"Dead" Exciton Layer and Exciton Anisotropy of Bulk MoS2 Extracted from Optical Measurements.

Excitons (electron-hole pairs bound by the Coulomb potential) play an important role in optical and electronic properties of layered materials. They can be used to modulate light with high frequencies due to the optical Pauli blocking. The properties of excitons in 2D materials are extremely anisotropic. However, due to nanometre sizes of excitons and their short life times, reliable tools to study this anisotropy are lacking. Here, we show how direct optical reflection measurements can be used to evaluate anisotropy of excitons in transition metal dichalcogenides MoS2. Using focused beam spectroscopic ellipsometry, we have measured the polarized optical reflection of bulk MoS2 for two crystal orientations: c-axis being perpendicular to the surface from which reflection is measured and c-axis being parallel to the surface from which reflection is measured. We found that for the parallel configuration the optical reflection near excitonic transitions is strongly affected by the presence of the exciton "dead" layer such that the excitonic reflection peaks become the excitonic dips due to light interference. At the same time, the optical reflection for the perpendicular orientation is not significantly altered by the exciton "dead" layer due to large anisotropy of exciton properties. Performing simultaneous Fresnel fitting for both geometries, we were able to evaluate exciton anisotropy in layered materials from simple optical measurements.

Out-of-equilibrium criticalities in graphene superlattices.

In thermodynamic equilibrium, current in metallic systems is carried by electronic states near the Fermi energy, whereas the filled bands underneath contribute little to conduction. Here, we describe a very different regime in which carrier distribution in graphene and its superlattices is shifted so far from equilibrium that the filled bands start playing an essential role, leading to a critical-current behavior. The criticalities develop upon the velocity of electron flow reaching the Fermi velocity. Key signatures of the out-of-equilibrium state are current-voltage characteristics that resemble those of superconductors, sharp peaks in differential resistance, sign reversal of the Hall effect, and a marked anomaly caused by the Schwinger-like production of hot electron-hole plasma. The observed behavior is expected to be common to all graphene-based superlattices.

Visualizing atomic structure and magnetism of 2D magnetic insulators via tunneling through graphene.

The discovery of two-dimensional (2D) magnetism combined with van der Waals (vdW) heterostructure engineering offers unprecedented opportunities for creating artificial magnetic structures with non-trivial magnetic textures. Further progress hinges on deep understanding of electronic and magnetic properties of 2D magnets at the atomic scale. Although local electronic properties can be probed by scanning tunneling microscopy/spectroscopy (STM/STS), its application to investigate 2D magnetic insulators remains elusive due to absence of a conducting path and their extreme air sensitivity. Here we demonstrate that few-layer CrI3 (FL-CrI3) covered by graphene can be characterized electronically and magnetically via STM by exploiting the transparency of graphene to tunneling electrons. STS reveals electronic structures of FL-CrI3 including flat bands responsible for its magnetic state. AFM-to-FM transition of FL-CrI3 can be visualized through the magnetic field dependent moiré contrast in the dI/dV maps due to a change of the electronic hybridization between graphene and spin-polarised CrI3 bands with different interlayer magnetic coupling. Our findings provide a general route to probe atomic-scale electronic and magnetic properties of 2D magnetic insulators for future spintronics and quantum technology applications.

Mechanical Properties of Atomically Thin Tungsten Dichalcogenides: WS2, WSe2, and WTe2.

Two-dimensional (2D) tungsten disulfide (WS2), tungsten diselenide (WSe2), and tungsten ditelluride (WTe2) draw increasing attention due to their attractive properties deriving from the heavy tungsten and chalcogenide atoms, but their mechanical properties are still mostly unknown. Here, we determine the intrinsic and air-aged mechanical properties of mono-, bi-, and trilayer (1-3L) WS2, WSe2, and WTe2 using a complementary suite of experiments and theoretical calculations. High-quality 1L WS2 has the highest Young's modulus (302.4 ± 24.1 GPa) and strength (47.0 ± 8.6 GPa) of the entire family, overpassing those of 1L WSe2 (258.6 ± 38.3 and 38.0 ± 6.0 GPa, respectively) and WTe2 (149.1 ± 9.4 and 6.4 ± 3.3 GPa, respectively). However, the elasticity and strength of WS2 decrease most dramatically with increased thickness among the three materials. We interpret the phenomenon by the different tendencies for interlayer sliding in an equilibrium state and under in-plane strain and out-of-plane compression conditions in the indentation process, revealed by the finite element method and density functional theory calculations including van der Waals interactions. We also demonstrate that the mechanical properties of the high-quality 1-3L WS2 and WSe2 are largely stable in air for up to 20 weeks. Intriguingly, the 1-3L WSe2 shows increased modulus and strength values with aging in the air. This is ascribed to oxygen doping, which reinforces the structure. The present study will facilitate the design and use of 2D tungsten dichalcogenides in applications such as strain engineering and flexible field-effect transistors.

Two-dimensional adaptive membranes with programmable water and ionic channels.

Membranes are ubiquitous in nature with primary functions that include adaptive filtering and selective transport of chemical/molecular species. Being critical to cellular functions, they are also fundamental in many areas of science and technology. Of particular importance are the adaptive and programmable membranes that can change their permeability or selectivity depending on the environment. Here, we explore implementation of such biological functions in artificial membranes and demonstrate two-dimensional self-assembled heterostructures of graphene oxide and polyamine macromolecules, forming a network of ionic channels that exhibit regulated permeability of water and monovalent ions. This permeability can be tuned by a change of pH or the presence of certain ions. Unlike traditional membranes, the regulation mechanism reported here relies on specific interactions between the membranes' internal components and ions. This allows fabrication of membranes with programmable, predetermined permeability and selectivity, governed by the choice of components, their conformation and their charging state.

Long-range ballistic transport of Brown-Zak fermions in graphene superlattices.

In quantizing magnetic fields, graphene superlattices exhibit a complex fractal spectrum often referred to as the Hofstadter butterfly. It can be viewed as a collection of Landau levels that arise from quantization of Brown-Zak minibands recurring at rational (p/q) fractions of the magnetic flux quantum per superlattice unit cell. Here we show that, in graphene-on-boron-nitride superlattices, Brown-Zak fermions can exhibit mobilities above 106 cm2 V-1 s-1 and the mean free path exceeding several micrometers. The exceptional quality of our devices allows us to show that Brown-Zak minibands are 4q times degenerate and all the degeneracies (spin, valley and mini-valley) can be lifted by exchange interactions below 1 K. We also found negative bend resistance at 1/q fractions for electrical probes placed as far as several micrometers apart. The latter observation highlights the fact that Brown-Zak fermions are Bloch quasiparticles propagating in high fields along straight trajectories, just like electrons in zero field.

Holographic reconstruction of the interlayer distance of bilayer two-dimensional crystal samples from their convergent beam electron diffraction patterns.

The convergent beam electron diffraction (CBED) patterns of twisted bilayer samples exhibit interference patterns in their CBED spots. Such interference patterns can be treated as off-axis holograms and the phase of the scattered waves, meaning the interlayer distance can be reconstructed. A detailed protocol of the reconstruction procedure is provided in this study. In addition, we derive an exact formula for reconstructing the interlayer distance from the recovered phase distribution, which takes into account the different chemical compositions of the individual monolayers. It is shown that one interference fringe in a CBED spot is sufficient to reconstruct the distance between the layers, which can be practical for imaging samples with a relatively small twist angle or when probing small sample regions. The quality of the reconstructed interlayer distance is studied as a function of the twist angle. At smaller twist angles, the reconstructed interlayer distance distribution is more precise and artefact free. At larger twist angles, artefacts due to the moiré structure appear in the reconstruction. A method for the reconstruction of the average interlayer distance is presented. As for resolution, the interlayer distance can be reconstructed by the holographic approach at an accuracy of ±0.5 Å, which is a few hundred times better than the intrinsic z-resolution of diffraction limited resolution, as expressed through the spread of the measured k-values. Moreover, we show that holographic CBED imaging can detect variations as small as 0.1 Å in the interlayer distance, though the quantitative reconstruction of such variations suffers from large errors.

Convergent beam electron diffraction of multilayer Van der Waals structures.

Convergent beam electron diffraction is routinely applied for studying deformation and local strain in thick crystals by matching the crystal structure to the observed intensity distributions. Recently, it has been demonstrated that CBED can be applied for imaging two-dimensional (2D) crystals where a direct reconstruction is possible and three-dimensional crystal deformations at a nanometre resolution can be retrieved. Here, we demonstrate that second-order effects allow for further information to be obtained regarding stacking arrangements between the crystals. Such effects are especially pronounced in samples consisting of multiple layers of 2D crystals. We show, using simulations and experiments, that twisted multilayer samples exhibit extra modulations of interference fringes in CBED patterns, i. e., a CBED moiré. A simple and robust method for the evaluation of the composition and the number of layers from a single-shot CBED pattern is demonstrated.

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.

Engineering Graphene Flakes for Wearable Textile Sensors via Highly Scalable and Ultrafast Yarn Dyeing Technique.

Multifunctional wearable e-textiles have been a focus of much attention due to their great potential for healthcare, sportswear, fitness, space, and military applications. Among them, electroconductive textile yarn shows great promise for use as next-generation flexible sensors without compromising the properties and comfort of usual textiles. However, the current manufacturing process of metal-based electroconductive textile yarn is expensive, unscalable, and environmentally unfriendly. Here we report a highly scalable and ultrafast production of graphene-based flexible, washable, and bendable wearable textile sensors. We engineer graphene flakes and their dispersions in order to select the best formulation for wearable textile application. We then use a high-speed yarn dyeing technique to dye (coat) textile yarn with graphene-based inks. Such graphene-based yarns are then integrated into a knitted structure as a flexible sensor and could send data wirelessly to a device via a self-powered RFID or a low-powered Bluetooth. The graphene textile sensor thus produced shows excellent temperature sensitivity, very good washability, and extremely high flexibility. Such a process could potentially be scaled up in a high-speed industrial setup to produce tonnes (∼1000 kg/h) of electroconductive textile yarns for next-generation wearable electronics applications.

Author Correction: Planar and van der Waals heterostructures for vertical tunnelling single electron transistors.

The original version of this Article contained an error in the spelling of the author Matthew Holwill, which was incorrectly given as Mathew Holwill. This has now been corrected in both the PDF and HTML versions of the Article.

Planar and van der Waals heterostructures for vertical tunnelling single electron transistors.

Despite a rich choice of two-dimensional materials, which exists these days, heterostructures, both vertical (van der Waals) and in-plane, offer an unprecedented control over the properties and functionalities of the resulted structures. Thus, planar heterostructures allow p-n junctions between different two-dimensional semiconductors and graphene nanoribbons with well-defined edges; and vertical heterostructures resulted in the observation of superconductivity in purely carbon-based systems and realisation of vertical tunnelling transistors. Here we demonstrate simultaneous use of in-plane and van der Waals heterostructures to build vertical single electron tunnelling transistors. We grow graphene quantum dots inside the matrix of hexagonal boron nitride, which allows a dramatic reduction of the number of localised states along the perimeter of the quantum dots. The use of hexagonal boron nitride tunnel barriers as contacts to the graphene quantum dots make our transistors reproducible and not dependent on the localised states, opening even larger flexibility when designing future devices.

Convergent beam electron holography for analysis of van der Waals heterostructures.

The van der Waals heterostructures, which explore the synergetic properties of 2D materials when assembled into 3D stacks, have already brought to life a number of exciting phenomena and electronic devices. Still, the interaction between the layers in such assembly, possible surface reconstruction, and intrinsic and extrinsic defects are very difficult to characterize by any method, because of the single-atomic nature of the crystals involved. Here we present a convergent beam electron holographic technique which allows imaging of the stacking order in such heterostructures. Based on the interference of electron waves scattered on different crystals in the stack, this approach allows one to reconstruct the relative rotation, stretching, and out-of-plane corrugation of the layers with atomic precision. Being holographic in nature, our approach allows extraction of quantitative information about the 3D structure of the typical defects from a single image covering thousands of square nanometers. Furthermore, qualitative information about the defects in the stack can be extracted from the convergent diffraction patterns even without reconstruction, simply by comparing the patterns in different diffraction spots. We expect that convergent beam electron holography will be widely used to study the properties of van der Waals heterostructures.