Macroscopic self-reorientation of interacting two-dimensional crystals

Modulating electronic structure by interlayer spacing and twist on bilayer bismuthene

Modulation of the electronic structure has played a crucial role in advancing the field of two-dimensional materials, but there are still many unexplored directions, such as the twist angle for a novel degree of freedom, for modulating the properties of heterostructures. We observed a distinct pattern in the energy bands of bilayer bismuthene, demonstrating that modulating the twist angle and interlayer spacing significantly influences interlayer interactions. Our study of various interlayer spacings and twist angles revealed a close relationship between bandgap size and interlayer spacing, while the twist angle notably affects the shape of the energy bands. Furthermore, we observed a synergistic effect between these two factors. As the twist angle decreases, the energy bands become flat, and flat bands can be generated without requiring a specific angle on bilayer bismuthene. Our results suggest a promising way to tailor the energy band structure of bilayer 2D materials by varying the interlayer spacing and twist angle.

Rational Design of Stimuli-Responsive Inorganic 2D Materials via Molecular Engineering: Toward Molecule-Programmable Nanoelectronics

The ability of electronic devices to act as switches makes digital information processing possible. Succeeding graphene, emerging inorganic 2D materials (i2DMs) have been identified as alternative 2D materials to harbor a variety of active molecular components to move the current silicon-based semiconductor technology forward to a post-Moore era focused on molecule-based information processing components. In this regard, i2DMs benefits are not only for their prominent physiochemical properties (e.g., the existence of bandgap), but also for their high surface-to-volume ratio rich in reactive sites. Nonetheless, since this field is still in an early stage, having knowledge of both i) the different strategies for molecularly functionalizing the current library of i2DMs, and ii) the different types of active molecular components is a sine qua non condition for a rational design of stimuli-responsive i2DMs capable of performing logical operations at the molecular level. Consequently, this Review provides a comprehensive tutorial for covalently anchoring ad hoc molecular components-as active units triggered by different external inputs-onto pivotal i2DMs to assess their role in the expanding field of molecule-programmable nanoelectronics for electrically monitoring bistable molecular switches. Limitations, challenges, and future perspectives of this emerging field which crosses materials chemistry with computation are critically discussed.

Tunable 1D van der Waals Nanostructures by Vapor-Liquid-Solid Growth

ConspectusVapor-liquid-solid (VLS) growth using molten metal catalysts has traditionally been used to synthesize nanowires from different 3D-crystalline semiconductors. With their anisotropic structure and properties, 2D/layered semiconductors create additional opportunities for materials design when shaped into 1D nanostructures. In contrast to hexagonal 2D crystals such as graphene, h-BN, and transition metal dichalcogenides, which tend to roll up into nanotubes, VLS growth of layered group III and group IV monochalcogenides produces diverse nanowire and nanoribbon morphologies that crystallize in a bulk-like layered structure with nanometer-scale footprint and lengths exceeding tens of micrometers. In this Account, we discuss the achievable morphologies, the mechanisms governing key structural features, and the emerging functional properties of these 1D van der Waals (vdW) architectures. Recent results highlight rich sets of phenomena that qualify these materials as a distinct class of nanostructures, far beyond a mere extension of 3D-crystalline VLS nanowires to vdW crystals.The main difference between 3D- and vdW crystals, the pronounced in-plane/cross-plane anisotropy of layered materials, motivates investigating the factors governing the layer orientation. Recent research suggests that the VLS catalyst plays a key role, and that its modification via the choice of chalcogens or through modifiers added to the growth precursor can switch both the nanostructure morphology and vdW layering. In many instances, ordinary layered structures are not formed but VLS growth is dominated by morphologies─often containing a crystal defect─that present reduced or vanishing layer nucleation barriers, thus achieving fast growth and emerging as the principal synthesis product. Prominent defect morphologies include vdW bicrystals growing by a twin-plane reentrant process and chiral nanowires formed by spiral growth around an axial screw dislocation. The latter carry particular promise, e.g., for twistronics. In vdW nanowires, Eshelby twist─a progressive crystal rotation caused by the dislocation stress field─translates into interlayer twist that is precisely tunable via the wire diameter. Projected onto a helicoid vdW interface, the resulting twist moirés not only modify the electronic structure but also realize configurations without equivalent in planar systems, such as continuously variable twist and twist homojunctions.1D vdW nanostructures derive distinct functionality from both their layered structure and embedded defects. Correlated electron microscopy methods including imaging, nanobeam diffraction, as well as electron-stimulated local absorption and luminescence spectroscopies combine to an exceptionally powerful probe of this emerging functionality, identifying twist-moiré induced electronic modulations and chiral photonic modes, demonstrating the benign nature of defects in optoelectronics, and uncovering ferroelectricity via symmetry-breaking by single-layer stacking faults in vdW nanowires. Far-reaching possibilities for tuning crystal structure, morphology, and defects create a rich playground for the discovery of new functional nanomaterials based on vdW crystals. Given the prominence of defects and extensive prospects for controlling their character and placement during synthesis, 1D vdW nanostructures have the potential to cause a paradigm shift in the science of electronic materials, replacing the traditional strategy of suppressing crystal imperfections with an alternative philosophy that embraces the use of individual defects with designed properties as drivers of technology.

Controlled alignment of supermoiré lattice in double-aligned graphene heterostructures

The supermoiré lattice, built by stacking two moiré patterns, provides a platform for creating flat mini-bands and studying electron correlations. An ultimate challenge in assembling a graphene supermoiré lattice is in the deterministic control of its rotational alignment, which is made highly aleatory due to the random nature of the edge chirality and crystal symmetry. Employing the so-called "golden rule of three", here we present an experimental strategy to overcome this challenge and realize the controlled alignment of double-aligned hBN/graphene/hBN supermoiré lattice, where the twist angles between graphene and top/bottom hBN are both close to zero. Remarkably, we find that the crystallographic edge of neighboring graphite can be used to better guide the stacking alignment, as demonstrated by the controlled production of 20 moiré samples with an accuracy better than ~ 0.2°. Finally, we extend our technique to low-angle twisted bilayer graphene and ABC-stacked trilayer graphene, providing a strategy for flat-band engineering in these moiré materials.

Twisting Dynamics of Large Lattice-Mismatch van der Waals Heterostructures

van der Waals (vdW) homo/heterostructures are ideal systems for studying interfacial tribological properties such as structural superlubricity. Previous studies concentrated on the mechanism of translational motion in vdW interfaces. However, detailed mechanisms and general properties of the rotational motion are barely explored. Here, we combine experiments and simulations to reveal the twisting dynamics of the MoS₂/graphite heterostructure. Unlike the translational friction falling into the superlubricity regime with no twist angle dependence, the dynamic rotational resistances highly depend on twist angles. Our results show that the periodic rotational resistance force originates from structural potential energy changes during the twisting. The structural potential energy of MoS₂/graphite heterostructure increases monotonically from 0° to 30° twist angles, and the estimated relative energy barrier is (1.43 ± 0.36) × 10^-3 J/m². The formation of Moiré superstructures in the graphene layer is the key to controlling the structural potential energy of the MoS₂/graphene heterostructure. Our results suggest that in twisting 2D heterostructures, even if the interface sliding friction is negligible, the evolving potential energy change results in a nonvanishing rotational resistance force. The structural change of the heterostructure can be an additional pathway for energy dissipation in the rotational motion, further enhancing the rotational friction force.

Nanoscale friction on MoS2/graphene heterostructures

Stacked hetero-structures of two-dimensional materials allow for a design of interactions with corresponding electronic and mechanical properties. We report structure, work function, and frictional properties of 1 to 4 layers of MoS₂ grown by chemical vapor deposition on epitaxial graphene on SiC(0001). Experiments were performed by atomic force microscopy in ultra-high vacuum. Friction is dominated by adhesion which is mediated by a deformation of the layers to adapt the shape of the tip apex. Friction decreases with increasing number of MoS₂ layers as the bending rigidity leads to less deformation. The dependence of friction on applied load and bias voltage can be attributed to variations in the atomic potential corrugation of the interface, which is enhanced by both load and applied bias. Minimal friction is obtained when work function differences are compensated.

The composition and structure of the ubiquitous hydrocarbon contamination on van der Waals materials

The behavior of single layer van der Waals (vdW) materials is profoundly influenced by the immediate atomic environment at their surface, a prime example being the myriad of emergent properties in artificial heterostructures. Equally significant are adsorbates deposited onto their surface from ambient. While vdW interfaces are well understood, our knowledge regarding atmospheric contamination is severely limited. Here we show that the common ambient contamination on the surface of: graphene, graphite, hBN and MoS₂ is composed of a self-organized molecular layer, which forms during a few days of ambient exposure. Using low-temperature STM measurements we image the atomic structure of this adlayer and in combination with infrared spectroscopy identify the contaminant molecules as normal alkanes with lengths of 20-26 carbon atoms. Through its ability to self-organize, the alkane layer displaces the manifold other airborne contaminant species, capping the surface of vdW materials and possibly dominating their interaction with the environment.

Here, the authors attribute the ambient surface contamination of van der Waals materials to a self-organized molecular layer of normal alkanes with lengths of 20-26 carbon atoms. The alkane adlayer displaces the manifold other airborne contaminant species, capping the surface of graphene, graphite, hBN and MoS₂.

Unravelling the electromechanical coupling in a graphene/bulk h-BN heterostructure

The stacking heterostructure of graphene on bulk h-BN produces a moiré pattern with topographic corrugation. The corrugation of the moiré pattern expectantly induces a considerable curvature and a flexoelectric response, which calls for a detailed study. In this work, we used lateral force microscopy, a scanning technique to locally observe the moiré pattern and topographic corrugation. The curvature and flexoelectric potentials are derived from the measured topographic corrugation, revealing a huge curvature of ∼10⁷ m^-1 and a flexoelectric potential of ∼10 mV in the hexagonal domain wall region (∼3-4 nm) of the moiré pattern. In addition, the domain walls of the moiré pattern also generate a clear electromechanical and frictional response, arising from the corrugation-induced flexoelectric response. In summary, the results of this work provide insights into the understanding of the flexoelectricity in the graphene/bulk h-BN and its associated electromechanical coupling behavior in the moiré pattern of a van der Waals stacking heterostructure.

Epitaxy of 2D Materials toward Single Crystals

Two-dimensional (2D) materials exhibit unique electronic, optical, magnetic, mechanical, and thermal properties due to their special crystal structure and thus have promising potential in many fields, such as in electronics and optoelectronics. To realize their real applications, especially in integrated devices, the growth of large-size single crystal is a prerequisite. Up to now, the most feasible way to achieve 2D single crystal growth is the epitaxy: growth of 2D materials of one or more specific orientations with single-crystal substrate. Only when the 2D domains have the same orientation, they can stitch together seamlessly and single-crystal 2D films can be obtained. In this view, four different epitaxy modes of 2D materials on various substrates are presented, including van der Waals epitaxy, edge epitaxy, step-guided epitaxy, and in-plane epitaxy focusing on the growth of graphene, hexagonal boron nitride (h-BN), and transition metal dichalcogenide (TMDC). The lattice symmetry relation and the interaction between 2D materials and the substrate are the key factors determining the epitaxy behaviors and thus are systematically discussed. Finally, the opportunities and challenges about the epitaxy of 2D single crystals in the future are summarized.

Reproducibility in the fabrication and physics of moiré materials

Overlaying two atomic layers with a slight lattice mismatch or at a small rotation angle creates a moiré superlattice, which has properties that are markedly modified from (and at times entirely absent in) the 'parent' materials. Such moiré materials have progressed the study and engineering of strongly correlated phenomena and topological systems in reduced dimensions. The fundamental understanding of the electronic phases, such as superconductivity, requires a precise control of the challenging fabrication process, involving the rotational alignment of two atomically thin layers with an angular precision below 0.1 degrees. Here we review the essential properties of moiré materials and discuss their fabrication and physics from a reproducibility perspective.

Improving the Optical Quality of MoSe2 and WS2 Monolayers with Complete h-BN Encapsulation by High-Temperature Annealing

We improved the optical quality and stability of an exfoliated monolayer (ML) MoSe₂ and chemical vapor deposition (CVD)-grown WS₂ MLs by encapsulating and sealing them with both top and bottom few-layer h-BN, as tested by subsequent high-temperature annealing up to 873 K and photoluminescence (PL) measurements. These transition-metal dichalcogenide (TMD) MLs remained stable up to this maximum temperature, as seen visually. After the heating/cooling cycle, the integrated photoluminescence (PL) intensity at 300 K in the MoSe₂ ML was ∼4 times larger than that before heating and that from exciton and trion PL in the analogous WS₂ ML sample was ∼14 times and ∼2.5 times larger at 77 K and the exciton peak was ∼9.5 times larger at 300 K. This is attributed to the reduction of impurities, the lateral expulsion of contamination leading to clean and atomically flat surfaces, and the sealing provided by the h-BN layers that prevents the diffusion of molecules such as trace O₂ and H₂O to the TMD ML. Stability and optical performance are much improved compared to that in earlier work using top h-BN only, in which the WS₂ ML PL intensity decreased even for an optimal gas environment. This complete encapsulation is particularly promising for CVD-grown TMD MLs because they have relatively more charge and other impurities than do exfoliated MLs. These results open a new route for improving the optical properties of TMD MLs and their performance and applications both at room and higher temperatures.

Unconventional van der Waals heterostructures beyond stacking

Two-dimensional crystals provide exceptional opportunities for integrating dissimilar materials and forming interfaces where distinct properties and phenomena emerge. To date, research has focused on two basic heterostructure types: vertical van der Waals stacks and laterally joined monolayer crystals with in-plane line interfaces. Much more diverse architectures and interface configurations can be realized in the few-layer and multilayer regime, and if mechanical stacking and single-layer growth are replaced by processes taking advantage of self-organization, conversions between polymorphs, phase separation, strain effects, and shaping into the third dimension. Here, we highlight such opportunities for engineering heterostructures, focusing on group IV chalcogenides, a class of layered semiconductors that lend themselves exceptionally well for exploring novel van der Waals architectures, as well as advanced methods including in situ microscopy during growth and nanometer-scale probes of light-matter interactions. The chosen examples point to fruitful future directions and inspire innovative developments to create unconventional van der Waals heterostructures beyond stacking.

Moiré superlattices and related moiré excitons in twisted van der Waals heterostructures

Recent advances in moiré superlattices and moiré excitons, such as quantum emission arrays, low-energy flat bands, and Mott insulators, have rapidly attracted attention in the fields of optoelectronics, materials, and energy research. The interlayer twist turns into a degree of freedom that alters the properties of the systems of materials, and the realization of moiré excitons also offers the feasibility of making artificial exciton crystals. Moreover, moiré excitons exhibit many exciting properties under the regulation of various external conditions, including spatial polarisation, alternating dipolar to alternating dipolar moments and gate-dependence to gate voltage dependence; all are pertinent to their applications in nano-photonics and quantum information. But the lag in theoretical development and the low-efficiency of processing technologies significantly limit the potential of moiré superlattice applications. In this review, we systematically summarise and discuss the recent progress in moiré superlattices and moiré excitons, and analyze the current challenges, and put forward relevant recommendations. There is no doubt that further research will lead to breakthroughs in their application and promote reforms and innovations in traditional solid-state physics and materials science.

Understanding Substrate-Guided Assembly in van der Waals Epitaxy by in Situ Laser Crystallization within a Transmission Electron Microscope

Understanding the bottom-up synthesis of atomically thin two-dimensional (2D) crystals and heterostructures is important for the development of new processing strategies to assemble 2D heterostructures with desired functional properties. Here, we utilize in situ laser-heating within a transmission electron microscope (TEM) to understand the stages of crystallization and coalescence of amorphous precursors deposited by pulsed laser deposition (PLD) as they are guided by 2D crystalline substrates into van der Waals (vdW) epitaxial heterostructures. Amorphous clusters of tungsten selenide were deposited by PLD at room temperature onto graphene or MoSe₂ monolayer crystals that were suspended on TEM grids. The precursors were then stepwise evolved into 2D heterostructures with pulsed laser heating treatments within the TEM. The lattice-matching provided by the MoSe₂ substrate is shown to guide the formation of large-domain, heteroepitaxial vdW WSe₂/MoSe₂ bilayers both during the crystallization process via direct templating and after crystallization by assisting the coalescence of nanosized domains through nonclassical particle attachment processes including domain rotation and grain boundary migration. The favorable energetics for domain rotation induced by lattice matching with the substrate were understood from first-principles calculations. These in situ TEM studies of pulsed laser-driven nonequilibrium crystallization phenomena represent a transformational tool for the rapid exploration of synthesis and processing pathways that may occur on extremely different length and time scales and lend insight into the growth of 2D crystals by PLD and laser crystallization.

Impact of synthesis conditions on the morphology and crystal structure of tungsten nitride nanomaterials

Nanocrystalline tungsten nitride (WN_x) aggregates and nanosheets are synthesized with a new alkylamine-based synthesis strategy for potential applications in nanoelectronics and catalysis. These applications preferentially require crystalline materials with controlled morphology, which has been rarely demonstrated for WN_x nanomaterials in the past. In the synthesis approach presented in this work, the morphology of nanoscale WN_x is controlled by long-chained amines that form lyotropic or lamellar phases depending on the surfactant concentration. The structural and chemical properties of the WN_x nanomaterials are studied in detail using different electron microscopic techniques in combination with electron spectroscopic analyses. Material synthesis and sample preparation for transmission electron microscopy (TEM) were performed in an argon atmosphere (Schlenk line and glovebox). The samples were inserted into the electron microscope via an air-tight TEM transfer holder to protect the material from hydrolysis and oxidation. From the lyotropic phase nanocrystalline WN_x aggregates were obtained, which consist of 2.4 ± 0.8 nm small crystallites of the cubic WN_x phase with a composition of WN_0.7. The lamellar phase with a higher surfactant concentration yields WN_x nanosheets with lateral dimensions up to 500 nm and a mean thickness of 2.1 ± 1.1 nm. The nanosheets are N rich with a composition WN_1.7–3.7 and occur in the hexagonal crystal structure. The nanosheets are often stacked on top of one another with frequent rotations of 4–6° around the hexagonal c axis, thereby forming commensurate interface structures between nanosheets. High stacking-fault densities and signs of nanotwins can be repeatedly observed in WN_x nanosheets.

Nanocrystalline tungsten nitride (WN_x) aggregates and nanosheets are synthesized with a new alkylamine-based synthesis strategy for potential applications in nanoelectronics and catalysis.

Band Engineering of Large-Twist-Angle Graphene/h-BN Moiré Superlattices with Pressure

Graphene interfacing hexagonal boron nitride (h-BN) forms lateral moiré superlattices that host a wide range of new physical effects such as the creation of secondary Dirac points and band gap opening. A delicate control of the twist angle between the two layers is required as the effects weaken or disappear at large twist angles. In this Letter, we show that these effects can be reinstated in large-angle (∼1.8°) graphene/h-BN moiré superlattices under high pressures. A graphene/h-BN moiré superlattice microdevice is fabricated directly on the diamond culet of a diamond anvil cell, where pressure up to 8.3 GPa is applied. The band gap at the primary Dirac point is opened by 40-60 meV, and fingerprints of the second Dirac band gap are also observed in the valence band. Theoretical calculations confirm the band engineering with pressure in large-angle graphene/h-BN bilayers.

Emergence of orbital angular moment at van Hove singularity in graphene/h-BN moiré superlattice

Bloch electrons lacking inversion symmetry exhibit orbital magnetic moments owing to the rotation around their center of mass; this moment induces a valley splitting in a magnetic field. For the graphene/h-BN moiré superlattice, inversion symmetry is broken by the h-BN. The superlattice potential generates a series of Dirac points (DPs) and van Hove singularities (vHSs) within an experimentally accessible low energy state, providing a platform to study orbital moments with respect to band structure. In this work, theoretical calculations and magnetothermoelectric measurements are combined to reveal the emergence of an orbital magnetic moment at vHSs in graphene/h-BN moiré superlattices. The thermoelectric signal for the vHS at the low energy side of the hole-side secondary DP exhibited significant magnetic field-induced valley splitting with an effective g-factor of approximately 130; splitting for other vHSs was negligible. This was attributed to the emergence of an orbital magnetic moment at the second vHS at the hole-side.

Broken mirror symmetry in excitonic response of reconstructed domains in twisted MoSe2/MoSe2 bilayers

Van der Waals heterostructures obtained via stacking and twisting have been used to create moiré superlattices¹, enabling new optical and electronic properties in solid-state systems. Moiré lattices in twisted bilayers of transition metal dichalcogenides (TMDs) result in exciton trapping^2-5, host Mott insulating and superconducting states⁶ and act as unique Hubbard systems^7-9 whose correlated electronic states can be detected and manipulated optically. Structurally, these twisted heterostructures feature atomic reconstruction and domain formation^10-14. However, due to the nanoscale size of moiré domains, the effects of atomic reconstruction on the electronic and excitonic properties have not been systematically investigated. Here we use near-0°-twist-angle MoSe₂/MoSe₂ bilayers with large rhombohedral AB/BA domains¹⁵ to directly probe the excitonic properties of individual domains with far-field optics. We show that this system features broken mirror/inversion symmetry, with the AB and BA domains supporting interlayer excitons with out-of-plane electric dipole moments in opposite directions. The dipole orientation of ground-state Γ-K interlayer excitons can be flipped with electric fields, while higher-energy K-K interlayer excitons undergo field-asymmetric hybridization with intralayer K-K excitons. Our study reveals the impact of crystal symmetry on TMD excitons and points to new avenues for realizing topologically non-trivial systems^16,17, exotic metasurfaces¹⁸, collective excitonic phases¹⁹ and quantum emitter arrays^20,21 via domain-pattern engineering.

Isothermal Growth and Stacking Evolution in Highly Uniform Bernal-Stacked Bilayer Graphene

Controlling the stacking order in bilayer graphene (BLG) allows realizing interesting physical properties. In particular, the possibility of tuning the band gap in Bernal-stacked (AB) BLG (AB-BLG) has a great technological importance for electronic and optoelectronic applications. Most of the current methods to produce AB-BLG suffer from inhomogeneous layer thickness and/or coexistence with twisted BLG. Here, we demonstrate a method to synthesize highly pure large-area AB-BLG by chemical vapor deposition using Cu-Ni films. Increasing the reaction time resulted in a gradual increase of the AB stacking, with the BLG eventually free from twist regions for the longer growth times (99.4% of BLG has AB stacking), due to catalyst-assisted continuous BLG reconstruction driven by carbon dissolution-segregation processes. The band gap opening was confirmed by the electrical measurements on field-effect transistors using two different device configurations. The concept of the continuous reconstruction to achieve highly pure AB-BLG offers a way to control the stacking order of catalytically grown two-dimensional materials.

Direct Observation of Incommensurate-Commensurate Transition in Graphene-hBN Heterostructures via Optical Second Harmonic Generation

Commensurability effects play a crucial role in the formation of electronic properties of novel layered heterostructures. The interest in these moiré superstructures has increased tremendously since the recent observation of a superconducting state (Nature 2018, 556, 43-50) and metal-insulator transition (Nature 2018, 556, 80-84) in twisted bilayer graphene. In this regard, a straightforward and efficient experimental technique for detection of the alignment of layered materials is desired. In this work, we use optical second harmonic generation, which is sensitive to the inversion symmetry breaking, to investigate the alignment of graphene/hexagonal boron nitride heterostructures. To achieve that, we activate a commensurate-incommensurate phase transition by a thermal annealing of the sample. We find that this structural change in the system can be directly observed via a strong modification of a nonlinear optical signal. Unambiguous interpretation of obtained results reveals the potential of a second harmonic generation technique for probing of structural changes in layered systems.

Composite super-moiré lattices in double-aligned graphene heterostructures

When two-dimensional (2D) atomic crystals are brought into close proximity to form a van der Waals heterostructure, neighbouring crystals may influence each other's properties. Of particular interest is when the two crystals closely match and a moiré pattern forms, resulting in modified electronic and excitonic spectra, crystal reconstruction, and more. Thus, moiré patterns are a viable tool for controlling the properties of 2D materials. However, the difference in periodicity of the two crystals limits the reconstruction and, thus, is a barrier to the low-energy regime. Here, we present a route to spectrum reconstruction at all energies. By using graphene which is aligned to two hexagonal boron nitride layers, one can make electrons scatter in the differential moiré pattern which results in spectral changes at arbitrarily low energies. Further, we demonstrate that the strength of this potential relies crucially on the atomic reconstruction of graphene within the differential moiré super cell.

Strain Engineering of 2D Materials: Issues and Opportunities at the Interface

Triggered by the growing needs of developing semiconductor devices at ever-decreasing scales, strain engineering of 2D materials has recently seen a surge of interest. The goal of this principle is to exploit mechanical strain to tune the electronic and photonic performance of 2D materials and to ultimately achieve high-performance 2D-material-based devices. Although strain engineering has been well studied for traditional semiconductor materials and is now routinely used in their manufacturing, recent experiments on strain engineering of 2D materials have shown new opportunities for fundamental physics and exciting applications, along with new challenges, due to the atomic nature of 2D materials. Here, recent advances in the application of mechanical strain into 2D materials are reviewed. These developments are categorized by the deformation modes of the 2D material-substrate system: in-plane mode and out-of-plane mode. Recent state-of-the-art characterization of the interface mechanics for these 2D material-substrate systems is also summarized. These advances highlight how the strain or strain-coupled applications of 2D materials rely on the interfacial properties, essentially shear and adhesion, and finally offer direct guidelines for deterministic design of mechanical strains into 2D materials for ultrathin semiconductor applications.

Bending of Multilayer van der Waals Materials

Out-of-plane deformation patterns, such as buckling, wrinkling, scrolling, and folding, formed by multilayer van der Waals materials have recently seen a surge of interest. One crucial parameter governing these deformations is bending rigidity, on which significant controversy still exists despite extensive research for more than a decade. Here, we report direct measurements of bending rigidity of multilayer graphene, molybdenum disulfide (MoS_{2}), and hexagonal boron nitride (hBN) based on pressurized bubbles. By controlling the sample thickness and bubbling deflection, we observe platelike responses of the multilayers and extract both their Young's modulus and bending rigidity following a nonlinear plate theory. The measured Young's moduli show good agreement with those reported in the literature (E_{graphene}>E_{hBN}>E_{MoS_{2}}), but the bending rigidity follows an opposite trend, D_{graphene}<D_{hBN}<D_{MoS_{2}} for multilayers with comparable thickness, in contrast to the classical plate theory, which is attributed to the interlayer shear effect in the van der Waals materials.

The Princess and the Nanoscale Pea: Long-Range Penetration of Surface Distortions into Layered Materials Stacks

The penetration of moiré out-of-plane distortions, formed at the heterogeneous interface of graphene and hexagonal boron nitride (h-BN), into the layered h-BN stack is investigated. For aligned contacts, the estimated characteristic penetration length of ∼4.7 nm suggests that even at the far surface of a ∼25 h-BN layer thick slab stacked atop the contact, a corrugation of ∼0.1 Å, well within experimental resolution, should still be clearly evident. The penetration length is found to strongly reduce with increasing misalignment angle of the graphene/h-BN junction, where the effect of thermal fluctuations conceals the moiré-induced corrugation in the bulk. These results can be rationalized by continuum elastic theory arguments for anisotropic media. Our findings, which are expected to generally apply for layered heterojunctions, may serve as a route to control the surface corrugation, adhesive properties, and tribological characteristics of two-dimensional materials.

Interlayer Difference of Bilayer-Stacked MoS2 Structure: Probing by Photoluminescence and Raman Spectroscopy

This work reports the interlayer difference of exciton and phonon performance between the top and bottom layer of a bilayer-stacked two-dimensional materials structure (BSS). Through photoluminescence (PL) and Raman spectroscopy, we find that, compared to that of the bottom layer, the top layer of BSS demonstrates PL redshift, Raman E 2 g 1 mode redshift, and lower PL intensity. Spatial inhomogeneity of PL and Raman are also observed in the BSS. Based on theoretical analysis, these exotic effects can be attributed to substrate-coupling-induced strain and doping. Our findings provide pertinent insight into film-substrate interaction, and are of great significance to researches on bilayer-stacked structures including twisted bilayer structure, Van der Waals hetero- and homo-structure.

Strain-Engineering of Twist-Angle in Graphene/hBN Superlattice Devices

The observation of novel physical phenomena such as Hofstadter's butterfly, topological currents, and unconventional superconductivity in graphene has been enabled by the replacement of SiO₂ with hexagonal boron nitride (hBN) as a substrate and by the ability to form superlattices in graphene/hBN heterostructures. These devices are commonly made by etching the graphene into a Hall-bar shape with metal contacts. The deposition of metal electrodes, the design, and specific configuration of contacts can have profound effects on the electronic properties of the devices possibly even affecting the alignment of graphene/hBN superlattices. In this work, we probe the strain configuration of graphene on hBN in contact with two types of metal contacts, two-dimensional (2D) top-contacts and one-dimensional edge-contacts. We show that top-contacts induce strain in the graphene layer along two opposing leads, leading to a complex strain pattern across the device channel. Edge-contacts, on the contrary, do not show such strain pattern. A finite-elements modeling simulation is used to confirm that the observed strain pattern is generated by the mechanical action of the metal contacts clamped to the graphene. Thermal annealing is shown to reduce the overall doping while increasing the overall strain, indicating an increased interaction between graphene and hBN. Surprisingly, we find that the two contact configurations lead to different twist-angles in graphene/hBN superlattices, which converge to the same value after thermal annealing. This observation confirms the self-locking mechanism of graphene/hBN superlattices also in the presence of strain gradients. Our experiments may have profound implications in the development of future electronic devices based on heterostructures and provide a new mechanism to induce complex strain patterns in 2D materials.

Accurate Gap Determination in Monolayer and Bilayer Graphene/ h-BN Moiré Superlattices

High mobility single and few-layer graphene sheets are in many ways attractive as nanoelectronic circuit hosts but lack energy gaps, which are essential to the operation of field-effect transistors. One of the methods used to create gaps in the spectrum of graphene systems is to form long period moiré patterns by aligning the graphene and hexagonal boron nitride ( h-BN) substrate lattices. Here, we use planar tunneling devices with thin h-BN barriers to obtain direct and accurate tunneling spectroscopy measurements of the energy gaps in single-layer and bilayer graphene- h-BN superlattice structures at charge neutrality (first Dirac point) and at integer moiré band occupancies (second Dirac point, SDP) as a function of external electric and magnetic fields and the interface twist angle. In single-layer graphene, we find, in agreement with previous work, that gaps are formed at neutrality and at the hole-doped SDP, but not at the electron-doped SDP. Both primary and secondary gaps can be determined accurately by extrapolating Landau fan patterns to a zero magnetic field and are as large as ≈17 meV for devices in near-perfect alignment. For bilayer graphene, we find that gaps occur only at charge neutrality where they can be modified by an external electric field.

Structural superlubricity and ultralow friction across the length scales

Structural superlubricity, a state of ultralow friction and wear between crystalline surfaces, is a fundamental phenomenon in modern tribology that defines a new approach to lubrication. Early measurements involved nanometre-scale contacts between layered materials, but recent experimental advances have extended its applicability to the micrometre scale. This is an important step towards practical utilization of structural superlubricity in future technological applications, such as durable nano- and micro-electromechanical devices, hard drives, mobile frictionless connectors, and mechanical bearings operating under extreme conditions. Here we provide an overview of the field, including its birth and main achievements, the current state of the art and the challenges to fulfilling its potential.

Twistable electronics with dynamically rotatable heterostructures

In heterostructures of two-dimensional materials, electronic properties can vary dramatically with relative interlayer angle. This effect makes it theoretically possible to realize a new class of twistable electronics in which properties can be manipulated on demand by means of rotation. We demonstrate a device architecture in which a layered heterostructure can be dynamically twisted in situ. We study graphene encapsulated by boron nitride, where, at small rotation angles, the device characteristics are dominated by coupling to a long-wavelength moiré superlattice. The ability to investigate arbitrary rotation angle in a single device reveals features of the optical, mechanical, and electronic response in this system not captured in static rotation studies. Our results establish the capability to fabricate twistable electronic devices with dynamically tunable properties.

Nanoscale liquid crystal lubrication controlled by surface structure and film composition

Liquid crystals have emerged as potential candidates for next-generation lubricants due to their tendency to exhibit long-range ordering. Here, we construct a full atomistic model of 4-cyano-4-hexylbiphenyl (6CB) nematic liquid crystal lubricants mixed with hexane and confined by mica surfaces. We explore the effect of the surface structure of mica, as well as lubricant composition and thickness, on the nanoscale friction in the system. Our results demonstrate the key role of the structure of the mica surfaces, specifically the positions of potassium (K+) ions, in determining the nature of sliding friction with monolayer lubricants, including the presence or absence of stick-slip dynamics. With the commensurate setup of confining surfaces, when the grooves created between the periodic K+ ions are parallel to the sliding direction we observe a lower friction force as compared to the perpendicular situation. Random positions of ions exhibit even smaller friction forces with respect to the previous two cases. For thicker lubrication layers the surface structure becomes less important and we observe a good agreement with the experimental data on bulk viscosity of 6CB and the additive hexane. In case of thicker lubrication layers, friction may still be controlled by tuning the relative concentrations of 6CB and hexane in the mixture.

Optical Imaging and Spectroscopic Characterization of Self-Assembled Environmental Adsorbates on Graphene

Topographic studies using scanning probes have found that graphene surfaces are often covered by micron-scale domains of periodic stripes with a 4 nm pitch. These stripes have been variously interpreted as structural ripples or as self-assembled adsorbates. We show that the stripe domains are optically anisotropic by imaging them using a polarization-contrast technique. Optical spectra between 1.1 and 2.8 eV reveal that the anisotropy in the in-plane dielectric function is predominantly real, reaching 0.6 for an assumed layer thickness of 0.3 nm. The spectra are incompatible with a rippled graphene sheet but would be quantitatively explained by the self-assembly of chainlike organic molecules into nanoscale stripes.

Synthesis, structure and applications of graphene-based 2D heterostructures

With the profuse amount of two-dimensional (2D) materials discovered and the improvements in their synthesis and handling, the field of 2D heterostructures has gained increased interest in recent years. Such heterostructures not only overcome the inherent limitations of each of the materials, but also allow the realization of novel properties by their proper combination. The physical and mechanical properties of graphene mean it has a prominent place in the area of 2D heterostructures. In this review, we will discuss the evolution and current state in the synthesis and applications of graphene-based 2D heterostructures. In addition to stacked and in-plane heterostructures with other 2D materials and their potential applications, we will also cover heterostructures realized with lower dimensionality materials, along with intercalation in few-layer graphene as a special case of a heterostructure. Finally, graphene heterostructures produced using liquid phase exfoliation techniques and their applications to energy storage will be reviewed.

Emergence of Interfacial Polarons from Electron-Phonon Coupling in Graphene/h-BN van der Waals Heterostructures

van der Waals heterostructures, vertical stacks of layered materials, offer new opportunities for novel quantum phenomena which are absent in their constituent components. Here we report the emergence of polaron quasiparticles at the interface of graphene/hexagonal boron nitride (h-BN) heterostructures. Using nanospot angle-resolved photoemission spectroscopy, we observe zone-corner replicas of h-BN valence band maxima, with energy spacing coincident with the highest phonon energy of the heterostructure, an indication of Fröhlich polaron formation due to forward-scattering electron-phonon coupling. Parabolic fitting of the h-BN bands yields an effective mass enhancement of ∼2.3, suggesting an intermediate coupling strength. Our theoretical simulations based on Migdal-Eliashberg theory corroborate the experimental results, allowing the extraction of microscopic physical parameters. Moreover, renormalization of graphene π-band is observed due to the hybridization with the h-BN band. Our work generalizes the polaron study from transition metal oxides to van der Waals heterostructures with higher material flexibility, highlighting interlayer coupling as an extra degree of freedom to explore emergent phenomena.

Greatly Enhanced Anticorrosion of Cu by Commensurate Graphene Coating

Metal corrosion is a long-lasting problem in history and ultrahigh anticorrosion is one ultimate pursuit in the metal-related industry. Graphene, in principle, can be a revolutionary material for anticorrosion due to its excellent impermeability to any molecule or ion (except for protons). However, in real applications, it is found that the metallic graphene forms an electrochemical circuit with the protected metals to accelerate the corrosion once the corrosive fluids leaks into the interface. Therefore, whether graphene can be used as an excellent anticorrosion material is under intense debate now. Here, graphene-coated Cu is employed to investigate the facet-dependent anticorrosion of metals. It is demonstrated that as-grown graphene can protect Cu(111) surface from oxidation in humid air lasting for more than 2.5 years, in sharp contrast with the accelerated oxidation of graphene-coated Cu(100) surface. Further atomic-scale characterization and ab initio calculations reveal that the strong interfacial coupling of the commensurate graphene/Cu(111) prevents H₂ O diffusion into the graphene/Cu(111) interface, but the one-dimensional wrinkles formed in the incommensurate graphene on Cu(100) can facilitate the H₂ O diffusion at the interface. This study resolves the contradiction on the anticorrosion capacity of graphene and opens a new opportunity for ultrahigh metal anticorrosion through commensurate graphene coating.

Sliding friction of graphene/hexagonal -boron nitride heterojunctions: a route to robust superlubricity

The origin of ultra-low friction exhibited by heterogeneous junctions of graphene and hexagonal boron nitride (h-BN) is revealed. For aligned interfaces, we identify a characteristic contact size, below which the junction behaves like its homogeneous counterparts with friction forces that grow linearly with the contact area. Superlubricity sets in due to the progressive appearance of Moiré patterns resulting in a collective stick-slip motion of the elevated super-structure ridges that turns into smooth soliton-like gliding with increasing contact size. Incommensurability effects are enhanced in misaligned contacts, where the friction coefficients further drop by orders of magnitude. Our fully atomistic simulations show that the superlubric regime in graphene/h-BN heterostructures persists up to significantly higher loads compared to the well-studied twisted homogeneous graphene interface. This indicates the potential of achieving robust superlubricity in practical applications using two-dimensional layered materials heterojunctions.

Wafer-Scale Single-Crystalline AB-Stacked Bilayer Graphene

Single-crystalline artificial AB-stacked bilayer graphene is formed by aligned transfer of two single-crystalline monolayers on a wafer-scale. The obtained bilayer has a well-defined interface and is electronically equivalent to exfoliated or direct-grown AB-stacked bilayers.

Lévy Flights due to Anisotropic Disorder in Graphene

We study transport properties of graphene with anisotropically distributed on-site impurities (adatoms) that are randomly placed on every third line drawn along carbon bonds. We show that stripe states characterized by strongly suppressed backscattering are formed in this model in the direction of the lines. The system reveals Lévy-flight transport in the stripe direction such that the corresponding conductivity increases as the square root of the system length. Thus, adding this type of disorder to clean graphene near the Dirac point strongly enhances the conductivity, which is in stark contrast with a fully random distribution of on-site impurities, which leads to Anderson localization. The effect is demonstrated both by numerical simulations using the Kwant code and by an analytical theory based on the self-consistent T-matrix approximation.