towards graphene-based qubits.

Exfoliation of natural van der Waals heterostructures to a single unit cell thickness.

Weak interlayer interactions in van der Waals crystals facilitate their mechanical exfoliation to monolayer and few-layer two-dimensional materials, which often exhibit striking physical phenomena absent in their bulk form. Here we utilize mechanical exfoliation to produce a two-dimensional form of a mineral franckeite and show that the phase segregation of chemical species into discrete layers at the sub-nanometre scale facilitates franckeite's layered structure and basal cleavage down to a single unit cell thickness. This behaviour is likely to be common in a wider family of complex minerals and could be exploited for a single-step synthesis of van der Waals heterostructures, as an alternative to artificial stacking of individual two-dimensional crystals. We demonstrate p-type electrical conductivity and remarkable electrochemical properties of the exfoliated crystals, showing promise for a range of applications, and use the density functional theory calculations of franckeite's electronic band structure to rationalize the experimental results.

Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride.

Strongly anisotropic media, where the principal components of the dielectric tensor have opposite signs, are called hyperbolic. Such materials exhibit unique nanophotonic properties enabled by the highly directional propagation of slow-light modes localized at deeply sub-diffractional length scales. While artificial hyperbolic metamaterials have been demonstrated, they suffer from high plasmonic losses and require complex nanofabrication, which in turn induces size-dependent limitations on optical confinement. The low-loss, mid-infrared, natural hyperbolic material hexagonal boron nitride is an attractive alternative. Here we report on three-dimensionally confined 'hyperbolic polaritons' in boron nitride nanocones that support four series (up to the seventh order) modes in two spectral bands. The resonant modes obey the predicted aspect ratio dependence and exhibit high-quality factors (Q up to 283) in the strong confinement regime (up to λ/86). These observations assert hexagonal boron nitride as a promising platform for studying novel regimes of light-matter interactions and nanophotonic device engineering.