Soliton-dependent plasmon reflection at bilayer graphene domain walls

Strain Solitons in an Epitaxially Strained van der Waals-like Material

Strain solitons are quasi-dislocations that form in van der Waals materials to relieve the energy associated with lattice or rotational mismatch. Novel electronic properties of strain solitons were predicted and observed. To date, strain solitons have been observed only in exfoliated crystals or mechanically strained crystals. The lack of a scalable approach toward the generation of strain solitons poses a significant challenge in the study of and use of their properties. Here, we report the formation of strain solitons with epitaxial growth of bismuth on InSb(111)B by molecular beam epitaxy. The morphology of the strain solitons for films of varying thickness is characterized with scanning tunneling microscopy, and the local strain state is determined from atomic resolution images. Bending in the solitons is attributed to interactions with the interface, and large angle bending is associated with edge dislocations. Our results enable the scalable generation of strain solitons.

Twisted moiré conductive thermal metasurface

Extensive investigations on the moiré magic angle in twisted bilayer graphene have unlocked the emerging field-twistronics. Recently, its optics analogue, namely opto-twistronics, further expands the potential universal applicability of twistronics. However, since heat diffusion neither possesses the dispersion like photons nor carries the band structure as electrons, the real magic angle in electrons or photons is ill-defined for heat diffusion, making it elusive to understand or design any thermal analogue of magic angle. Here, we introduce and experimentally validate the twisted thermotics in a twisted diffusion system by judiciously tailoring thermal coupling, in which twisting an analog thermal magic angle would result in the function switching from cloaking to concentration. Our work provides insights for the tunable heat diffusion control, and opens up an unexpected branch for twistronics -- twisted thermotics, paving the way towards field manipulation in twisted configurations including but not limited to fluids.

Twisted van der Waals Quantum Materials: Fundamentals, Tunability, and Applications

Twisted van der Waals (vdW) quantum materials have emerged as a rapidly developing field of two-dimensional (2D) semiconductors. These materials establish a new central research area and provide a promising platform for studying quantum phenomena and investigating the engineering of novel optoelectronic properties such as single photon emission, nonlinear optical response, magnon physics, and topological superconductivity. These captivating electronic and optical properties result from, and can be tailored by, the interlayer coupling using moiré patterns formed by vertically stacking atomic layers with controlled angle misorientation or lattice mismatch. Their outstanding properties and the high degree of tunability position them as compelling building blocks for both compact quantum-enabled devices and classical optoelectronics. This paper offers a comprehensive review of recent advancements in the understanding and manipulation of twisted van der Waals structures and presents a survey of the state-of-the-art research on moiré superlattices, encompassing interdisciplinary interests. It delves into fundamental theories, synthesis and fabrication, and visualization techniques, and the wide range of novel physical phenomena exhibited by these structures, with a focus on their potential for practical device integration in applications ranging from quantum information to biosensors, and including classical optoelectronics such as modulators, light emitting diodes, lasers, and photodetectors. It highlights the unique ability of moiré superlattices to connect multiple disciplines, covering chemistry, electronics, optics, photonics, magnetism, topological and quantum physics. This comprehensive review provides a valuable resource for researchers interested in moiré superlattices, shedding light on their fundamental characteristics and their potential for transformative applications in various fields.

Role of Local Conductivities in the Plasmon Reflections at the Edges and Stacking Domain Boundaries of Trilayer Graphene

We employed infrared scattering-type scanning near-field optical microscopy (IR-sSNOM) to study surface plasmon polaritons (SPPs) in trilayer graphene (TLG). Our study reveals systematic differences in near-field IR spectra and SPP wavelengths between Bernal (ABA) and rhombohedral (ABC) TLG domains on SiO2, which can be explained by stacking-dependent intraband conductivities. We also observed that the SPP reflection profiles at ABA-ABC boundaries could be mostly accounted for by an idealized domain boundary defined by the conductivity discontinuity. However, we identified distinct shapes in the SPP profiles at the edges of the ABA and ABC TLG, which cannot be solely attributed to idealized edges with stacking-dependent conductivities. Instead, this can be explained by the presence of various edge structures with local conductivities differing from those of bulk TLGs. Our findings unveil a new structural element that can control SPP, and provide insights into the structures and electronic states of the edges of few-layer graphene.

Polaritons in Van der Waals Heterostructures

2D monolayers supporting a wide variety of highly confined plasmons, phonon polaritons, and exciton polaritons can be vertically stacked in van der Waals heterostructures (vdWHs) with controlled constituent layers, stacking sequence, and even twist angles. vdWHs combine advantages of 2D material polaritons, rich optical structure design, and atomic scale integration, which have greatly extended the performance and functions of polaritons, such as wide frequency range, long lifetime, ultrafast all-optical modulation, and photonic crystals for nanoscale light. Here, the state of the art of 2D material polaritons in vdWHs from the perspective of design principles and potential applications is reviewed. Some fundamental properties of polaritons in vdWHs are initially discussed, followed by recent discoveries of plasmons, phonon polaritons, exciton polaritons, and their hybrid modes in vdWHs. The review concludes with a perspective discussion on potential applications of these polaritons such as nanophotonic integrated circuits, which will benefit from the intersection between nanophotonics and materials science.

Wrinkles, Ridges, Miura-Ori, and Moiré Patterns in MoSe2 Using Neural Networks

Effects of lateral compression on out-of-plane deformation of two-dimensional MoSe₂ layers are investigated. A MoSe₂ monolayer develops periodic wrinkles under uniaxial compression and Miura-Ori patterns under biaxial compression. When a flat MoSe₂ monolayer is placed on top of a wrinkled MoSe₂ layer, the van der Waals (vdW) interaction transforms wrinkles into ridges and generates mixed 2H and 1T phases and chain-like defects. Under a biaxial strain, the vdW interaction induces regions of Miura-Ori patterns in bilayers. Strained systems analyzed using a convolutional neural network show that the compressed system consists of semiconducting 2H and metallic 1T phases. The energetics, mechanical response, defect structure, and dynamics are analyzed as bilayers undergo wrinkle-ridge transformations under uniaxial compression and moiré transformations under biaxial compression. Our results indicate that in-plane compression can induce self-assembly of out-of-plane metasurfaces with controllable semiconducting and metallic phases and moiré patterns with unique optoelectronic properties.

A primer on twistronics: a massless Dirac fermion's journey to moiré patterns and flat bands in twisted bilayer graphene

The recent discovery of superconductivity in magic-angle twisted bilayer graphene (TBLG) has sparked a renewed interest in the strongly-correlated physics ofsp²carbons, in stark contrast to preliminary investigations which were dominated by the one-body physics of the massless Dirac fermions. We thus provide a self-contained, theoretical perspective of the journey of graphene from its single-particle physics-dominated regime to the strongly-correlated physics of the flat bands. Beginning from the origin of the Dirac points in condensed matter systems, we discuss the effect of the superlattice on the Fermi velocity and Van Hove singularities in graphene and how it leads naturally to investigations of the moiré pattern in van der Waals heterostructures exemplified by graphene-hexagonal boron-nitride and TBLG. Subsequently, we illuminate the origin of flat bands in TBLG at the magic angles by elaborating on a broad range of prominent theoretical works in a pedagogical way while linking them to available experimental support, where appropriate. We conclude by providing a list of topics in the study of the electronic properties of TBLG not covered by this review but may readily be approached with the help of this primer.

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

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.

Experimental Observation of ABCB Stacked Tetralayer Graphene

In tetralayer graphene, three inequivalent layer stackings should exist; however, only rhombohedral (ABCA) and Bernal (ABAB) stacking have so far been observed. The three stacking sequences differ in their electronic structure, with the elusive third stacking (ABCB) being unique as it is predicted to exhibit an intrinsic bandgap as well as locally flat bands around the K points. Here, we use scattering-type scanning near-field optical microscopy and confocal Raman microscopy to identify and characterize domains of ABCB stacked tetralayer graphene. We differentiate between the three stacking sequences by addressing characteristic interband contributions in the optical conductivity between 0.28 and 0.56 eV with amplitude and phase-resolved near-field nanospectroscopy. By normalizing adjacent flakes to each other, we achieve good agreement between theory and experiment, allowing for the unambiguous assignment of ABCB domains in tetralayer graphene. These results establish near-field spectroscopy at the interband transitions as a semiquantitative tool, enabling the recognition of ABCB domains in tetralayer graphene flakes and, therefore, providing a basis to study correlation physics of this exciting phase.

Criterion for photonic topological transition in two-dimensional heterostructures

The anisotropic van der Waals material α-MoO₃ has recently attracted considerable attention because of the ability to support ellipse and hyperbolic phonon polaritons with extreme field confinement and long lifetimes, which can be used in topological transition and transformation polaritonics. However, the dispersion theory of some phonon polaritons in complex heterojunctions often requires tedious computation, which makes it difficult to simply judge and analyze the physical process of the photonic topological transition. Here we obtain the equivalent permittivity distribution of two-dimensional (2D) heterostructures by the effective medium theory and analyze the rotation-induced topological transitions and stack-dependent topological transitions of phonon polaritons. Unlike the previous discussion, we can predict the topological transition points by a parameter ɛ_x/y(i.e., the permittivity ratio along the in-plane crystal axis of the equivalent medium) and design precisely the phonon polaritons in the stacked materials by controlling the equivalent permittivity after simple calculation. The feasibility of the effective medium theory is verified based on the 2D approximation model and the non-2D approximation model under the limit of an ultrathin slab. Meanwhile, we compare the field distributions and dispersions of the 2D heterostructures and the corresponding equivalent structure. The simulation suggests that the elliptic/hyperbolic responses of the stacked materials depend on the sign of ɛ_x/y. The new, to the best of our knowledge, method not only provides an easier and clearer criterion for the study of photonic topological transition in anisotropic polaritons, but also shows great potential in designing some multilayer 2D heterostructures.

Impact of Electric Field Disorder on Broken-Symmetry States in Ultraclean Bilayer Graphene

Bilayer graphene (BLG) has multiple internal degrees of freedom and a constant density of states down to the charge neutrality point when trigonal warping is ignored. Consequently, it is susceptible to various competing ground states. However, a coherent experimental determination of the ground state has been challenging due to the interaction-disorder interplay. Here we present an extensive transport study in a series of dually gated freestanding BLG devices and identify the layer-antiferromagnet as the ground state with a continuous strength across all devices. This strength correlates with the width of the state in the electric field. We systematically identify electric-field disorder─spatial variations in the interlayer potential difference─as the main source responsible for the observations. Our results pinpoint for the first time the importance of electric-field disorder on spontaneous symmetry breaking in BLG and solve a long-standing debate on its ground state. The electric-field disorder should be universal to all 2D materials.

Magnetic moiré effects and two types of topological transition in a twisted-bilayer hyperbolic metasurface with double-split ring arrays

Moiré configurations have recently attracted much attention due to their ability to enhance photonic responses and manipulate surface waves in the subwavelength ranges. However, previous studies have usually been focused on natural hyperbolic materials with limitations on patterning procedures, controlling rotation angles, and merely manipulating electric surface plasmons. Here, we theoretically and numerically investigate a novel magnetic moiré hyperbolic metasurface in the terahertz region, which enables two types of topological transition and a plethora of unusual magnetic moiré effects (magnetic surface wave manipulation, dispersion engineering, magic angles, spacer-dependent topological transition, and local field enhancement). This work extends twistronics and moiré physics to the terahertz region and magnetic polaritons, with potential applications in quantum physics, energy transfer, and planarized magnetic plasmonic devices.

Molding Broadband Dispersion in Twisted Trilayer Hyperbolic Polaritonic Surfaces

Recent advancement in twisted layered metasurfaces can be employed to control the nanoscale flow of light, including the exotic hyperbolic-to-elliptic topological transitions in twisted bilayers (tBL). Such topological transitions can only occur to limited frequency ranges, restricted by the intrinsic in-plane dispersion of individual hyperbolic surfaces. Here, we report that, by controlling interlayer evanescent coupling in twisted polaritonic trilayers, moldable topological transitions of light can be achieved in broadband. We reveal that the required minimum open angle of the individual hyperbolic polaritonic surface for open-to-close topological transitions can be significantly lowered compared to that of the twisted bilayer counterpart. This increases the degree of freedom to enhance and control near-field light-matter interactions and energy management. As an example, we demonstrate a knob to manipulate near-field radiative heat transfer (NFRHT). By rotating the relative angles of trilayers, exotic and tunable thermal conductance can be achieved. Our findings enrich the controllability of light at the nanoscale in broadband, bringing twisted optical materials one step closer to practical applications.

One-Dimensional Strain Solitons Manipulated Superlubricity on Graphene Interface

The frictional properties of a uniaxial tensile strained graphene interface are studied using molecular dynamics simulations. A misfit interval statistical method (MISM) is applied to characterize the atomistic misfits at the interface and strain soliton pattern. During sliding along both armchair and zigzag directions, the lateral force depends on the ratio of graphene flake length (L) to strain soliton spacing (L_s) and becomes nearly zero when L is an integer multiple of 3L_s. Furthermore, the strain solitons propagate along the armchair sliding direction dynamically, while fission and fusion are repeatedly evidenced along the zigzag sliding direction. The underlying superlubric mechanism is revealed by a single-atom quasi-static model. The cancellation of lateral force for the contacting atoms exhibits a dynamic balance when sliding along the armchair direction but a quasi-static balance along the zigzag direction. A diagram of flake length with respect to tensile strain (L-ε) is proposed to predict the critical condition for the transition from nonsuperlubricity to superlubricity. Our results provide insights on the design of superlubric devices.

Interplay between topological valley and quantum Hall edge transport

An established way of realising topologically protected states in a two-dimensional electron gas is by applying a perpendicular magnetic field thus creating quantum Hall edge channels. In electrostatically gapped bilayer graphene intriguingly, even in the absence of a magnetic field, topologically protected electronic states can emerge at naturally occurring stacking domain walls. While individually both types of topologically protected states have been investigated, their intriguing interplay remains poorly understood. Here, we focus on the interplay between topological domain wall states and quantum Hall edge transport within the eight-fold degenerate zeroth Landau level of high-quality suspended bilayer graphene. We find that the two-terminal conductance remains approximately constant for low magnetic fields throughout the distinct quantum Hall states since the conduction channels are traded between domain wall and device edges. For high magnetic fields, however, we observe evidence of transport suppression at the domain wall, which can be attributed to the emergence of spectral minigaps. This indicates that stacking domain walls potentially do not correspond to a topological domain wall in the order parameter.

Plasmonic sensors based on graphene and graphene hybrid materials

The past decade has witnessed a rapid growth of graphene plasmonics and their applications in different fields. Compared with conventional plasmonic materials, graphene enables highly confined plasmons with much longer lifetimes. Moreover, graphene plasmons work in an extended wavelength range, i.e., mid-infrared and terahertz regime, overlapping with the fingerprints of most organic and biomolecules, and have broadened their applications towards plasmonic biological and chemical sensors. In this review, we discuss intrinsic plasmonic properties of graphene and strategies both for tuning graphene plasmons as well as achieving higher performance by integrating graphene with plasmonic nanostructures. Next, we survey applications of graphene and graphene-hybrid materials in biosensors, chemical sensors, optical sensors, and sensors in other fields. Lastly, we conclude this review by providing a brief outlook and challenges of the field. Through this review, we aim to provide an overall picture of graphene plasmonic sensing and to suggest future trends of development of graphene plasmonics.

Moiré-Driven Topological Transitions and Extreme Anisotropy in Elastic Metasurfaces

The twist angle between a pair of stacked 2D materials has been recently shown to control remarkable phenomena, including the emergence of flat-band superconductivity in twisted graphene bilayers, of higher-order topological phases in twisted moiré superlattices, and of topological polaritons in twisted hyperbolic metasurfaces. These discoveries, at the foundations of the emergent field of twistronics, have so far been mostly limited to explorations in atomically thin condensed matter and photonic systems, with limitations on the degree of control over geometry and twist angle, and inherent challenges in the fabrication of carefully engineered stacked multilayers. Here, this work extends twistronics to widely reconfigurable macroscopic elastic metasurfaces consisting of LEGO pillar resonators. This work demonstrates highly tailored anisotropy over a single-layer metasurface driven by variations in the twist angle between a pair of interleaved spatially modulated pillar lattices. The resulting quasi-periodic moiré patterns support topological transitions in the isofrequency contours, leading to strong tunability of highly directional waves. The findings illustrate how the rich phenomena enabled by twistronics and moiré physics can be translated over a single-layer metasurface platform, introducing a practical route toward the observation of extreme phenomena in a variety of wave systems, potentially applicable to both quantum and classical settings without multilayered fabrication requirements.

Dissipation-enabled hydrodynamic conductivity in a tunable bandgap semiconductor

Electronic transport in the regime where carrier-carrier collisions are the dominant scattering mechanism has taken on new relevance with the advent of ultraclean two-dimensional materials. Here, we present a combined theoretical and experimental study of ambipolar hydrodynamic transport in bilayer graphene demonstrating that the conductivity is given by the sum of two Drude-like terms that describe relative motion between electrons and holes, and the collective motion of the electron-hole plasma. As predicted, the measured conductivity of gapless, charge-neutral bilayer graphene is sample- and temperature-independent over a wide range. Away from neutrality, the electron-hole conductivity collapses to a single curve, and a set of just four fitting parameters provides quantitative agreement between theory and experiment at all densities, temperatures, and gaps measured. This work validates recent theories for dissipation-enabled hydrodynamic conductivity and creates a link between semiconductor physics and the emerging field of viscous electronics.

Active control of micrometer plasmon propagation in suspended graphene

Due to the two-dimensional character of graphene, the plasmons sustained by this material have been invariably studied in supported samples so far. The substrate provides stability for graphene but often causes undesired interactions (such as dielectric losses, phonon hybridization, and impurity scattering) that compromise the quality and limit the intrinsic flexibility of graphene plasmons. Here, we demonstrate the visualization of plasmons in suspended graphene at room temperature, exhibiting high-quality factor Q~33 and long propagation length > 3 μm. We introduce the graphene suspension height as an effective plasmonic tuning knob that enables in situ change of the dielectric environment and substantially modulates the plasmon wavelength, propagation length, and group velocity. Such active control of micrometer plasmon propagation facilitates near-unity-order modulation of nanoscale energy flow that serves as a plasmonic switch with an on-off ratio above 14. The suspended graphene plasmons possess long propagation length, high tunability, and controllable energy transmission simultaneously, opening up broad horizons for application in nano-photonic devices.

Graphene plasmons hold potential for infrared optoelectronic devices, but the interaction with the substrate often degrades their quality. Here, the authors report the characterization of plasmons in suspended graphene with tunable suspension height, showing enhanced quality factors and propagation lengths at room temperature.

Simulation of scanning near-field optical microscopy spectra of 1D plasmonic graphene junctions

We present numerical simulations of scattering-type scanning near-field optical microscopy (s-SNOM) of 1D plasmonic graphene junctions. A comprehensive analysis of simulated s-SNOM spectra is performed for three types of junctions. We find conditions when the conventional interpretation of the plasmon reflection coefficients from s-SNOM measurements does not apply. Our approach can be used for other conducting 2D materials to provide a comprehensive understanding of the s-SNOM techniques for probing the local transport properties of 2D materials.

Moiré bands in twisted trilayer black phosphorene: effects of pressure and electric field

Twist-induced moiré bands and accompanied correlated phenomena have been extensively investigated in twisted hexagonal lattices with weak interlayer coupling. However, the formation of moiré bands in strongly coupled layered materials and their controlled tuning remain largely unexplored. Here, we systematically study the moiré bands in twisted trilayer black phosphorene (TTbP) and the influences of pressure and electric field on them. Moiré states can form in various TTbPs even when the twist angle is larger than 16° similar to that of twisted bilayer bP. However, different TTbPs show different localization patterns depending on the twisting layer, leading to distinct dipolar behaviors. While these moiré states become quasi-one-dimensional (1D) as the twist angle decreases, external pressure causes the crossover of moiré states from quasi-1D to 0D with a dramatic change in localization areas and greatly reduced bandwidth. Interestingly, compared to twisted bilayer and pristine bP, TTbPs show a much larger electric-field induced Stark effect, controllable by either the twist angle or twist layer. Our work thus demonstrates TTbP as an attractive platform to explore moiré-controlled electronic and optical properties, as well as tunable optoelectronic applications.

Optical Inspection of 2D Materials: From Mechanical Exfoliation to Wafer-Scale Growth and Beyond

Optical inspection is a rapid and non-destructive method for characterizing the properties of two-dimensional (2D) materials. With the aid of optical inspection, in situ and scalable monitoring of the properties of 2D materials can be implemented industrially to advance the development and progress of 2D material-based devices toward mass production. This review discusses the optical inspection techniques that are available to characterize various 2D materials, including graphene, transition metal dichalcogenides (TMDCs), hexagonal boron nitride (h-BN), group-III monochalcogenides, black phosphorus (BP), and group-IV monochalcogenides. First, the authors provide an introduction to these 2D materials and the processes commonly used for their fabrication. Then they review several of the important structural properties of 2D materials, and discuss how to characterize them using appropriate optical inspection tools. The authors also describe the challenges and opportunities faced when applying optical inspection to recently developed 2D materials, from mechanically exfoliated to wafer-scale-grown 2D materials. Most importantly, the authors summarize the techniques available for largely and precisely enhancing the optical signals from 2D materials. This comprehensive review of the current status and perspective of future trends for optical inspection of the structural properties of 2D materials will facilitate the development of next-generation 2D material-based devices.

Strain Engineering of Low-Dimensional Materials for Emerging Quantum Phenomena and Functionalities

Recent discoveries of exotic physical phenomena, such as unconventional superconductivity in magic-angle twisted bilayer graphene, dissipationless Dirac fermions in topological insulators, and quantum spin liquids, have triggered tremendous interest in quantum materials. The macroscopic revelation of quantum mechanical effects in quantum materials is associated with strong electron-electron correlations in the lattice, particularly where materials have reduced dimensionality. Owing to the strong correlations and confined geometry, altering atomic spacing and crystal symmetry via strain has emerged as an effective and versatile pathway for perturbing the subtle equilibrium of quantum states. This review highlights recent advances in strain-tunable quantum phenomena and functionalities, with particular focus on low-dimensional quantum materials. Experimental strategies for strain engineering are first discussed in terms of heterogeneity and elastic reconfigurability of strain distribution. The nontrivial quantum properties of several strain-quantum coupled platforms, including 2D van der Waals materials and heterostructures, topological insulators, superconducting oxides, and metal halide perovskites, are next outlined, with current challenges and future opportunities in quantum straintronics followed. Overall, strain engineering of quantum phenomena and functionalities is a rich field for fundamental research of many-body interactions and holds substantial promise for next-generation electronics capable of ultrafast, dissipationless, and secure information processing and communications.

Quantum anomalous Hall octet driven by orbital magnetism in bilayer graphene

The quantum anomalous Hall (QAH) effect-a macroscopic manifestation of chiral band topology at zero magnetic field-has been experimentally realized only by the magnetic doping of topological insulators^1-3 and the delicate design of moiré heterostructures^4-8. However, the seemingly simple bilayer graphene without magnetic doping or moiré engineering has long been predicted to host competing ordered states with QAH effects^9-11. Here we explore states in bilayer graphene with a conductance of 2 e² h^-1 (where e is the electronic charge and h is Planck's constant) that not only survive down to anomalously small magnetic fields and up to temperatures of five kelvin but also exhibit magnetic hysteresis. Together, the experimental signatures provide compelling evidence for orbital-magnetism-driven QAH behaviour that is tunable via electric and magnetic fields as well as carrier sign. The observed octet of QAH phases is distinct from previous observations owing to its peculiar ferrimagnetic and ferrielectric order that is characterized by quantized anomalous charge, spin, valley and spin-valley Hall behaviour⁹.

Interface nano-optics with van der Waals polaritons

Polaritons are hybrid excitations of matter and photons. In recent years, polaritons in van der Waals nanomaterials-known as van der Waals polaritons-have shown great promise to guide the flow of light at the nanoscale over spectral regions ranging from the visible to the terahertz. A vibrant research field based on manipulating strong light-matter interactions in the form of polaritons, supported by these atomically thin van der Waals nanomaterials, is emerging for advanced nanophotonic and opto-electronic applications. Here we provide an overview of the state of the art of exploiting interface optics-such as refractive optics, meta-optics and moiré engineering-for the control of van der Waals polaritons. This enhanced control over van der Waals polaritons at the nanoscale has not only unveiled many new phenomena, but has also inspired valuable applications-including new avenues for nano-imaging, sensing, on-chip optical circuitry, and potentially many others in the years to come.

Direct Visualization and Manipulation of Stacking Orders in Few-Layer Graphene by Dynamic Atomic Force Microscopy

Stacking order plays a central role in governing a wide range of properties in layered two-dimensional materials. In the case of few-layer graphene, there are two common stacking configurations: ABA and ABC stacking, which have been proven to exhibit dramatically different electronic properties. However, the controllable characterization and manipulation between them remain a great challenge. Here, we report that ABA- and ABC-stacked domains can be directly visualized in phase imaging by tapping-mode atomic force microscopy with much higher spatial resolution than conventional optical spectroscopy. The contrasting phase is caused by the different energy dissipation by the tip-sample interaction. We further demonstrate controllable manipulation on the ABA/ABC domain walls by means of propagating stress transverse waves generated by the tapping of tip. Our results offer a reliable strategy for direct imaging and precise control of the atomic structures in few-layer graphene, which can be extended to other two-dimensional materials.

Topological kink states in graphene

Due to the unique band structure, graphene exhibits a number of exotic electronic properties that have not been observed in other materials. Among them, it has been demonstrated that there exist the one-dimensional valley-polarized topological kink states localized in the vicinity of the domain wall of graphene systems, where a bulk energy gap opens due to the inversion symmetry breaking. Notably, the valley-momentum locking nature makes the topological kink states attractive to the property manipulation in valleytronics. This paper systematically reviews both the theoretical research and experimental progress on topological kink states in monolayer graphene, bilayer graphene and graphene-like classical wave systems. Besides, various applications of topological kink states, including the valley filter, current partition, current manipulation, Majorana zero modes and etc, are also introduced.

Efficient and Tunable Reflection of Phonon Polaritons at Built-In Intercalation Interfaces

Phonon polaritons-light coupled to lattice vibrations-in polar van der Waals crystals offer unprecedented opportunities for controlling light at the nanoscale due to their anisotropic and ultralow-loss propagation. While their analog plasmon polaritons-light coupled to electron oscillations-have long been studied and exhibit interesting reflections at geometrical edges and electronic boundaries, whether phonon polaritons can be reflected by such barriers has been elusive. Here, the effective and tunable reflection of phonon polaritons at embedded interfaces formed in hydrogen-intercalated α-MoO₃ flakes is elaborated upon. Without breaking geometrical continuity, such intercalation interfaces can reflect phonon polaritons with low losses, yielding the distinct phase changes of -0.8π and -0.3π associated with polariton propagation, high efficiency of 50%, and potential electrical tunability. The results point to a new approach to construct on-demand polariton reflectors, phase modulators, and retarders, which may be transplanted into building future polaritonic circuits using van der Waals crystals.

Fabrication Strategies of Twisted Bilayer Graphenes and Their Unique Properties

Twisted bilayer graphene (tBLG) exhibits a host of innovative physical phenomena owing to the formation of moiré superlattice. Especially, the discovery of superconducting behavior has generated new interest in graphene. The growing studies of tBLG mainly focus on its physical properties, while the fabrication of high-quality tBLG is a prerequisite for achieving the desired properties due to the great dependence on the twist angle and the interfacial contact. Here, the cutting-edge preparation strategies and challenges of tBLG fabrication are reviewed. The advantages and disadvantages of chemical vapor deposition, epitaxial growth on silicon carbide, stacking monolayer graphene, and folding monolayer graphene methods for the fabrication of tBLG are analyzed in detail, providing a reference for further development of preparation methods. Moreover, the characterization methods of twist angle for the tBLG are presented. Then, the unique physicochemical properties and corresponding applications of tBLG, containing correlated insulating and superconducting states, ferromagnetic state, soliton, enhanced optical absorption, tunable bandgap, and lithium intercalation and diffusion, are described. Finally, the opportunities and challenges for fabricating high-quality and large-area tBLG are discussed, unique physical properties are displayed, and new applications inferred from its angle-dependent features are explored, thereby impelling the commercialization of tBLG from laboratory to market.

Nano-imaging photoresponse in a moiré unit cell of minimally twisted bilayer graphene

Graphene-based moiré superlattices have recently emerged as a unique class of tuneable solid-state systems that exhibit significant optoelectronic activity. Local probing at length scales of the superlattice should provide deeper insight into the microscopic mechanisms of photoresponse and the exact role of the moiré lattice. Here, we employ a nanoscale probe to study photoresponse within a single moiré unit cell of minimally twisted bilayer graphene. Our measurements reveal a spatially rich photoresponse, whose sign and magnitude are governed by the fine structure of the moiré lattice and its orientation with respect to measurement contacts. This results in a strong directional effect and a striking spatial dependence of the gate-voltage response within the moiré domains. The spatial profile and carrier-density dependence of the measured photocurrent point towards a photo-thermoelectric induced response that is further corroborated by good agreement with numerical simulations. Our work shows sub-diffraction photocurrent spectroscopy is an exceptional tool for uncovering the optoelectronic properties of moiré superlattices.

Pattern Development and Control of Strained Solitons in Graphene Bilayers

Engineering strain and interlayer registry in 2D crystals have been demonstrated as effective controls of their properties. Separation of domains with different interlayer registries in graphene bilayer has been reported, but the pattern control of strained solitons has not yet been achieved. We show here that, by pulling a graphene bilayer apart, soliton structures with a regularly modulated interlayer registry arise from the competition between elastic deformation in monolayers and local slip at the van der Waals interfaces. The commensurate-incommensurate transition with strain localization is identified as the interlayer overlap exceeds a critical size, where the continuum description of load transfer through the tension-shear chain breaks down. Birth, development and annihilation processes of the strained solitons can be controlled by the loading conditions. The effects of lattice symmetry and mechanical constraints are also discussed, completing the picture for microstructural evolution processes in the homo- or heterostructures of 2D crystals.

Tunable s-SNOM for Nanoscale Infrared Optical Measurement of Electronic Properties of Bilayer Graphene

Here we directly probe the electronic properties of bilayer graphene using s-SNOM measurements with a broadly tunable laser source over the energy range from 0.3 to 0.54 eV. We tune an OPO/OPA system around the interband resonance of Bernal stacked bilayer graphene (BLG) and extract amplitude and phase of the scattered light. This enables us to retrieve and reconstruct the complex optical conductivity resonance in BLG around 0.39 eV with nanoscale resolution. Our technique opens the door toward nanoscopic noncontact measurements of the electronic properties in complex hybrid 2D and van der Waals material systems, where scanning tunneling spectroscopy cannot access the decisive layers.

Enhanced tunable plasmonic resonance in crumpled graphene resonators loaded with gate tunable metamaterials

Graphene devices have been widely explored for photonic applications, as they serve as promising candidates for controlling light interactions resulting in extreme confinement and tunability of graphene plasmons. The ubiquitous presence of surface crumples in graphene, very less is known on how the crumples in graphene can affect surface plasmon resonance and its absorption properties. In this article, a novel approach based on the crumpled graphene is investigated to realize broadband tunability of plasmonic resonance through the mechanical reconfiguration of crumpled graphene resonators. The mechanical reconfiguration of graphene crumples combined with dual electrostatic gating (i.e. raising the Fermi level from 0.2-0.4 eV) of graphene serves as a tuning knob enabling broad spectral tunability of plasmonic resonance in the wavelength range of 14-24 µm. The crumpled region in the resonators exhibits an effective trapping potential where it extremely confines the surface plasmonic field on the surfaces of crumples providing localized surface plasmon resonance at the apices of these crumples. Finally, to achieve near-unity absorption >99% at the resonance wavelengths (17 µm and 22 µm) crumpled graphene resonators are loaded with four ring shaped metamaterials which result in the enhanced near-field intensity of ≈1.4×10⁶. This study delivers insight into the tunability of crumpled graphene and their coupling mechanism by providing a new platform for the flexible and gate tunable graphene sensors at the infrared region.

Configurable phonon polaritons in twisted α-MoO3

Moiré engineering is being intensively investigated as a method to tune the electronic, magnetic and optical properties of twisted van der Waals materials. Advances in moiré engineering stem from the formation of peculiar moiré superlattices at small, specific twist angles. Here we report configurable nanoscale light-matter waves-phonon polaritons-by twisting stacked α-phase molybdenum trioxide (α-MoO₃) slabs over a broad range of twist angles from 0° to 90°. Our combined experimental and theoretical results reveal a variety of polariton wavefront geometries and topological transitions as a function of the twist angle. In contrast to the origin of the modified electronic band structure in moiré superlattices, the polariton twisting configuration is attributed to the electromagnetic interaction of highly anisotropic hyperbolic polaritons in stacked α-MoO₃ slabs. These results indicate twisted α-MoO₃ to be a promising platform for nanophotonic devices with tunable functionalities.

Light-induced irreversible structural phase transition in trilayer graphene

A crystal structure has a profound influence on the physical properties of the corresponding material. By synthesizing crystals with particular symmetries, one can strongly tune their properties, even for the same chemical configuration (compare graphite and diamond, for instance). Even more interesting opportunities arise when the structural phases of crystals can be changed dynamically through external stimulations. Such abilities, though rare, lead to a number of exciting phenomena, such as phase-change memory effects. In the case of trilayer graphene, there are two common stacking configurations (ABA and ABC) that have distinct electronic band structures and exhibit very different behaviors. Domain walls exist in the trilayer graphene with both stacking orders, showing fascinating new physics such as the quantum valley Hall effect. Extensive efforts have been dedicated to the phase engineering of trilayer graphene. However, the manipulation of domain walls to achieve precise control of local structures and properties remains a considerable challenge. Here, we experimentally demonstrate that we can switch from one structural phase to another by laser irradiation, creating domains of different shapes in trilayer graphene. The ability to control the position and orientation of the domain walls leads to fine control of the local structural phases and properties of graphene, offering a simple but effective approach to create artificial two-dimensional materials with designed atomic structures and electronic and optical properties.

Growth and Grain Boundaries in 2D Materials

Grain boundaries (GBs) are a kind of lattice imperfection widely existing in two-dimensional materials, playing a critical role in materials' properties and device performance. Related key issues in this area have drawn much attention and are still under intense investigation. These issues include the characterization of GBs at different length scales, the dynamic formation of GBs during the synthesis, the manipulation of the configuration and density of GBs for specific material functionality, and the understanding of structure-property relationships and device applications. This review will provide a general introduction of progress in this field. Several techniques for characterizing GBs, such as direct imaging by high-resolution transmission electron microscopy, visualization techniques of GBs by optical microscopy, plasmon propagation, or second harmonic generation, are presented. To understand the dynamic formation process of GBs during the growth, a general geometric approach and theoretical consideration are reviewed. Moreover, strategies controlling the density of GBs for GB-free materials or materials with tunable GB patterns are summarized, and the effects of GBs on materials' properties are discussed. Finally, challenges and outlook are provided.

In situ nanoscale imaging of moiré superlattices in twisted van der Waals heterostructures

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.

Soliton-Dependent Electronic Transport across Bilayer Graphene Domain Wall

Layer-stacking domain wall in bilayer graphene is one type of topological defects that can greatly affect the electronic properties of bilayer graphene and therefore lead to nontrivial transport behaviors. An outstanding question on the layer stacking domain wall is how the electrons hop between two adjacent stacking domains. Here we report the first experimental observation of electronic transport across bilayer graphene domain walls by combining near-field infrared nanoscopy and scanning voltage microscopy techniques. We observe markedly different electron transport behaviors across the tensile- and shear-type domain walls. The tensile-type domain wall is highly reflective of low-energy incident electrons, but becomes more transparent when the electron density and the Fermi energy are increased by electrostatic gating. In contrast, the shear-type domain wall is always highly transparent at different gate voltages. Such soliton-dependent electronic transport can open up new routes to engineer novel nanoelectronic devices based on layer-stacking domain walls in bilayer graphene.

Topological polaritons and photonic magic angles in twisted α-MoO3 bilayers

Twisted two-dimensional bilayer materials exhibit many exotic electronic phenomena. Manipulating the 'twist angle' between the two layers enables fine control of the electronic band structure, resulting in magic-angle flat-band superconductivity^1,2, the formation of moiré excitons^3-8 and interlayer magnetism⁹. However, there are limited demonstrations of such concepts for photons. Here we show how analogous principles, combined with extreme anisotropy, enable control and manipulation of the photonic dispersion of phonon polaritons in van der Waals bilayers. We experimentally observe tunable topological transitions from open (hyperbolic) to closed (elliptical) dispersion contours in bilayers of α-phase molybdenum trioxide (α-MoO₃), arising when the rotation between the layers is at a photonic magic twist angle. These transitions are induced by polariton hybridization and are controlled by a topological quantity. At the transitions the bilayer dispersion flattens, exhibiting low-loss tunable polariton canalization and diffractionless propagation with a resolution of less than λ₀/40, where λ₀ is the free-space wavelength. Our findings extend twistronics¹⁰ and moiré physics to nanophotonics and polaritonics, with potential applications in nanoimaging, nanoscale light propagation, energy transfer and quantum physics.

Moiré Hyperbolic Metasurfaces

Recent advances in twistronics of low-dimensional materials, such as bilayer graphene and transition-metal dichalcogenides, have enabled a plethora of unusual phenomena associated with moiré physics. However, several of these effects require demanding manipulation of superlattices at the atomic scale, such as the careful control of rotation angle between two closely spaced atomic lattices. Here, we study moiré hyperbolic plasmons in pairs of hyperbolic metasurfaces (HMTSs), unveiling analogous phenomena at the mesoscopic scale. HMTSs are known to support confined surface waves collimated toward specific directions determined by the metasurface dispersion. By rotating two evanescently coupled HMTSs with respect to one another, we unveil rich dispersion engineering, topological transitions at magic angles, broadband field canalization, and plasmon spin-Hall phenomena. These findings open remarkable opportunities to advance metasurface optics, enriching it with moiré physics and twistronic concepts.

Global Control of Stacking-Order Phase Transition by Doping and Electric Field in Few-Layer Graphene

The layer stacking order has profound effects on the physical properties of two-dimensional van der Waals heterostructures. For example, graphene multilayers can have distinct electronic band structures and exhibit completely different behaviors depending on the stacking order. Fascinating physical phenomena, such as correlated insulators, superconductors, and ferromagnetism, can also emerge with a periodic variation of the layer stacking order, which is known as the moiré superlattice in van der Waals materials. In this work, we realize the global phase transition between different graphene layer stacking orders and elucidate its microscopic origin. We experimentally determine the energy difference between different stacking orders with the accuracy of μeV/atom. We reveal that both the carrier doping and the electric field can drive the layer-stacking phase transition through different mechanisms: carrier doping can change the energy difference because of a non-negligible work function difference between different stacking orders; the electric field, on the other hand, induces a band-gap opening in ABC-stacked graphene and hence changes the energy difference. Our findings provide a fundamental understanding of the electrically driven stacking-order phase transition in few-layer graphene and demonstrate a reversible and noninvasive method to globally control the stacking order.

Nano-photocurrent Mapping of Local Electronic Structure in Twisted Bilayer Graphene

We report a combined nano-photocurrent and infrared nanoscopy study of twisted bilayer graphene (TBG) enabling access to the local electronic phenomena at length scales as short as 20 nm. We show that the photocurrent changes sign at carrier densities tracking the local superlattice density of states of TBG. We use this property to identify domains of varying local twist angle by local photothermoelectric effect. Consistent with the photocurrent study, infrared nanoimaging experiments reveal optical conductivity features dominated by twist-angle-dependent interband transitions. Our results provide a fast and robust method for mapping the electronic structure of TBG and suggest that similar methods can be broadly applied to probe electronic inhomogeneities of Moiré superlattices in other van der Waals heterostructures.

Two Phases with Different Domain Wall Networks and a Reentrant Phase Transition in Bilayer Graphene under Strain

The analytical two-chain Frenkel-Kontorova model is used to describe domain wall networks in bilayer graphene upon biaxial stretching of one of the layers. We show that the commensurate-incommensurate phase transition leading to formation of a regular triangular domain wall network at the relative biaxial elongation of 3.0×10^{-3} is followed by the transition to another incommensurate phase with a striped network at the elongation of 3.7×10^{-3}. The reentrant transition to the phase with a triangular domain wall network is predicted for the elongation ∼10^{-2}.

Molecular dynamics simulation on the formation and development of interlayer dislocations in bilayer graphene

Molecular dynamics simulations are used to study the formation and development of interlayer dislocations in bilayer graphene (BLG) subjected to uniaxial tension. Two different BLGs are employed for the simulation: armchair (AC-BLG) and zigzag (ZZ-BLG). The atomic-level strains are calculated and the parameter 'dislocation intensity' is introduced to identify the dislocations. The interlayer dislocation is found to start at the edge and propagate to the center. For AC-BLG, the dislocations arise successively with the increase of applied strain, and all dislocations have the same width. For ZZ-BLG, the first dislocation arises alone. After that, two dislocations with different widths appear together every time. The simulated dislocation widths are in good agreement with existing experimental results. Across every dislocation, there is a transition from AB stacking to AC stacking, or vice versa. When temperature is taken into account, the dislocation boundaries become indistinct and the formation of dislocations is postponed due to the existence of dispersive small slippages. Due to the disturbance of temperature, dislocations present reciprocating movement. These findings contribute to the understanding of interlayer dislocations in two-dimensional materials, and will enable the exploration of many more strain related fundamental science problems and application challenges.

Stochastic Stress Jumps Due to Soliton Dynamics in Two-Dimensional van der Waals Interfaces

The creation and movement of dislocations determine the nonlinear mechanics of materials. At the nanoscale, the number of dislocations in structures become countable, and even single defects impact material properties. While the impact of solitons on electronic properties is well studied, the impact of solitons on mechanics is less understood. In this study, we construct nanoelectromechanical drumhead resonators from Bernal stacked bilayer graphene and observe stochastic jumps in frequency. Similar frequency jumps occur in few-layer but not twisted bilayer or monolayer graphene. Using atomistic simulations, we show that the measured shifts are a result of changes in stress due to the creation and annihilation of individual solitons. We develop a simple model relating the magnitude of the stress induced by soliton dynamics across length scales, ranging from <0.01 N/m for the measured 5 μm diameter to ∼1.2 N/m for the 38.7 nm simulations. These results demonstrate the sensitivity of 2D resonators are sufficient to probe the nonlinear mechanics of single dislocations in an atomic membrane and provide a model to understand the interfacial mechanics of different kinds of van der Waals structures under stress, which is important to many emerging applications such as engineering quantum states through electromechanical manipulation and mechanical devices like highly tunable nanoelectromechanical systems, stretchable electronics, and origami nanomachines.

Large-area epitaxial growth of curvature-stabilized ABC trilayer graphene

The properties of van der Waals (vdW) materials often vary dramatically with the atomic stacking order between layers, but this order can be difficult to control. Trilayer graphene (TLG) stacks in either a semimetallic ABA or a semiconducting ABC configuration with a gate-tunable band gap, but the latter has only been produced by exfoliation. Here we present a chemical vapor deposition approach to TLG growth that yields greatly enhanced fraction and size of ABC domains. The key insight is that substrate curvature can stabilize ABC domains. Controllable ABC yields ~59% were achieved by tailoring substrate curvature levels. ABC fractions remained high after transfer to device substrates, as confirmed by transport measurements revealing the expected tunable ABC band gap. Substrate topography engineering provides a path to large-scale synthesis of epitaxial ABC-TLG and other vdW materials.

The semiconducting ABC configuration of trilayer graphene is more challenging to grow on large scales than its semimetallic ABA counterpart. Here, an approach to trilayer growth via chemical vapor deposition is presented that utilizes substrate curvature to yield enhanced fraction and size of ABC domains.