Theory of Moiré Magnetism in Twisted Bilayer α-RuCl3

Motivated by the recent developments in moiré superlattices of van der Waals magnets and the desire to control the magnetic interactions of α-RuCl3, here we present a comprehensive theory of the long-range ordered magnetic phases of twisted bilayer α-RuCl3. Using a combination of first-principles calculations and atomistic simulations, we show that the stacking-dependent interlayer exchange gives rise to an array of magnetic phases that can be realized by controlling the twist angle. In particular, we discover a complex hexagonal domain structure in which multiple zigzag orders coexist. This multidomain order minimizes the interlayer energy while enduring the energy cost due to domain wall formation. Further, we show that quantum fluctuations can be enhanced across the phase transitions. Our results indicate that magnetic frustration due to stacking-dependent interlayer exchange in moiré superlattices can be exploited to tune quantum fluctuations and the magnetic ground state of α-RuCl3.

Moiré-Pattern Modulated Electronic Structures of GaSe/HOPG Heterostructure

Conventional two-dimensional electron gas (2DEG) typically occurs at the interface of semiconductor heterostructures and noble metal surfaces, but it is scarcely observed in individual 2D semiconductors. In this study, few-layer gallium selenide (GaSe) grown on highly ordered pyrolytic graphite (HOPG) is demonstrated using scanning tunneling microscopy and spectroscopy (STM/STS), revealing that the coexistence of quantum well states (QWS) and 2DEG. The QWS are located in the valence bands and exhibit a peak feature, with the number of quantum wells being equal to the number of atomic layers. Meanwhile, the 2DEG is located in the conduction bands and exhibits a standing-wave feature. Additionally, monolayer GaSe/HOPG heterostructures with different stacking angles (0°, 33°, 8°) form distinct moiré patterns that arise from lattice mismatch and angular rotation between adjacent atomic layers in 2D materials, which effectively modulate the electron effective mass, charge redistribution, and band gap of GaSe. Overall, this work reveals a paradigm of band engineering based on layer numbers and moiré patterns that can modulate the electronic properties of 2D materials.

Atomic Resolution Imaging of Highly Air-Sensitive Monolayer and Twisted-Bilayer WTe2

Bulk Td-WTe2 is a semimetal, while its monolayer counterpart is a two-dimensional (2D) topological insulator. Recently, electronic transport resembling a Luttinger liquid state was found in twisted-bilayer WTe2 (tWTe2) with a twist angle of ∼5°. Despite the strong interest in 2D WTe2 systems, little experimental information is available about their intrinsic microstructure, leaving obstacles in modeling their physical properties. The monolayer, and consequently tWTe2, are highly air-sensitive, and therefore, probing their atomic structures is difficult. In this study, we develop a robust method for atomic-resolution visualization of monolayers and tWTe2 obtained through mechanical exfoliation and fabrication. We confirm the high crystalline quality of mechanically exfoliated WTe2 samples and observe that tWTe2 with twist angles of ∼5 and ∼2° retains its pristine moiré structure without substantial deformations or reconstructions. The results provide a structural foundation for future electronic modeling of monolayer and tWTe2 moiré lattices.

Tailoring the Angular Mismatch in MoS2 Homobilayers through Deformation Fields

Ultrathin MoS₂ has shown remarkable characteristics at the atomic scale with an immutable disorder to weak external stimuli. Ion beam modification unlocks the potential to selectively tune the size, concentration, and morphology of defects produced at the site of impact in 2D materials. Combining experiments, first-principles calculations, atomistic simulations, and transfer learning, it is shown that irradiation-induced defects can induce a rotation-dependent moiré pattern in vertically stacked homobilayers of MoS₂ by deforming the atomically thin material and exciting surface acoustic waves (SAWs). Additionally, the direct correlation between stress and lattice disorder by probing the intrinsic defects and atomic environments are demonstrated. The method introduced in this paper sheds light on how engineering defects in the lattice can be used to tailor the angular mismatch in van der Waals (vdW) solids.

Learning Moiré Pattern Elimination in Both Frequency and Spatial Domains for Image Demoiréing

Recently, with the rapid development of mobile sensing technology, capturing scene information by mobile sensing devices in the form of images or videos has become a prevalent recording method. However, the moiré pattern phenomenon may occur when the scene contains digital screens or regular strips, which greatly degrade the visual performance and image quality. In this paper, considering the complexity and diversity of moiré patterns, we propose a novel end-to-end image demoiré method, which can learn moiré pattern elimination in both the frequency and spatial domains. To be specific, in the frequency domain, considering the signal energy of moiré pattern is widely distributed in the frequency, we introduce a wavelet transform to decompose the multi-scale image features, which can help the model identify the moiré features more precisely to suppress them effectively. On the other hand, we also design a spatial domain demoiré block (SDDB). The SDDB module can extract moiré features from the mixed features, then subtract them to obtain clean image features. The combination of the frequency domain and the spatial domain enhances the model's ability in terms of moiré feature recognition and elimination. Finally, extensive experiments demonstrate the superior performance of our proposed method to other state-of-the-art methods. The Grad-CAM results in our ablation study fully indicate the effectiveness of the two proposed blocks in our method.

Observation of Coexisting Dirac Bands and Moiré Flat Bands in Magic-Angle Twisted Trilayer Graphene

Moiré superlattices that consist of two or more layers of 2D materials stacked together with a small twist angle have emerged as a tunable platform to realize various correlated and topological phases, such as Mott insulators, unconventional superconductivity, and quantum anomalous Hall effect. Recently, magic-angle twisted trilayer graphene (MATTG) has shown both robust superconductivity similar to magic-angle twisted bilayer graphene and other unique properties, including the Pauli-limit violating and re-entrant superconductivity. These rich properties are deeply rooted in its electronic structure under the influence of distinct moiré potential and mirror symmetry. Here, combining nanometer-scale spatially resolved angle-resolved photoemission spectroscopy and scanning tunneling microscopy/spectroscopy, the as-yet unexplored band structure of MATTG near charge neutrality is systematically measured. These measurements reveal the coexistence of the distinct dispersive Dirac band with the emergent moiré flat band, showing nice agreement with the theoretical calculations. These results serve as a stepstone for further understanding of the unconventional superconductivity in MATTG.

Dirac Fermion Cloning, Moiré Flat Bands, and Magic Lattice Constants in Epitaxial Monolayer Graphene

Tuning interactions between Dirac states in graphene has attracted enormous interest because it can modify the electronic spectrum of the 2D material, enhance electron correlations, and give rise to novel condensed-matter phases such as superconductors, Mott insulators, Wigner crystals, and quantum anomalous Hall insulators. Previous works predominantly focus on the flat band dispersion of coupled Dirac states from different twisted graphene layers. In this work, a new route to realizing flat band physics in monolayer graphene under a periodic modulation from substrates is proposed. Graphene/SiC heterostructure is taken as a prototypical example and it is demonstrated experimentally that the substrate modulation leads to Dirac fermion cloning and, consequently, the proximity of the two Dirac cones of monolayer graphene in momentum space. Theoretical modeling captures the cloning mechanism of the Dirac states and indicates that moiré flat bands can emerge at certain magic lattice constants of the substrate, specifically when the period of modulation becomes nearly commensurate with the ( 3   ×   3 ) R 30 o \[(\sqrt 3 \; \times \;\sqrt 3 )R{30^o}\] supercell of graphene. The results show that epitaxial single monolayer graphene on suitable substrates is a promising platform for exploring exotic many-body quantum phases arising from interactions between Dirac electrons.

Moiré-Induced Vibrational Coupling in Double-Walled Carbon Nanotubes

Moiré patterns are additional, long-range periodicities in twisted crystalline bilayers. They are known to fundamentally change the electronic states of the layers, but similar effects on their mechanical and vibrational properties have not been discussed so far. Here we show that the moiré potential shifts the radial breathing mode in double-walled carbon nanotubes (DWCNTs). The change in frequency is expected to be proportional to the shift in optical transition energies, which are induced by the moiré patterns. To verify our model, we performed resonance Raman scattering on purified and sorted semiconducting DWCNTs. We find that the radial breathing mode shifts up to 14 cm^-1 higher in energy followed by displacement of optical transition energies of up to 200 meV to lower energies, in comparison to the single-walled tubes. We show how to identify the strong coupling condition in DWCNTs from their phonon frequencies and construct a Kataura plot to aid their future experimental assignment.

Moiré Skyrmions and Chiral Magnetic Phases in Twisted CrX3 (X = I, Br, and Cl) Bilayers

We present a comprehensive theory of the magnetic phases in twisted bilayer chromium trihalides through a combination of first-principles calculations and atomistic simulations. We show that the stacking-dependent interlayer exchange leads to an effective moiré field that is mostly ferromagnetic with antiferromagnetic patches. A wide range of noncollinear magnetic phases can be stabilized as a function of the twist angle and Dzyaloshinskii-Moriya interaction as a result of the competing interlayer antiferromagnetic coupling and the energy cost for forming domain walls. In particular, we demonstrate that for small twist angles various skyrmion crystal phases can be stabilized in both CrI₃ and CrBr₃. Our results provide an interpretation for the recent observation of noncollinear magnetic phases in twisted bilayer CrI₃ and demonstrate the possibility of engineering further nontrivial magnetic ground states in twisted bilayer chromium trihalides.

Moiré-Potential-Induced Band Structure Engineering in Graphene and Silicene

A moiré pattern results from the projection of one periodic pattern to another with relative lattice constant or misalignment and provides great periodic potential to modify the electronic properties of pristine materials. In this Review, recent research on the effect of the moiré superlattice on the electronic structures of graphene and silicene, both of which possess a honeycomb lattice, is focused on. The moiré periodic potential is introduced by the interlayer interaction to realize abundant phenomena, including new generation of Dirac cones, emergence of Van Hove singularities (vHs) at the cross point of two sets of Dirac cones, Mott-like insulating behavior at half-filling state, unconventional superconductivity, and electronic Kagome lattice and flat band with nontrivial edge state. The role of interlayer coupling strength, which is determined by twist angle and buckling degree, in these exotic properties is discussed in terms of both the theoretical prediction and experimental measurement, and finally, the challenges and outlook for this field are discussed.

Intrinsic Defects in MoS2 Grown by Pulsed Laser Deposition: From Monolayers to Bilayers

Pulsed laser deposition (PLD) can be considered a powerful method for the growth of two-dimensional (2D) transition-metal dichalcogenides (TMDs) into van der Waals heterostructures. However, despite significant progress, the defects in 2D TMDs grown by PLD remain largely unknown and yet to be explored. Here, we combine atomic resolution images and first-principles calculations to reveal the atomic structure of defects, grains, and grain boundaries in mono- and bilayer MoS₂ grown by PLD. We find that sulfur vacancies and Mo_S antisites are the predominant point defects in 2D MoS₂. We predict that the aforementioned point defects are thermodynamically favorable under a Mo-rich/S-poor environment. The MoS₂ monolayers are polycrystalline and feature nanometer size grains connected by a high density of grain boundaries. In particular, the coalescence of nanometer grains results in the formation of 180° mirror twin boundaries consisting of distinct 4- and 8-membered rings. We show that PLD synthesis of bilayer MoS₂ results in various structural symmetries, including AA' and AB, but also turbostratic with characteristic moiré patterns. Moreover, we report on the experimental demonstration of an electron beam-driven transition between the AB and AA' stacking orientations in bilayer MoS₂. These results provide a detailed insight into the atomic structure of monolayer MoS₂ and the role of the grain boundaries on the growth of bilayer MoS₂, which has importance for future applications in optoelectronics.

High-Performance Ultrathin Active Chiral Metamaterials

Ultrathin active chiral metamaterials with dynamically tunable and responsive optical chirality enable new optical sensors, modulators, and switches. Herein, we develop ultrathin active chiral metamaterials of highly tunable chiroptical responses by inducing tunable near-field coupling in the metamaterials and exploit the metamaterials as ultrasensitive sensors to detect trace amounts of solvent impurities. To demonstrate the active chiral metamaterials mediated by tunable near-field coupling, we design moiré chiral metamaterials (MCMs) as model metamaterials, which consist of two layers of identical Au nanohole arrays stacked upon one another in moiré patterns with a dielectric spacer layer between the Au layers. Our simulations, analytical fittings, and experiments reveal that spacer-dependent near-field coupling exists in the MCMs, which significantly enhances the spectral shift and line shape change of the circular dichroism (CD) spectra of the MCMs. Furthermore, we use a silk fibroin thin film as the spacer layer in the MCM. With the solvent-controllable swelling of the silk fibroin thin films, we demonstrate actively tunable near-field coupling and chiroptical responses of the silk-MCMs. Impressively, we have achieved the spectral shift over a wavelength range that is more than one full width at half-maximum and the sign inversion of the CD spectra in a single ultrathin (1/5 of wavelength in thickness) MCM. Finally, we apply the silk-MCMs as ultrasensitive sensors to detect trace amounts of solvent impurities down to 200 ppm, corresponding to an ultrahigh sensitivity of >10⁵ nm/refractive index unit (RIU) and a figure of merit of 10⁵/RIU.

Heterogeneous Pyrolysis: A Route for Epitaxial Growth of hBN Atomic Layers on Copper Using Separate Boron and Nitrogen Precursors

Growth of hBN on metal substrates is often performed via chemical vapor deposition from a single precursor (e.g., borazine) and results in hBN monolayers limited by the substrates catalyzing effect. Departing from this paradigm, we demonstrate close control over the growth of mono-, bi-, and trilayers of hBN on copper using triethylborane and ammonia as independent sources of boron and nitrogen. Using density functional theory (DFT) calculations and reactive force field molecular dynamics, we show that the key factor enabling the growth beyond the first layer is the activation of ammonia through heterogeneous pyrolysis with boron-based radicals at the surface. The hBN layers grown are in registry with each other and assume a perfect or near perfect epitaxial relation with the substrate. From atomic force microscopy (AFM) characterization, we observe a moiré superstructure in the first hBN layer with an apparent height modulation and lateral periodicity of ∼10 nm. While this is unexpected given that the moiré pattern of hBN/Cu(111) does not have a significant morphological corrugation, our DFT calculations reveal a spatially modulated interface dipole layer which determines the unusual AFM response. These findings have improved our understanding of the mechanisms involved in growth of hBN and may help generate new growth methods for applications in which control over the number of layers and their alignment is crucial (such as tunneling barriers, ultrathin capacitors, and graphene-based devices).

Laterally Ordered Sub-10 nm Features Obtained From Directed Self-Assembly of Si-Containing Block Copolymer Thin Films

Laterally ordered sub-10 nm features are produced from the directed self-assembly of poly(1,1-dimethyl silacyclo-butane)-block-poly(methyl methacrylate) (PDMSB-b-PMMA) thin films on sinusoidal azobenzene-containing patterns. The use of sinusoidal surface relief grating enables the formation of very large grain areas (over several µm(2) ) consisting of out-of-plane PMMA cylinders.