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When single layers of 2D materials are stacked on top of one another with a small twist in orientation, the resulting structure often involves incommensurate moiré patterns. In these patterns, the loss of angstrom-scale periodicity poses a significant theoretical challenge, and the new moiré length scale leads to emergent physical phenomena. The range of physics arising from twisted bilayers has led to significant advances that are shaping into a new field, twistronics. At the moiré scale, the large number of atoms in these systems can make their accurate simulation daunting, necessitating the development of efficient multiscale methods. In this Review, we summarize and compare such modelling methods — focusing in particular on density functional theory, tight-binding Hamiltonians and continuum models — and provide examples spanning a broad range of materials and geometries. When single layers of 2D materials are stacked on top of one another with a small twist, the resulting moiré pattern introduces new electronic properties. This Review surveys and compares the modelling techniques used in this emerging field of twistronics.

We demonstrate a photonic analog of twisted bilayer graphene that has ultra-flat photonic bands and exhibits extreme slow-light behavior. Our twisted bilayer photonic device, which has an operating wavelength in the C-band of the telecom window, uses two crystalline silicon photonic crystal slabs separated by a methyl methacrylate tunneling layer. We numerically determine the magic angle using a finite-element method and the corresponding photonic band structure, which exhibits a flat band over the entire Brillouin zone. This flat band causes the group velocity to approach zero and introduces light localization, which enhances the electromagnetic field at the expense of bandwidth. Using our original plane-wave continuum model, we find that the photonic system has a larger band asymmetry. The band structure can easily be engineered by adjusting the device geometry, giving significant freedom in the design of devices. Our work provides a fundamental understanding of the photonic properties of twisted bilayer photonic crystals and opens the door to the nanoscale-based enhancement of nonlinear effects.The twisted bilayer photonic crystals have near-zero group velocity over the Brillouin zone and provide access to light localization that is far out of the reach of conventional photonic crystals.

Conventional antiferroelectric materials with atomic-scale anti-aligned dipoles undergo a transition to a ferroelectric (FE) phase under strong electric fields. The moiré superlattice formed in the twisted stacks of van der Waals crystals exhibits polar domains alternating in moiré length with anti-aligned dipoles. In this moiré domain antiferroelectic (MDAF) arrangement, the distribution of electric dipoles is distinguished from that of two-dimensional FEs, suggesting dissimilar domain dynamics. Here we performed an operando transmission electron microscopy investigation on twisted bilayer WSe2 to observe the polar domain dynamics in real time. We find that the topological protection, provided by the domain wall network, prevents the MDAF-to-FE transition. As one decreases the twist angle, however, this transition occurs as the domain wall network disappears. Exploiting stroboscopic operando transmission electron microscopy on the FE phase, we measure a maximum domain wall velocity of 300 μm s–1. Domain wall pinnings by various disorders limit the domain wall velocity and cause Barkhausen noises in the polarization hysteresis loop. Atomic-scale analysis of the pinning disorders provides structural insight on how to improve the switching speed of van der Waals FEs.Polar domains have been observed in twist-stacked van der Waals layers, but their dynamics are unexplored. Here, using operando electron microscopy, it is found that polar domains in an antiferroelectric arrangement cannot transition to a ferroelectric state due to topological protection of the domain wall network.

The RAS gene family is frequently mutated in human cancers, and the quest for compounds that bind to mutant RAS remains a major goal, as it also does for inhibitors of protein–protein interactions. We have refined crystallization conditions for KRAS169 Q61H-yielding crystals suitable for soaking with compounds and exploited this to assess new RAS-binding compounds selected by screening a protein–protein interaction-focused compound library using surface plasmon resonance. Two compounds, referred to as PPIN-1 and PPIN-2, with related structures from 30 initial RAS binders showed binding to a pocket where compounds had been previously developed, including RAS effector protein–protein interaction inhibitors selected using an intracellular antibody fragment (called Abd compounds). Unlike the Abd series of RAS binders, PPIN-1 and PPIN-2 compounds were not competed by the inhibitory anti-RAS intracellular antibody fragment and did not show any RAS-effector inhibition properties. By fusing the common, anchoring part from the two new compounds with the inhibitory substituents of the Abd series, we have created a set of compounds that inhibit RAS-effector interactions with increased potency. These fused compounds add to the growing catalog of RAS protein–protein inhibitors and show that building a chemical series by crossing over two chemical series is a strategy to create RAS-binding small molecules.

Amino acid profiles could aid in diabetes risk assessment, as a five-amino-acid signature had highly significant associations with the development of future diabetes in two large, independent cohorts. Emerging technologies allow the high-throughput profiling of metabolic status from a blood specimen (metabolomics). We investigated whether metabolite profiles could predict the development of diabetes. Among 2,422 normoglycemic individuals followed for 12 years, 201 developed diabetes. Amino acids, amines and other polar metabolites were profiled in baseline specimens by liquid chromatography–tandem mass spectrometry (LC-MS). Cases and controls were matched for age, body mass index and fasting glucose. Five branched-chain and aromatic amino acids had highly significant associations with future diabetes: isoleucine, leucine, valine, tyrosine and phenylalanine. A combination of three amino acids predicted future diabetes (with a more than fivefold higher risk for individuals in top quartile). The results were replicated in an independent, prospective cohort. These findings underscore the potential key role of amino acid metabolism early in the pathogenesis of diabetes and suggest that amino acid profiles could aid in diabetes risk assessment.

In this paper, the authors review current literature on retail formats and propose a new customer-centric framework for retailers to focus on as they continue to innovate and evolve. Specifically, they review the literature on how formats compare in their attributes and compete with each other; the role of customer behavior in format choice; and developments in multichannel and omnichannel retailing. They propose a framework for retail formats suggesting two paths – either reduce friction in the customer journey or enhance customer experience. They discuss the challenges faced by offline (physical store-first) and online (digital-first) retailers and elaborate on strategies each type of retailer is pursuing to address these challenges. Finally, they offer directions for future research in this domain. They conclude by calling for newer digital-first and physical-first players to continue coming up with different customer-centric formats, which they predict will slowly morph into integrated retailers, leaving space for newer players to enter the market and hence keep the wheel of retailing spinning.

Targeting specific protein–protein interactions (PPIs) is an attractive concept for drug development, but hard to implement since intracellular antibodies do not penetrate cells and most small-molecule drugs are considered unsuitable for PPI inhibition. A potential solution to these problems is to select intracellular antibody fragments to block PPIs, use these antibody fragments for target validation in disease models and finally derive small molecules overlapping the antibody-binding site. Here, we explore this strategy using an anti-mutant RAS antibody fragment as a competitor in a small-molecule library screen for identifying RAS-binding compounds. The initial hits are optimized by structure-based design, resulting in potent RAS-binding compounds that interact with RAS inside the cells, prevent RAS-effector interactions and inhibit endogenous RAS-dependent signalling. Our results may aid RAS-dependent cancer drug development and demonstrate a general concept for developing small compounds to replace intracellular antibody fragments, enabling rational drug development to target validated PPIs. Intracellular antibodies can inhibit disease-relevant protein interactions, but inefficient cellular uptake limits their utility. Using a RAS-targeting intracellular antibody as a screening tool, the authors here identify small molecules that inhibit RAS-effector interactions and readily penetrate cells.

Direct visualization of nanometer-scale properties of moiré superlattices in van der Waals heterostructure devices is a critically needed diagnostic tool for study of the electronic and optical phenomena induced by the periodic variation of atomic structure in these complex systems. Conventional imaging methods are destructive and insensitive to the buried device geometries, preventing practical inspection. Here we report a versatile scanning probe microscopy employing infrared light for imaging moiré superlattices of twisted bilayers graphene encapsulated by hexagonal boron nitride. We map the pattern using the scattering dynamics of phonon polaritons launched in hexagonal boron nitride capping layers via its interaction with the buried moiré superlattices. We explore the origin of the double-line features imaged and show the mechanism of the underlying effective phase change of the phonon polariton reflectance at domain walls. The nano-imaging tool developed provides a non-destructive analytical approach to elucidate the complex physics of moiré engineered heterostructures. Direct visualization of moiré superlattices in van der Waals heterostructures is a needed diagnostic tool for the study of periodicity-induced electronic and optical phenomena. Here, the authors demonstrate that the moiré pattern in twisted bilayer graphene can be indirectly imaged by imaging the phonon polariton interference on the top hexagonal boron nitride encapsulation layer.

Lattice reconstruction and corresponding strain accumulation plays a key role in defining the electronic structure of two-dimensional moiré superlattices, including those of transition metal dichalcogenides (TMDs). Imaging of TMD moirés has so far provided a qualitative understanding of this relaxation process in terms of interlayer stacking energy, while models of the underlying deformation mechanisms have relied on simulations. Here, we use interferometric four-dimensional scanning transmission electron microscopy to quantitatively map the mechanical deformations through which reconstruction occurs in small-angle twisted bilayer MoS 2 and WSe 2 /MoS 2 heterobilayers. We provide direct evidence that local rotations govern relaxation for twisted homobilayers, while local dilations are prominent in heterobilayers possessing a sufficiently large lattice mismatch. Encapsulation of the moiré layers in hBN further localizes and enhances these in-plane reconstruction pathways by suppressing out-of-plane corrugation. We also find that extrinsic uniaxial heterostrain, which introduces a lattice constant difference in twisted homobilayers, leads to accumulation and redistribution of reconstruction strain, demonstrating another route to modify the moiré potential. Lattice reconstruction crucially influences the electronic properties of twisted van der Waals structures. Here, the authors report a quantitative characterization of the mechanical deformations occurring in small-angle twisted bilayers and heterobilayers of 2D semiconductors via interferometric 4D scanning transmission electron microscopy.

The emerging field of twistronics, which harnesses the twist angle between two-dimensional materials, represents a promising route for the design of quantum materials, as the twist-angle-induced superlattices offer means to control topology and strong correlations. At the small twist limit, and particularly under strain, as atomic relaxation prevails, the emergent moiré superlattice encodes elusive insights into the local interlayer interaction. Here we introduce moiré metrology as a combined experiment-theory framework to probe the stacking energy landscape of bilayer structures at the 0.1 meV/atom scale, outperforming the gold-standard of quantum chemistry. Through studying the shapes of moiré domains with numerous nano-imaging techniques, and correlating with multi-scale modelling, we assess and refine first-principle models for the interlayer interaction. We document the prowess of moiré metrology for three representative twisted systems: bilayer graphene, double bilayer graphene and H-stacked MoSe 2 /WSe 2 . Moiré metrology establishes sought after experimental benchmarks for interlayer interaction, thus enabling accurate modelling of twisted multilayers. Here, a combined experiment-theory framework based on different nano-imaging techniques and first-principle calculations is used to analyse the shapes of moiré patterns in twisted van der Waals structures, enabling an accurate description of the coupling between the atomically thin layers.