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Two-dimensional materials such as graphene allow direct access to the entirety of atoms constituting the crystal. While this makes shaping by lithography particularly attractive as a tool for band structure engineering through quantum confinement effects, edge disorder and contamination have so far limited progress towards experimental realization. Here, we define a superlattice in graphene encapsulated in hexagonal boron nitride, by etching an array of holes through the heterostructure with minimum feature sizes of 12–15 nm. We observe a magnetotransport regime that is distinctly different from the characteristic Landau fan of graphene, with a sizeable bandgap that can be tuned by a magnetic field. The measurements are accurately described by transport simulations and analytical calculations. Finally, we observe strong indications that the lithographically engineered band structure at the main Dirac point is cloned to a satellite peak that appears due to moiré interactions between the graphene and the encapsulating material.Dense nanostructuring of hBN-encapsulated graphene enables band structure engineering with distinct magnetotransport signatures and a tunable bandgap.

The assembly of individual two-dimensional materials into van der Waals heterostructures enables the construction of layered three-dimensional materials with desirable electronic and optical properties. A core problem in the fabrication of these structures is the formation of clean interfaces between the individual two-dimensional materials which would affect device performance. We present here a technique for the rapid batch fabrication of van der Waals heterostructures, demonstrated by the controlled production of 22 mono-, bi- and trilayer graphene stacks encapsulated in hexagonal boron nitride with close to 100% yield. For the monolayer devices, we found semiclassical mean-free paths up to 0.9 μm, with the narrowest samples showing clear indications of the transport being affected by boundary scattering. The presented method readily lends itself to fabrication of van der Waals heterostructures in both ambient and controlled atmospheres, while the ability to assemble pre-patterned layers paves the way for complex three-dimensional architectures. The reliable assembly of two-dimensional materials into van der Waals heterostructures is a critical step towards nanoscale electronic integration. Here the authors present a technique for batch fabrication of graphene/boron nitride stacks with clean interfaces and high-yield.

Conductance quantization is the quintessential feature of electronic transport in non-interacting mesoscopic systems. This phenomenon is observed in quasi one-dimensional conductors at zero magnetic field B, and the formation of edge states at finite magnetic fields results in wider conductance plateaus within the quantum Hall regime. Electrostatic interactions can change this picture qualitatively. At finite B, screening mechanisms in narrow, gated ballistic conductors are predicted to give rise to an increase in conductance and a suppression of quantization due to the appearance of additional conduction channels. Despite being a universal effect, this regime has proven experimentally elusive because of difficulties in realizing one-dimensional systems with sufficiently hard-walled, disorder-free confinement. Here, we experimentally demonstrate the suppression of conductance quantization within the quantum Hall regime for graphene nanoconstrictions with low edge roughness. Our findings may have profound impact on fundamental studies of quantum transport in finite-size, two-dimensional crystals with low disorder. Conductance quantization is the hallmark of non-interacting confined systems. The authors show that the quantization in graphene nanoconstrictions with low edge disorder is suppressed in the quantum Hall regime. This is explained by the addition of new conductance channels due to electrostatic screening.

With the increasing availability of large-area graphene, the ability to rapidly and accurately assess the quality of the electrical properties has become critically important. For practical applications, spatial variability in carrier density and carrier mobility must be controlled and minimized. We present a simple framework for assessing the quality and homogeneity of large-area graphene devices. The field effect in both exfoliated graphene devices encapsulated in hexagonal boron nitride and chemical vapor-deposited （CVD） devices was measured in dual current-voltage configurations and used to derive a single, gate-dependent effective shape factor, t, for each device, β is a sensitive indicator of spatial homogeneity that can be obtained from samples of arbitrary shape. All 50 devices investigated in this study show a variation （up to tenfold） in β as a function of the gate bias. Finite element simulations suggest that spatial doping inhomogeneity, rather than mobility inhomogeneity, is the primary cause of the gate dependence of β, and that measurable variations of β can be caused by doping variations as small as 10^10 cm^-2. Our results suggest that local variations in the position of the Dirac point alter the current flow and thus the effective sample shape as a function of the gate bias. We also found that such variations lead to systematic errors in carrier mobility calculations, which can be revealed by inspecting the corresponding β factor.

The pace of two-dimensional materials (2DM) research has been greatly accelerated by the ability to identify exfoliated thicknesses down to a monolayer from their optical contrast. Since this process requires time-consuming and error-prone manual assignment to avoid false-positives from image features with similar contrast, efforts towards fast and reliable automated assignments schemes is essential. We show that by modelling the expected 2DM contrast in digitally captured images, we can automatically identify candidate regions of 2DM. More importantly, we show a computationally-light machine vision strategy for eliminating false-positives from this set of 2DM candidates through the combined use of binary thresholding, opening and closing filters, and shape-analysis from edge detection. Calculation of data pyramids for arbitrarily high-resolution optical coverage maps of two-dimensional materials produced in this way allows the real-time presentation and processing of this image data in a zoomable interface, enabling large datasets to be explored and analysed with ease. The result is that a standard optical microscope with CCD camera can be used as an analysis tool able to accurately determine the coverage, residue/contamination concentration, and layer number for a wide range of presented 2DMs.

We experimentally investigate the charge induction mechanism across gated, narrow, ballistic graphene devices with different degrees of edge disorder. By using magnetoconductance measurements as the probing technique, we demonstrate that devices with large edge disorder exhibit a nearly homogeneous capacitance profile across the device channel, close to the case of an infinitely large graphene sheet. In contrast, devices with lower edge disorder (< 1 nm roughness) are strongly influenced by the fringing electrostatic field at graphene boundaries, in quantitative agreement with theoretical calculations for pristine systems. Specifically, devices with low edge disorder present a large effective capacitance variation across the device channel with a nontrivial, inhomogeneous profile due not only to classical electrostatics but also to quantum mechanical effects. We show that such quantum capacitance contribution, occurring due to the low density of states (DOS) across the device in the presence of an external magnetic field, is considerably altered as a result of the gate electrostatics in the ballistic graphene device. Our conclusions can be extended to any two dimensional (2D) electronic system confined by a hard-wall potential and are important for understanding the electronic structure and device applications of conducting 2D materials.

Massive Dirac fermions are low-energy electronic excitations characterized by a hyperbolic band dispersion. They play a central role in several emerging physical phenomena such as topological phase transitions, anomalous Hall effects and superconductivity. This work demonstrates that massive Dirac fermions can be controllably induced by lithographically patterning superstructures of nanoscale holes in a graphene device. Their band dispersion is systematically visualized using angle-resolved photoemission spectroscopy with nanoscale spatial resolution. A linear scaling of effective mass with feature sizes is discovered, underlining the Dirac nature of the superstructures. In situ electrostatic doping dramatically enhances the effective hole mass and leads to the direct observation of an electronic band gap that results in a peak-to-peak band separation of (0.64 \\(\\pm\\) 0.03) eV, which is shown via first-principles calculations to be strongly renormalized by carrier-induced screening. The presented methodology outlines a new approach for band structure engineering guided by directly viewing structurally- and electrically-tunable massive Dirac quasiparticles in lithographic superstructures at the nanoscale.

Nanostructuring allows altering of the electronic and photonic properties of two-dimensional (2D) materials. The efficiency, flexibility, and convenience of top-down lithography processes are however compromised by nm-scale edge roughness and resolution variability issues, which especially affects the performance of 2D materials. Here we study how dry anisotropic etching of multilayer 2D materials with sulfur hexafluoride (SF6) may overcome some of these issues, showing results for hexagonal boron nitride (hBN), tungsten disulfide (WS2), tungsten diselenide (WSe2), molybdenum disulfide (MoS2), molybdenum ditelluride (MoTe2). Scanning and transmission electron microscopy reveal that etching leads to anisotropic hexagonal features in the studied transition metal dichalcogenides, with the relative degree of anisotropy ranked as: WS2 > WSe2 > MoTe2 / MoS2. Etched holes are terminated by zigzag edges while etched dots (protrusions) are terminated by armchair edges. This can be explained by Wulff constructions, taking the relative stabilities of the edges and the AA stacking order into account. Patterns in WS2 are transferred to an underlying graphite layer, demonstrating a possible use for creating sub-10 nm features. In contrast, multilayer hBN exhibits no lateral anisotropy, but shows consistent vertical etch angles, independent of crystal orientation. This is used to create super-resolution lithographic patterns with ultra-sharp corners at the base of the hBN crystal, which are transferred into an underlying graphite crystal. We find that the anisotropic SF6 reactive ion etching process makes it possible to downsize nanostructures to obtain smooth edges, sharp corners, and feature sizes significantly below the resolution limit of electron beam lithography. The nanostructured 2D materials can be used themselves or as etch-masks to pattern other nanomaterials.

The assembly of individual two-dimensional materials into van der Waals heterostructures enables the construction of layered three-dimensional materials with desirable electronic and optical properties. A core problem in the fabrication of these structures is the formation of clean interfaces between the individual two-dimensional materials which would affect device performance. We present here a technique for the rapid batch fabrication of van der Waals heterostructures, demonstrated by the controlled production of 22 mono-, bi- and trilayer graphene stacks encapsulated in hexagonal boron nitride with close to 100% yield. For the monolayer devices we found semiclassical mean free paths up to 0.9 micrometer, with the narrowest samples showing clear indications of the transport being affected by boundary scattering. The presented method readily lends itself to fabrication of van der Waals heterostructures in both ambient and controlled atmospheres, while the ability to assemble pre-patterned layers paves the way for complex three-dimensional architectures.

Engineering light-matter interactions up to the strong-coupling regime at room temperature is one of the cornerstones of modern nanophotonics. Achieving this goal will enable new platforms for potential applications such as quantum information processing, quantum light sources and even quantum metrology. Materials like transition metal dichalcogenides (TMDC) and in particular tungsten disulfide (WS\\(_2\\)) possess large transition dipole moments comparable to semiconductor-based quantum dots, and strong exciton binding energies allowing the detailed exploration of light-matter interactions at room temperature. Additionally, recent works have shown that coupling TMDCs to plasmonic nanocavities with light tightly focused on the nanometer scale can reach the strong-coupling regime at ambient conditions. Here, we use ultra-thin single-crystalline gold nanodisks featuring large in-plane electromagnetic dipole moments aligned with the exciton transition-dipole moments located in monolayer WS\\(_2\\). Through scattering and reflection spectroscopy we demonstrate strong coupling at room temperature with a Rabi splitting of \\(\\sim\\)108 meV. In order to go further into the strong-coupling regime and inspired by recent experimental work by St\"uhrenberg et al., we couple these nanodisks to multilayer WS\\(_2\\). Due to an increase in the number of excitons coupled to our nanodisks, we achieve a Rabi splitting of \\(\\sim\\)175 meV, a major increase of 62%. To our knowledge, this is the highest Rabi splitting reported for TMDCs coupled to open plasmonic cavities. Our results suggest that ultra-thin single-crystalline gold nanodisks coupled to WS\\(_2\\) represent an exquisite platform to explore light-matter interactions.