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Topologically derived dislocation theory for twist and stretch moiré superlattices in bilayer graphene

In this work, we develop a continuum dislocation description of twist and stretch moiré superlattices in two-dimensional material bilayers. The continuum formulation is based on the topological constraints introduced by the periodic dislocation network associated with the moiré structure. The approach is based on solving analytically for the structural distortion and displacement fields that satisfy the topological constraints and that minimize the total energy. The total energy is described by both the strain energy of each individual distorted layer and a Peierls-Nabarro-like interfacial contribution arising from stacking disregistry. The dislocation core emerges naturally within the formalism as a result of the competition between the two contributions. The approach presented here captures the structure and energetics of twist and stretch moiré superlattices of dislocations with arbitrary direction and character, without assuming an analytical solution a priori and while accounting naturally for dislocation-dislocation image interactions. In comparisons to atomistic simulations using classical potentials, the maximum structure deviation is 6%, while the maximum line energy deviation is 0.019 eV/Å. Several applications of our model are shown, including predicting the variation of structure with twist angle and describing dislocation line tension and junction energies.

36 MATERIALS SCIENCE↗

Thermodynamic Stability and Site‐Specific Distribution of Graphitic and Pyridinic Nitrogen in Graphene Moiré on Ru(0001)

Abstract Graphene‐like materials are of interest for large‐scale hydrogen storage applications due to their lightweight, durable, and scalable properties. Nitrogen‐doping minimizes kinetic limitations in diffusion and recombination on surfaces, however, the role of graphitic nitrogen (GN) and pyridinic nitrogen (PN) is not well understood. Nitrogen‐doped graphene is synthesized on Ru(0001) using chemical vapor deposition (CVD) of pyridine and ion irradiation. Scanning tunneling microscopy (STM), x‐ray photoelectron spectroscopy (XPS), and density functional theory (DFT) are used to identify the structure, location, and thermodynamic stability of nitrogen species within the graphene moiré. CVD of pyridine results in a low nitrogen concentration (<0.1at%), while the post‐growth nitrogen ion irradiation allows us to increase the concentration further. The concentration of GN and PN is controlled by varying the ion dose and annealing temperature. Comparison of measured and simulated STM images of GN and PN yield an excellent agreement, allowing us to confidently establish that GN is preferentially located near the center of the Atop region, while PN is located in the valley region of the graphene moiré. This report explicitly confirms the site assignments and provides a foundation for the site synthesis and analysis of structural and electronic properties that drive the reactivity of N‐doped graphene.

Gedara, Buddhika S. A. [Physical and Computational↗

Moiré engineering in van der Waals heterostructures

Isolated atomic planes can be assembled into a multilayer van der Waals (vdW) heterostructure in a precisely chosen sequence. These heterostructures feature moiré patterns if the constituent 2D material layers are stacked in an incommensurable way, due to a lattice mismatch or twist. This design-by-stacking has opened up the promising area of moiré engineering, a term that can be understood in two different perspectives, namely, (i) structural—engineering a moiré pattern by introducing twist, relative strain, or defects that affect the commensurability of the layers and (ii) functional—exploiting a moiré pattern to find and tune resulting physical properties of a vdW heterostructure. The latter meaning, referring to the application of a moiré pattern, is seen in the literature in the specific context of the observation of correlated electronic states and unconventional superconductivity in twisted bilayer graphene. The former meaning, referring to the design of the moiré pattern itself, is present in the literature but less commonly discussed or less understood. The underlying link between these two perspectives lies in the deformation field of the moiré superlattice. In this Perspective, we describe a path from designing a moiré pattern to employing the moiré pattern to tune physical properties of a vdW heterostructure. We also discuss the concept of moiré engineering in the context of twistronics, strain engineering, and defect engineering in vdW heterostructures. Although twistronics is always associated with moiré superlattices, strain and defect engineering are often not. Here, in this work, we demonstrate how strain and defect engineering can be understood within the context of moiré engineering. Adopting this perspective, we note that moiré engineering creates a compelling opportunity to design and develop multiscale electronic devices.

2D materials↗

Edge-Confined Excitons in Monolayer Black Phosphorus

Quantum confinement of two-dimensional excitons in van der Waals materials via electrostatic trapping, lithographic patterning, Moiré potentials, and chemical implantation has enabled significant advances in tailoring light emission from nanostructures. While such approaches rely on complex preparation of materials, natural edges are a ubiquitous feature in layered materials and provide a different approach for investigating quantum-confined excitons. Here, we observe that certain edge sites of monolayer black phosphorus (BP) strongly localize the intrinsic quasi-one-dimensional excitons, yielding sharp spectral lines in photoluminescence, with nearly an order of magnitude line width reduction. Through structural characterization of BP edges using transmission electron microscopy and first-principles GW plus Bethe–Salpeter equation (GW-BSE) calculations of exemplary BP nanoribbons, we find that certain atomic reconstructions can strongly quantum-confine excitons resulting in distinct emission features, mediated by local strain and screening. Here we observe linearly polarized luminescence emission from edge reconstructions that preserve the mirror symmetry of the parent BP lattice, in agreement with calculations. Furthermore, we demonstrate efficient electrical switching of localized edge excitonic luminescence, whose sites act as excitonic transistors for emission. Localized emission from BP edges motivates exploration of nanoribbons and quantum dots as hosts for tunable narrowband light generation, with future potential to create atomic-like structures for quantum information processing applications as well as exploration of exotic phases that may reside in atomic edge structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Polarization-driven band topology evolution in twisted MoTe 2 and WSe 2

Motivated by recent experimental observations of opposite Chern numbers in R-type twisted MoTe 2 and WSe 2 homobilayers, we perform large-scale density-functional-theory calculations with machine learning force fields to investigate moiré band topology across a range of twist angles in both materials. We find that the Chern numbers of the moiré frontier bands change sign as a function of twist angle, and this change is driven by the competition between moiré ferroelectricity and piezoelectricity. Our large-scale calculations, enabled by machine learning methods, reveal crucial insights into interactions across different scales in twisted bilayer systems. The interplay between atomic-level relaxation effects and moiré-scale electrostatic potential variation opens new avenues for the design of intertwined topological and correlated states, including the possibility of mimicking higher Landau level physics in the absence of magnetic field.

36 MATERIALS SCIENCE↗

Magnetism and metallicity in moiré transition metal dichalcogenides

The ability to control the properties of twisted bilayer transition metal dichalcogenides in situ makes them an ideal platform for investigating the interplay of strong correlations and geometric frustration. Of particular interest are the low energy scales, which make it possible to experimentally access both temperature and magnetic fields that are of the order of the bandwidth or the correlation scale. In this manuscript, we analyze the moiré Hubbard model, believed to describe the low energy physics of an important subclass of the twisted bilayer compounds. We establish its magnetic and the metal–insulator phase diagram for the full range of magnetic fields up to the fully spin-polarized state. We find a rich phase diagram including fully and partially polarized insulating and metallic phases of which we determine the interplay of magnetic order, Zeeman-field, and metallicity, and make connection to recent experiments.

36 MATERIALS SCIENCE↗

Correlated insulating states at fractional fillings of the WS 2 /WSe 2 moiré lattice

Moiré superlattices of van der Waals materials, such as twisted graphene and transitional metal dichalcogenides, have recently emerged as a fascinating platform to study strongly correlated states in two dimensions (2D), thanks to the strong electron interaction in the moiré minibands. In most systems, the correlated states appear when the moiré lattice is filled by integer number of electrons per moiré unit cell. Recently, correlated states at fractional fillings of 1/3 and 2/3 holes per moiré unit cell has been reported in the WS 2 /WSe 2 heterobilayer, hinting the long range nature of the electron interaction. In this work, employing a scanning microwave impedance microscopy technique that is sensitive to local electrical properties, we observe a series of correlated insulating states at fractional fillings of the moiré minibands on both electron- and hole-doped sides in angle-aligned WS 2 /WSe 2 hetero-bilayers, with certain states persisting at temperatures up to 120 K. Monte Carlo simulations reveal that these insulating states correspond to ordering of electrons in the moiré lattice with a periodicity much larger than the moiré unit cell, indicating a surprisingly strong and long-range interaction beyond the nearest neighbors. Our findings usher in unprecedented opportunities in the study of strongly correlated states in two dimensions.

36 MATERIALS SCIENCE↗

Lithography-Defined Semiconductor Moirés with Anomalous In-Gap Quantum Hall States

Quantum materials and phenomena have attracted great interest for their potential applications in next-generation microelectronics and quantum-information technologies. In one especially interesting class of quantum materials, moiré superlattices (MSLs) formed by twisted bilayers of 2D materials, a wide range of novel phenomena are observed. However, there exist daunting challenges such as reproducibility and scalability of utilizing 2D MSLs for microelectronics and quantum technologies due to their exfoliate-tear-stack method. Here, we propose lithography-defined semiconductor MSLs, in which three fundamental parameters electron−electron interaction, spin−orbit coupling, and band topology are designable. We experimentally investigate quantum-transport properties in a moiré specimen made in an InAs quantum well. Strong anomalous in-gap states are observed within the same integer quantum Hall state. Our work opens up new horizons for studying 2D quantum-materials phenomena in semiconductors featuring superior industry-level quality and state-of-the-art technologies, and they may potentially enable new quantum-information and microelectronics technologies.

36 MATERIALS SCIENCE↗

Signatures of moiré trions in WSe 2 /MoSe 2 heterobilayers

Moiré superlattices formed by van der Waals materials can support a wide range of electronic phases, including Mott insulators superconductors and generalized Wigner crystals2. When excitons are confined by a moiré superlattice, a new class of exciton emerges, which holds promise for realizing artificial excitonic crystals and quantum optical effects. When such moiré excitons are coupled to charge carriers, correlated states may arise. However, no experimental evidence exists for charge-coupled moiré exciton states, nor have their properties been predicted by theory. In this work, we report the optical signatures of trions coupled to the moiré potential in tungsten diselenide/molybdenum diselenide heterobilayers. The moiré trions show multiple sharp emission lines with a complex charge-density dependence, in stark contrast to the behaviour of conventional trions. We infer distinct contributions to the trion emission from radiative decay in which the remaining carrier resides in different moiré minibands. Variation of the trion features is observed in different devices and sample areas, indicating high sensitivity to sample inhomogeneity and variability. The observation of these trion features motivates further theoretical and experimental studies of higher-order electron correlation effects in moiré superlattices.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Large moiré superstructure of stacked incommensurate charge density waves

This article reports how two different charge density waves with slightly different wavevectors can exist in the same crystal and create moiré superstructure. Advances in heterostructure fabrication have opened new frontiers in moiré physics. Here we extend moiré engineering from artificially assembled thin flakes with mismatched lattice parameters to materials that host incommensurate orders, presenting a long-period moiré superlattice in a layered charge-density-wave compound, EuTe 4 . Using high-momentum-resolution X-ray diffraction, we found two coexisting incommensurate charge density waves with slightly mismatched in-plane wavevectors. The interaction between these two charge density waves leads to joint commensuration with the lattice and a moiré superstructure with a period of ~13.6 nm, offering key insights into the unique properties of EuTe4, such as the temperature-invariant incommensurate wavevectors and unconventional in-gap states. Owing to interlayer phase shifts, the moiré superstructure exhibits a clear thermal hysteresis, accounting for the large hysteresis in electrical resistivity and numerous metastable states. Our findings open new directions for moiré engineering based on incommensurate lattices and highlight the important role of interlayer ordering in stacked structures.

36 MATERIALS SCIENCE↗

Light Confinement in Twisted Single-Layer 2D+ Moiré Photonic Crystals and Bilayer Moiré Photonic Crystals

Twisted photonic crystals are photonic analogs of twisted monolayer materials such as graphene and their optical property studies are still in their infancy. This paper reports optical properties of twisted single-layer 2D+ moiré photonic crystals where there is a weak modulation in z direction, and bilayer moiré-overlapping-moiré photonic crystals. In weak-coupling bilayer moiré-overlapping-moiré photonic crystals, the light source is less localized with an increasing twist angle, similar to the results reported by the Harvard research group in References 37 and 38 on twisted bilayer photonic crystals, although there is a gradient pattern in the former case. In a strong-coupling case, however, the light source is tightly localized in AA-stacked region in bilayer PhCs with a large twist angle. For single-layer 2D+ moiré photonic crystals, the light source in Ex polarization can be localized and forms resonance modes when the single-layer 2D+ moiré photonic crystal is integrated on a glass substrate. This study leads to a potential application of 2D+ moiré photonic crystal in future on-chip optoelectronic integration.

36 MATERIALS SCIENCE↗

Helical dislocation in twisted bilayer graphene

Here, we observe helical dislocation network in twisted bilayer graphene (tBLG), which is accompanied by large out-of-plane deformation. By atomistic calculations, we demonstrate two distinct out-of-plane deformation modes, breathing mode with small out-of-plane deformation and bending mode with one order larger corrugation magnitude compared to the breathing mode. The out-of-plane deformation is caused by inhomogeneous interlayer coupling resulting from the periodic stacking order of the tBLG moiré superlattice. Instead of commonly observed screw dislocation in tBLG, we demonstrate a slip-induced helical dislocation network in the bending mode tBLG. We show that bending mode deformation is more stable at low twist angles, as the energy savings due to interface energy exceeds the energy penalty due to the strain energy caused by the large out-of-plane deformation. Our work provides a detailed picture of a new helical dislocation structure in tBLG and establishes a direct connection between the dislocation and deformation. Therefore, understanding the dislocation mechanics of tBLG may open up the possibility to control the corrugation, and reveal an opportunity to tune the intriguing physical properties of twisted bilayer graphene.

36 MATERIALS SCIENCE↗

Super-moiré spin textures in twisted two-dimensional antiferromagnets

Stacking two-dimensional layered materials offers a platform to engineer electronic and magnetic states. In general, the resulting states—such as moiré magnetism—have a periodicity at the length scale of the moiré unit cell. Here we study magnetic order in twisted double-bilayer chromium triiodide by means of scanning nitrogen-vacancy microscopy. We observe long-range magnetic textures extending beyond the single moiré unit cell, which we dub a super-moiré magnetic state. At small twist angles, the size of the spontaneous magnetic texture increases with twist angle, opposite to the underlying moiré wavelength. The spin-texture size reaches a maximum of about 300 nm in 1.1° twisted devices, an order of magnitude larger than the underlying moiré wavelength, and vanishes at twist angles above 2°. The obtained magnetic field maps suggest the formation of antiferromagnetic Néel-type skyrmions spanning multiple moiré cells. The twist-angle-dependent study, combined with large-scale atomistic Monte Carlo simulations, suggests that the magnetic competition between the Dzyaloshinskii–Moriya interaction, magnetic anisotropy and exchange interactions—which all depend on the relative rotation of the layers—produces the topological textures that emerge in the super-moiré spin order.

Wong, King Cho [Univ. of Stuttgart (Germany)] (ORC↗

Unconventional non-local relaxation dynamics in a twisted trilayer graphene moiré superlattice

Abstract The electronic and structural properties of atomically thin materials can be controllably tuned by assembling them with an interlayer twist. During this process, constituent layers spontaneously rearrange themselves in search of a lowest energy configuration. Such relaxation phenomena can lead to unexpected and novel material properties. Here, we study twisted double trilayer graphene (TDTG) using nano-optical and tunneling spectroscopy tools. We reveal a surprising optical and electronic contrast, as well as a stacking energy imbalance emerging between the moiré domains. We attribute this contrast to an unconventional form of lattice relaxation in which an entire graphene layer spontaneously shifts position during assembly, resulting in domains of ABABAB and BCBACA stacking. We analyze the energetics of this transition and demonstrate that it is the result of a non-local relaxation process, in which an energy gain in one domain of the moiré lattice is paid for by a relaxation that occurs in the other.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Tailoring the Angular Mismatch in MoS 2 Homobilayers through Deformation Fields

Ultrathin MoS 2 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 MoS 2 by deforming the atomically thin material and exciting surface acoustic waves (SAWs). Furthermore, 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.

2D materials↗

Unconventional ferroelectricity in moiré heterostructures

Although all matter is composed of component particles, these particles can arrange themselves in various ways, giving rise to emergent phenomena that can be surprisingly rich and often cannot be understood by studying only the individual constituents. Discovering and understanding novel forms of emergence in quantum materials, especially in those where multiple degrees of freedom or energy scales are delicately balanced, is of great fundamental interest to condensed matter research. In this work, we report on the surprising observation of emergent ferroelectricity in graphene-based moiré heterostructures. Ferroelectric materials exhibit an electrically-switchable electric dipole, which is usually formed by spatial separation between the averaged centers of positive and negative charge within the unit cell. Based on this, it is difficult to imagine graphene, a material composed only of carbon atoms, exhibiting ferroelectricity. However, in this work, we indeed realize switchable ferroelectricity in Bernal-stacked bilayer graphene sandwiched between two hexagonal boron nitride (BN) layers. By introducing a moiré superlattice potential (via aligning bilayer graphene with the top and/or bottom BN crystals), we observe prominent and robust hysteretic behavior of the graphene resistance with an externally applied out-of-plane displacement field. Our systematic transport measurements reveal rich and striking response as a function of displacement field and electron filling, not previously observed in any 2D systems, and beyond the framework of conventional ferroelectrics. We further directly probe the ferroelectric polarization through a nonlocal monolayer graphene sensor. Our results suggest an unconventional, odd parity electronic ordering in the bilayer graphene/BN moiré system. This emergent moiré ferroelectricity may pave the way for ultrafast, programmable, and atomically thin carbon-based memory devices.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗