Universal classification of twisted, strained and sheared graphene moiré superlattices

Structure of Graphene Grown on Cu(111): X-Ray Standing Wave Measurement and Density Functional Theory Prediction

We report the quantitative adsorption structure of pristine graphene on Cu(111) determined using the normal incidence x-ray standing wave technique. The experiments constitute an important benchmark reference for the development of density functional theory approximations able to capture long-range dispersion interactions. Electronic structure calculations based on many-body dispersion-inclusive density functional theory are able to accurately predict the absolute measure and variation of adsorption height when the coexistence of multiple moiré superstructures is considered. This provides a structural model consistent with scanning probe microscopy results.

A weakened Fermi level pinning induced adsorption energy non-charge-transfer mechanism during O2 adsorption in silicene/graphene heterojunctions

Understanding the mechanisms of gas adsorption on a solid surface and making this process tunable are of great significance in fundamental science and industrial applications. Bond creation and charge transfer are often used to explain the origin of adsorption energy (Ead). However, in this study, a new mechanism is observed in O2 adsorption on pure silicene (PS) and silicene/graphene heterojunction (SGH) surfaces, in which the charge distribution remains almost unchanged, but Ead still has a significant change in the order of 0.3 eV. The weakened Fermi level pinning effect is found to be responsible for this interesting behavior and the variation of Ead is approximately equal to the change of work function. Furthermore, this effect is independent of the twist angles in the van der Waals SGH. Our results are consistent with experimental observations in overcoming the degradation of silicene in air.

High-throughput ab initio design of atomic interfaces using InterMatch

Forming a hetero-interface is a materials-design strategy that can access an astronomically large phase space. However, the immense phase space necessitates a high-throughput approach for an optimal interface design. Here we introduce a high-throughput computational framework, InterMatch, for efficiently predicting charge transfer, strain, and superlattice structure of an interface by leveraging the databases of individual bulk materials. Specifically, the algorithm reads in the lattice vectors, density of states, and the stiffness tensors for each material in their isolated form from the Materials Project. From these bulk properties, InterMatch estimates the interfacial properties. We benchmark InterMatch predictions for the charge transfer against experimental measurements and supercell density-functional theory calculations. We then use InterMatch to predict promising interface candidates for doping transition metal dichalcogenide MoSe2. Finally, we explain experimental observation of factor of 10 variation in the supercell periodicity within a few microns in graphene/α-RuCl3 by exploring low energy superlattice structures as a function of twist angle using InterMatch. We anticipate our open-source InterMatch algorithm accelerating and guiding ever-growing interfacial design efforts. Moreover, the interface database resulting from the InterMatch searches presented in this paper can be readily accessed online.

Giant Atomic Swirl in Graphene Bilayers with Biaxial Heterostrain

The study of moiré engineering started with the advent of van der Waals heterostructures, in which stacking 2D layers with different lattice constants leads to a moiré pattern controlling their electronic properties. The field entered a new era when it was found that adjusting the twist between two graphene layers led to strongly-correlated-electron physics and topological effects associated with atomic relaxation. A twist is now routinely used to adjust the properties of 2D materials. This study investigates a new type of moiré superlattice in bilayer graphene when one layer is biaxially strained with respect to the other-so-called biaxial heterostrain. Scanning tunneling microscopy measurements uncover spiraling electronic states associated with a novel symmetry-breaking atomic reconstruction at small biaxial heterostrain. Atomistic calculations using experimental parameters as inputs reveal that a giant atomic swirl forms around regions of aligned stacking to reduce the mechanical energy of the bilayer. Tight-binding calculations performed on the relaxed structure show that the observed electronic states decorate spiraling domain wall solitons as required by topology. This study establishes biaxial heterostrain as an important parameter to be harnessed for the next step of moiré engineering in van der Waals multilayers.

Growth mechanisms of monolayer hexagonal boron nitride (h-BN) on metal surfaces: theoretical perspectives

Two-dimensional hexagonal boron nitride (h-BN) has appeared as a promising material in diverse areas of applications, including as an excellent substrate for graphene devices, deep-ultraviolet emitters, and tunneling barriers, thanks to its outstanding stability, flat surface, and wide-bandgap. However, for achieving such exciting applications, controllable mass synthesis of high-quality and large-scale h-BN is a precondition. The synthesis of h-BN on metal surfaces using chemical vapor deposition (CVD) has been extensively studied, aiming to obtain large-scale and high-quality materials. The atomic-scale growth process, which is a prerequisite for rationally optimizing growth circumstances, is a key topic in these investigations. Although theoretical investigations on h-BN growth mechanisms are expected to reveal numerous new insights and understandings, different growth methods have completely dissimilar mechanisms, making theoretical research extremely challenging. In this article, we have summarized the recent cutting-edge theoretical research on the growth mechanisms of h-BN on different metal substrates. On the frequently utilized Cu substrate, h-BN development was shown to be more challenging than a simple adsorption-dehydrogenation-growth scenario. Controlling the number of surface layers is also an important challenge. Growth on the Ni surface is controlled by precipitation. An unusual reaction-limited aggregation growth behavior has been seen on interfaces having a significant lattice mismatch to h-BN. With intensive theoretical investigations employing advanced simulation approaches, further progress in understanding h-BN growth processes is predicted, paving the way for guided growth protocol design.

Two-Way Twisting of a Confined Monolayer: Orientational Ordering within the van der Waals Gap between Graphene and Its Crystalline Substrate

Two-dimensional confinement of lattices produces a variety of order and disorder phenomena. When the confining walls have atomic granularity, unique structural phases are expected, of relevance in nanotribology, porous materials, or intercalation compounds where, e.g., electronic states can emerge accordingly. The interlayer's own order is frustrated by the competing interactions exerted by the two confining surfaces. We revisit the concept of orientational ordering, introduced by Novaco and McTague to describe the twist of incommensurate monolayers on crystalline surfaces. We predict a two-way twist of the monolayer as its density increases. We discover such a behavior in alkali atom monolayers (sodium, cesium) confined between graphene and an iridium surface, using scanning tunneling microscopy and electron diffraction.

Heterostrain Determines Flat Bands in Magic-Angle Twisted Graphene Layers

The moiré of twisted graphene bilayers can generate flat bands in which charge carriers do not possess enough kinetic energy to escape Coulomb interactions with each other, leading to the formation of novel strongly correlated electronic states. This exceptionally rich physics relies on the precise arrangement between the layers. Here, we survey published scanning tunneling microscope measurements to prove that near the magic-angle, native heterostrain, the relative deformations between the layers, dominates twist in determining the flat bands as opposed to the common belief. This is demonstrated at full filling where electronic correlations have a weak effect and where we also show that tip-induced strain can have a strong influence. In the opposite situation of zero doping, we find that electronic correlation further renormalizes the flat bands in a way that strongly depends on experimental details.

Mapping Modified Electronic Levels in the Moiré Patterns in MoS2/WSe2 Using Low-Loss EELS

Hybrid/moiré interlayer and intralayer excitons have been realized in twisted two-dimensional transition metal chalcogenides (2D-TMD) due to variation in local moiré potential within a moiré supercell. Though moiré excitons have been detected in TMD heterostructures by macroscopic spectroscopic techniques, their spatial distribution is experimentally unknown. In the present work, using high-resolution scanning transmission electron microscopy (STEM) and electron energy-loss spectroscopy (EELS), we explore the effect of the twist angle in MoS₂/WSe₂ heterostructures. We observe weak interaction between the layers at higher twist angles (>5°) and stronger interaction for lower twist angles. The optical response of the heterostructure varies within the moiré supercell, with a lower energy absorption peak appearing in regions with the AA stacking.

Method for the Manual Analysis of Moiré Structures in STM images

A method is presented to manually determine the lattice parameters of commensurate hexagonal moiré structures resolved by STM. It solves the problem that lattice parameters of moiré structures usually cannot be determined by inspection of an STM image, so that computer-based analyses are required. The lattice vector of a commensurate moiré structure is a sum of integer multiples both of the two basis vectors of the substrate and of the adsorbed layer. The method extracts the two factors with respect to the adsorbed layer from an analysis of the Fourier transform of an STM image. These two factors are related to the two factors with respect to the substrate layer. Using the cell augmentation method, six possible moiré structures are identified by algebra. When the orientation and lattice constant of the substrate are roughly known, this information is usually sufficient to determine a unique moiré structure and its lattice parameters.

On the propagation of Dirac fermions in graphene with strain-induced inhomogeneous Fermi velocity

We consider systems described by a two-dimensional Dirac equation where the Fermi velocity is inhomogeneous as a consequence of mechanical deformations. We show that the mechanical deformations can lead to deflection and focusing of the wave packets. The analogy with known reflectionless quantum systems is pointed out. Furthermore, with the use of the qualitative spectral analysis, we discuss how inhomogeneous strains can be used to create waveguides for valley polarized transport of partially dispersionless wave packets.

Temperature-Controlled Rotational Epitaxy of Graphene

When graphene is placed on a crystalline surface, the periodic structures within the layers superimpose and moiré superlattices form. Small lattice rotations between the two materials in contact strongly modify the moiré lattice parameter, upon which many electronic, vibrational, and chemical properties depend. While precise adjustment of the relative orientation in the degree- and sub-degree-range can be achieved via careful deterministic transfer of graphene, we report on the spontaneous reorientation of graphene on a metallic substrate, Ir(111). We find that selecting a substrate temperature between 1530 and 1000 K during the growth of graphene leads to distinct relative rotational angles of 0°, ± 0.6°, ±1.1°, and ±1.7°. When modeling the moiré superlattices as two-dimensional coincidence networks, we can ascribe the observed rotations to favorable low-strain graphene structures. The dissimilar thermal expansion of the substrate and graphene is regarded as an effective compressive biaxial pressure that is more easily accommodated in graphene by small rotations rather than by compression.

Characterisation of graphene electrodes for microsystems and microfluidic devices

Fabrication of microsystems is traditionally achieved with photolithography. However, this fabrication technique can be expensive and non-ideal for integration with microfluidic systems. As such, graphene fabrication is explored as an alternative. This graphene fabrication can be achieved with graphite oxide undergoing optical exposure, using optical disc drives, to impose specified patterns and convert to graphene. This work characterises such a graphene fabrication, and provides fabrication, electrical, microfluidic, and scanning electron microscopy (SEM) characterisations. In the fabrication characterisation, a comparison is performed between traditional photolithography fabrication and the new graphene fabrication. (Graphene fabrication details are also provided.) Here, the minimum achievable feature size is identified and graphene fabrication is found to compare favourably with traditional photolithography fabrication. In the electrical characterisation, the resistivity of graphene is measured as a function of fabrication dose in the optical disc drive and saturation effects are noted. In the microfluidic characterisation, the wetting properties of graphene are shown through an investigation of the contact angle of a microdroplet positioned on a surface that is treated with varying fabrication dose. In the SEM characterisation, the observed effects in the previous characterisations are attributed to chemical or physical effects through measurement of SEM energy dispersive X-ray spectra and SEM images, respectively. Overall, graphene fabrication is revealed to be a viable option for development of microsystems and microfluidics.

Tailoring sample-wide pseudo-magnetic fields on a graphene-black phosphorus heterostructure

Spatially tailored pseudo-magnetic fields (PMFs) can give rise to pseudo-Landau levels and the valley Hall effect in graphene. At an experimental level, it is highly challenging to create the specific strain texture that can generate PMFs over large areas. Here, we report that superposing graphene on multilayer black phosphorus creates shear-strained superlattices that generate a PMF over an entire graphene-black phosphorus heterostructure with edge size of tens of micrometres. The PMF is intertwined with the spatial period of the moiré pattern, and its spatial distribution and intensity can be modified by changing the relative orientation of the two materials. We show that the emerging pseudo-Landau levels influence the transport properties of graphene-black phosphorus field-effect transistor devices with Hall bar geometry. The application of an external magnetic field allows us to enhance or reduce the effective field depending on the valley polarization with the prospect of developing a valley filter.

Size-Selective Carbon Clusters as Obstacles to Graphene Growth on a Metal

Chemical vapor deposition (CVD) on metals is so far the best suited method to produce high-quality, large-area graphene. We discovered an unprecedentedly large family of small size-selective carbon clusters that form together with graphene during CVD. Using scanning tunneling microscopy (STM) and density functional theory (DFT), we unambiguously determine their atomic structure. For that purpose, we use grids based on a graphene moiré and a dilute atomic lattice that unambiguously reveal the binding geometry of the clusters. We find that the observed clusters bind in metastable configurations on the substrate, while the thermodynamically stable configurations are not observed. We argue that the clusters are formed under kinetic control and establish that the evolution of the smallest clusters is blocked. They are hence products of surface reactions in competition with graphene growth, rather than intermediary species to the formation of extended graphene, as often assumed in the literature. We expect such obstacles to the synthesis of perfect graphene to be ubiquitous on a variety of metallic surfaces.

Dirac electrons in a dodecagonal graphene quasicrystal

Quantum states of quasiparticles in solids are dictated by symmetry. We have experimentally demonstrated quantum states of Dirac electrons in a two-dimensional quasicrystal without translational symmetry. A dodecagonal quasicrystalline order was realized by epitaxial growth of twisted bilayer graphene rotated exactly 30°. We grew the graphene quasicrystal up to a millimeter scale on a silicon carbide surface while maintaining the single rotation angle over an entire sample and successfully isolated the quasicrystal from a substrate, demonstrating its structural and chemical stability under ambient conditions. Multiple Dirac cones replicated with the 12-fold rotational symmetry were observed in angle-resolved photoemission spectra, which revealed anomalous strong interlayer coupling with quasi-periodicity. Our study provides a way to explore physical properties of relativistic fermions with controllable quasicrystalline orders.

Electronic Spectrum of Twisted Graphene Layers under Heterostrain

We demonstrate that stacking layered materials allows a strain engineering where each layer is strained independently, which we call heterostrain. We combine detailed structural and spectroscopic measurements with tight-binding calculations to show that small uniaxial heterostrain suppresses Dirac cones and leads to the emergence of flat bands in twisted graphene layers (TGLs). Moreover, we demonstrate that heterostrain reconstructs, much more severely, the energy spectrum of TGLs than homostrain for which both layers are strained identically, a result which should apply to virtually all van der Waals structures opening exciting possibilities for straintronics with 2D materials.

Corrugation in the Weakly Interacting Hexagonal-BN/Cu(111) System: Structure Determination by Combining Noncontact Atomic Force Microscopy and X-ray Standing Waves

Atomically thin hexagonal boron nitride (h-BN) layers on metallic supports represent a promising platform for the selective adsorption of atoms, clusters, and molecular nanostructures. Specifically, scanning tunneling microscopy (STM) studies revealed an electronic corrugation of h-BN/Cu(111), guiding the self-assembly of molecules and their energy level alignment. A detailed characterization of the h-BN/Cu(111) interface including the spacing between the h-BN sheet and its support-elusive to STM measurements-is crucial to rationalize the interfacial interactions within these systems. To this end, we employ complementary techniques including high-resolution noncontact atomic force microscopy, STM, low-energy electron diffraction, X-ray photoelectron spectroscopy, the X-ray standing wave method, and density functional theory. Our multimethod study yields a comprehensive, quantitative structure determination including the adsorption height and the corrugation of the sp² bonded h-BN layer on Cu(111). Based on the atomic contrast in atomic force microscopy measurements, we derive a measurable-hitherto unrecognized-geometric corrugation of the h-BN monolayer. This experimental approach allows us to spatially resolve minute height variations in low-dimensional nanostructures, thus providing a benchmark for theoretical modeling. Regarding potential applications, e.g., as a template or catalytically active support, the recognition of h-BN on Cu(111) as a weakly bonded and moderately corrugated overlayer is highly relevant.

Electronic and optical properties of strained graphene and other strained 2D materials: a review

This review presents the state of the art in strain and ripple-induced effects on the electronic and optical properties of graphene. It starts by providing the crystallographic description of mechanical deformations, as well as the diffraction pattern for different kinds of representative deformation fields. Then, the focus turns to the unique elastic properties of graphene, and to how strain is produced. Thereafter, various theoretical approaches used to study the electronic properties of strained graphene are examined, discussing the advantages of each. These approaches provide a platform to describe exotic properties, such as a fractal spectrum related with quasicrystals, a mixed Dirac-Schrödinger behavior, emergent gravity, topological insulator states, in molecular graphene and other 2D discrete lattices. The physical consequences of strain on the optical properties are reviewed next, with a focus on the Raman spectrum. At the same time, recent advances to tune the optical conductivity of graphene by strain engineering are given, which open new paths in device applications. Finally, a brief review of strain effects in multilayered graphene and other promising 2D materials like silicene and materials based on other group-IV elements, phosphorene, dichalcogenide- and monochalcogenide-monolayers is presented, with a brief discussion of interplays among strain, thermal effects, and illumination in the latter material family.

Preferential Alignment of Incommensurate Block Copolymer Dot Arrays Forming Moiré Superstructures

Block copolymer (BCP) self-assembly is of great interest as a cost-effective method for large-scale, high-resolution nanopattern fabrication. Directed self-assembly can induce long-range order and registration, reduce defect density, and enable access to patterns of higher complexity. Here we demonstrate preferential orientation of two incommensurate BCP dot arrays. A bottom layer of hexagonal silica dots is prepared via typical self-assembly from a PS-b-PDMS block copolymer. Self-assembly of a second, or top, layer of a different PS-b-PDMS block copolymer that forms a hexagonal dot pattern with different periodicity results in a predictable moiré superstructure. Four distinct moiré superstructures were demonstrated through a combination of different BCPs and different order of annealing. The registration force of the bottom layer of hexagonal dots is sufficient to direct the self-assembly of the top layer to adopt a preferred relative angle of rotation. Large-area helium ion microscopy imaging enabled quantification of the distributions of relative rotations between the two lattices in the moiré superstructures, yielding statistically meaningful results for each combination. It was also found that if the bottom layer dots were too large, the resulting moiré pattern was lost. A small reduction in the bottom layer dot size, however, resulted in large-area moiré superstructures, suggesting a specific size regime where interlayer registration forces can induce long-range preferential alignment of incommensurate BCP dot arrays.

Growth of two dimensional silica and aluminosilicate bilayers on Pd(111): from incommensurate to commensurate crystalline

2D silicate lattice strain energy was significantly reduced by Al-doping resulting in a structural transition from incommensurate to commensurate crystalline.

1,3,5-Benzenetribenzoic Acid on Cu(111) and Graphene/Cu(111): A Comparative STM Study

The self-assembly of 1,3,5-benzenetribenzoic acid (BTB) molecules on both Cu(111) and epitaxial graphene grown on Cu(111) were studied by scanning tunneling microscopy (STM) and low-energy electron diffraction (LEED) under ultrahigh vacuum conditions. On Cu(111), the BTB molecules were found to mainly arrange in close-packed structures through H-bonding between the (partially) deprotonated carboxylic acid groups. In addition, porous structures formed by intact BTB molecules-and also based on H-bonding-were observed. On graphene grown on Cu(111) the BTB molecules mainly form porous structures accompanied by small patches of disordered close-packed structures. Upon annealing, BTB adsorbed on Cu(111) is fully deprotonated and arranges in the close-packed structure while in contrast on graphene/Cu(111) the porous network is exclusively formed. This shows that the molecular self-assembly behavior is highly dependent on the first substrate layer: one graphene layer is sufficient to considerably alter the interplay of molecule substrate and intermolecular interactions in favor of the latter interactions.