Charge-polarized interfacial superlattices in marginally twisted hexagonal boron nitride

Efficient Charge Transfer in Graphene/CrOCl Heterostructures by van der Waals Interfacial Coupling

Due to the large volume of exposed atoms and electrons at the surface of two-dimensional materials, interfacial charge coupling has been proven as an efficient strategy to engineer the electronic structures of two-dimensional materials assembled in van der Waals heterostructures. Recently, heterostructures formed by graphene stacked with CrOCl have demonstrated intriguing quantum states, including a distorted quantum Hall phase in the monolayer graphene and the unconventional correlated insulator in the bilayer graphene. Yet, the understanding of the interlayer charge coupling in the heterostructure remains challenging. Here, we demonstrate clear evidences of efficient hole doping in the interfacial-coupled graphene/CrOCl heterostructure by detailed Raman spectroscopy and electrical transport measurements. The observation of significant blue shifts and stiffness of graphene Raman modes quantitatively determines the concentration of hole injection of about 1.2 × 1013 cm-2 from CrOCl to graphene, which is highly consistent with the enhanced conductivity of graphene. First-principles calculations based on density functional theory reveal that due to the large work function difference and the electronegativity of Cl atoms in CrOCl, the electrons are efficiently transferred from graphene to CrOCl, leading to hole doping in graphene. Our findings provide clues for understanding the exotic physical properties of graphene/CrOCl heterostructures, paving the way for further engineering of quantum electronic states by efficient interfacial charge coupling in van der Waals heterostructures.

Tunable Phonon Polariton Hybridization in a Van der Waals Hetero-Bicrystal

Phonon polaritons, the hybrid quasiparticles resulting from the coupling of photons and lattice vibrations, have gained significant attention in the field of layered van der Waals heterostructures. Particular interest has been paid to hetero-bicrystals composed of molybdenum oxide (MoO3) and hexagonal boron nitride (hBN), which feature polariton dispersion tailorable via avoided polariton mode crossings. In this work, the polariton eigenmodes in MoO3-hBN hetero-bicrystals self-assembled on ultrasmooth gold are systematically studied using synchrotron infrared nanospectroscopy. It is experimentally demonstrated that the spectral gap in bicrystal dispersion and corresponding regimes of negative refraction can be tuned by material layer thickness, and these results are quantitatively matched with a simple analytic model. Polaritonic cavity modes and polariton propagation along "forbidden" directions are also investigated in microscale bicrystals, which arise from the finite in-plane dimension of the synthesized MoO3 micro-ribbons. The findings shed light on the unique dispersion properties of polaritons in van der Waals heterostructures and pave the way for applications leveraging deeply sub-wavelength mid-infrared light-matter interactions.

Vapor Deposition of Bilayer 3R MoS2 with Room-Temperature Ferroelectricity

Two-dimensional ultrathin ferroelectrics have attracted much interest due to their potential application in high-density integration of non-volatile memory devices. Recently, 2D van der Waals ferroelectric based on interlayer translation has been reported in twisted bilayer h-BN and transition metal dichalcogenides (TMDs). However, sliding ferroelectricity is not well studied in non-twisted homo-bilayer TMD grown directly by chemical vapor deposition (CVD). In this paper, for the first time, experimental observation of a room-temperature out-of-plane ferroelectric switch in semiconducting bilayer 3R MoS2 synthesized by reverse-flow CVD is reported. Piezoelectric force microscopy (PFM) hysteretic loops and first principle calculations demonstrate that the ferroelectric nature and polarization switching processes are based on interlayer sliding. The vertical Au/3R MoS2/Pt device exhibits a switchable diode effect. Polarization modulated Schottky barrier height and polarization coupling of interfacial deep states trapping/detrapping may serve in coordination to determine switchable diode effect. The room-temperature ferroelectricity of CVD-grown MoS2 will proceed with the potential wafer-scale integration of 2D TMDs in the logic circuit.

Quasi-1D Moiré superlattices in self-twisted two-allotropic antimonene heterostructures

Two-dimensional heterostructures, characterized by a twist angle between individual sublayers, offer unique and tunable properties distinct from standalone layers. These structures typically introduce a realm of exotic quantum phenomena due to the appearance of new, long range periodicities associated with Moiré superlattices. Using molecular beam epitaxy, we demonstrate the growth of bi-allotropic 2D-Sb heterostructures on a W(110) substrate composed of twisted α (α-Sb) and β (β-Sb) phases of antimonene. Due to the relatively weak interaction between sublayers, the twist angle is intrinsically determined for each heterostructure, revealing its inherent self-twisted nature. The different atomic lattice symmetries of both allotropes lead to the formation of distinctive quasi-1D Moiré superlattices, while the random nature of the twist angle allows for a wide modulation of the Moiré potential landscape. The observed Moiré patterns on β-Sb/α-Sb heterostructures were compared with a simple model, revealing satisfactory agreement with the experiments and strongly validating the formation of self-twisted β-Sb/α-Sb heterostructures. The samples were characterized in situ using low energy electron microscopy and diffraction techniques providing a real-time tracking of the growth process and insight into the atomic structure of the synthesized nanostructures.

Sliding Memristor in Parallel-Stacked Hexagonal Boron Nitride

Sliding ferroelectricity in 2D materials, arising from interlayer sliding-induced interlayer hybridization and charge redistribution at the van der Waals interface, offers a means to manipulate spontaneous polarization at the atomic scale through various methods such as stacking order, interfacial contact, and electric field. However, the practical application of extending 2D sliding ferroelectricity remains challenging due to the contentious mechanisms and the complex device structures required for ferroelectric switching. Here, a sliding memristor based on a graphene/parallel-stacked hexagonal boron nitride/graphene tunneling device, featuring a stable memristive hysteresis induced by interfacial polarizations and barrier height modulations, is presented. As the tunneling current density increases, the memristive window broadens, achieving an on/off ratio of ≈103 and 2 order decrease of the trigger current density, attributed to the interlayer migration of positively charged boron ions and the formation of conductive filaments, as supported by the theoretical calculations. The findings open a path for exploring the sliding memristor via a tunneling device and bridge the gap between sliding ferroelectricity and memory applications.

Ultrafast high-endurance memory based on sliding ferroelectrics

The persistence of voltage-switchable collective electronic phenomena down to the atomic scale has extensive implications for area- and energy-efficient electronics, especially in emerging nonvolatile memory technology. We investigate the performance of a ferroelectric field-effect transistor (FeFET) based on sliding ferroelectricity in bilayer boron nitride at room temperature. Sliding ferroelectricity represents a different form of atomically thin two-dimensional (2D) ferroelectrics, characterized by the switching of out-of-plane polarization through interlayer sliding motion. We examined the FeFET device employing monolayer graphene as the channel layer, which demonstrated ultrafast switching speeds on the nanosecond scale and high endurance exceeding 1011 switching cycles, comparable to state-of-the-art FeFET devices. These characteristics highlight the potential of 2D sliding ferroelectrics for inspiring next-generation nonvolatile memory technology.

Interlayer Electric Multipoles Induced by In-Plane Field from Quantum Geometric Origins

We show that interlayer charge transfer in 2D materials can be driven by an in-plane electric field, giving rise to electrical multipole generation in linear and second order in-plane field. The linear and nonlinear effects have quantum geometric origins in the Berry curvature and quantum metric, respectively, defined in extended parameter spaces characteristic of layered materials. We elucidate their symmetry characters and demonstrate sizable dipole and quadrupole polarizations, respectively, in twisted bilayers and trilayers of transition metal dichalcogenides. Furthermore, we show that this effect is strongly enhanced during the topological phase transition tuned by interlayer translation. The effects point to a new electric control on the layer quantum degree of freedom.

Toward Fully Multiferroic van der Waals SpinFETs: Basic Design and Quantum Calculations

Manipulating spin transport enhances the functionality of electronic devices, allowing them to surpass physical constraints related to speed and power. For this reason, the use of van der Waals multiferroics at the interface of heterostructures offers promising prospects for developing high-performance devices, enabling the electrical control of spin information. Our work focuses primarily on a mechanism for multiferroicity in two-dimensional van der Waals materials that stems from an interplay between antiferromagnetism and the breaking of inversion symmetry in certain bilayers. We provide evidence for spin-electrical couplings that include manipulating van der Waals multiferroic edges via external voltages and the subsequent control of spin transport including for fully multiferroic spin field-effect transistors.

Polarization Saturation in Multilayered Interfacial Ferroelectrics

Van der Waals polytypes of broken inversion and mirror symmetries  have been recently shown to exhibit switchable electric polarization even at the ultimate two-layer thin limit. Their out-of-plane polarization has been found to accumulate in a ladder-like fashion with each successive layer, offering 2D building blocks for the bottom-up construction of 3D ferroelectrics. Here, it is demonstrated experimentally that beyond a critical stack thickness, the accumulated polarization in rhombohedral polytypes of molybdenum disulfide saturates. The underlying saturation mechanism, deciphered via density functional theory and self-consistent Poisson-Schrödinger calculations, point to a purely electronic redistribution involving: 1. Polarization-induced bandgap closure that allows for cross-stack charge transfer and the emergence of free surface charge; 2. Reduction of the polarization saturation value, as well as the critical thickness at which it is obtained, by the presence of free carriers. The resilience of polar layered structures to atomic surface reconstruction, which is essentially unavoidable in polar 3D crystals, potentially allows for the design of new devices with mobile surface charges. The findings, which are of general nature, should be accounted for when designing switching and/or conductive devices based on ferroelectric layered materials.

Topological Network Modes in a Twisted Moiré Phononic Crystal

Twisted moiré materials, a new class of layered structures with different twist angles for neighboring layers, are attracting great attention because of the rich intriguing physical phenomena associated with them. Of particular interest are the topological network modes, first proposed in the small angle twisted bilayer graphene under interlayer bias. Here we report the observations of such topological network modes in twisted moiré phononic crystals without requiring the external bias fields. Acoustic topological network modes that can be constructed in a wide range of twist angles are both observed in the domain walls with and without reconstructions, which serve as the analogy of the lattice relaxations in electronic moiré materials. Topological robustness of the topological network modes is observed by introducing valley-preserved defects to the network channel. Furthermore, the network can be reconfigured into two-dimensional patterns with any desired connectivity, offering a unique prototype platform for acoustic applications.

Tunnel junctions based on interfacial two dimensional ferroelectrics

Van der Waals heterostructures have opened new opportunities to develop atomically thin (opto)electronic devices with a wide range of functionalities. The recent focus on manipulating the interlayer twist angle has led to the observation of out-of-plane room temperature ferroelectricity in twisted rhombohedral bilayers of transition metal dichalcogenides. Here we explore the switching behaviour of sliding ferroelectricity using scanning probe microscopy domain mapping and tunnelling transport measurements. We observe well-pronounced ambipolar switching behaviour in ferroelectric tunnelling junctions with composite ferroelectric/non-polar insulator barriers and support our experimental results with complementary theoretical modelling. Furthermore, we show that the switching behaviour is strongly influenced by the underlying domain structure, allowing the fabrication of diverse ferroelectric tunnelling junction devices with various functionalities. We show that to observe the polarisation reversal, at least one partial dislocation must be present in the device area. This behaviour is drastically different from that of conventional ferroelectric materials, and its understanding is an important milestone for the future development of optoelectronic devices based on sliding ferroelectricity.

Ultra-flat bands at large twist angles in group-V twisted bilayer materials

Flat bands in 2D twisted materials are key to the realization of correlation-related exotic phenomena. However, a flat band often was achieved in the large system with a very small twist angle, which enormously increases the computational and experimental complexity. In this work, we proposed group-V twisted bilayer materials, including P, As, and Sb in the β phase with large twist angles. The band structure of twisted bilayer materials up to 2524 atoms has been investigated by a deep learning method DeepH, which significantly reduces the computational time. Our results show that the bandgap and the flat bandwidth of twisted bilayer β-P, β-As, and β-Sb reduce gradually with the decreasing of twist angle, and the ultra-flat band with bandwidth approaching 0 eV is achieved. Interestingly, we found that a twist angle of 9.43° is sufficient to achieve the band flatness for β-As comparable to that of twist bilayer graphene at the magic angle of 1.08°. Moreover, we also find that the bandgap reduces with decreasing interlayer distance while the flat band is still preserved, which suggests interlayer distance as an effective routine to tune the bandgap of flat band systems. Our research provides a feasible platform for exploring physical phenomena related to flat bands in twisted layered 2D materials.

Polarization-driven band topology evolution in twisted MoTe2 and WSe2

Motivated by recent experimental observations of opposite Chern numbers in R-type twisted MoTe2 and WSe2 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.

Van der Waals Ferroelectrics: Theories, Materials, and Device Applications

In recent years, an increasing number of 2D van der Waals (vdW) materials are theory-predicted or laboratory-validated to possess in-plane (IP) and/or out-of-plane (OOP) spontaneous ferroelectric polarization. Due to their dangling-bond-free surfaces, interlayer charge coupling, robust polarization, tunable energy band structures, and compatibility with silicon-based technologies, vdW ferroelectric materials exhibit great promise in ferroelectric memories, neuromorphic computing, nanogenerators, photovoltaic devices, spintronic devices, and so on. Here, the very recent advances in the field of vdW ferroelectrics (FEs) are reviewed. First, theories of ferroelectricity are briefly discussed. Then, a comprehensive summary of the non-stacking vdW ferroelectric materials is provided based on their crystal structures and the emerging sliding ferroelectrics. In addition, their potential applications in various branches/frontier fields are enumerated, with a focus on artificial intelligence. Finally, the challenges and development prospects of vdW ferroelectrics are discussed.

Bevel-edge epitaxy of ferroelectric rhombohedral boron nitride single crystal

Within the family of two-dimensional dielectrics, rhombohedral boron nitride (rBN) is considerably promising owing to having not only the superior properties of hexagonal boron nitride1-4-including low permittivity and dissipation, strong electrical insulation, good chemical stability, high thermal conductivity and atomic flatness without dangling bonds-but also useful optical nonlinearity and interfacial ferroelectricity originating from the broken in-plane and out-of-plane centrosymmetry5-23. However, the preparation of large-sized single-crystal rBN layers remains a challenge24-26, owing to the requisite unprecedented growth controls to coordinate the lattice orientation of each layer and the sliding vector of every interface. Here we report a facile methodology using bevel-edge epitaxy to prepare centimetre-sized single-crystal rBN layers with exact interlayer ABC stacking on a vicinal nickel surface. We realized successful accurate fabrication over a single-crystal nickel substrate with bunched step edges of the terrace facet (100) at the bevel facet (110), which simultaneously guided the consistent boron-nitrogen bond orientation in each BN layer and the rhombohedral stacking of BN layers via nucleation near each bevel facet. The pure rhombohedral phase of the as-grown BN layers was verified, and consequently showed robust, homogeneous and switchable ferroelectricity with a high Curie temperature. Our work provides an effective route for accurate stacking-controlled growth of single-crystal two-dimensional layers and presents a foundation for applicable multifunctional devices based on stacked two-dimensional materials.

Strain Engineering of Twisted Bilayer Graphene: The Rise of Strain-Twistronics

The layer-by-layer stacked van der Waals structures (termed vdW hetero/homostructures) offer a new paradigm for materials design-their physical properties can be tuned by the vertical stacking sequence as well as by adding a mechanical twist, stretch, and hydrostatic pressure to the atomic structure. In particular, simple twisting and stacking of two layers of graphene can form a uniform and ordered Moiré superlattice, which can effectively modulate the electrons of graphene layers and lead to the discovery of unconventional superconductivity and strong correlations. However, the twist angle of twisted bilayer graphene (tBLG) is almost unchangeable once the interlayer stacking is determined, while applying mechanical elastic strain provides an alternative way to deeply regulate the electronic structure by controlling the lattice spacing and symmetry. In this review, diverse experimental advances are introduced in straining tBLG by in-plane and out-of-plane modes, followed by the characterizations and calculations toward quantitatively tuning the strain-engineered electronic structures. It is further discussed that the structural relaxation in strained Moiré superlattice and its influence on electronic structures. Finally, the conclusion entails prospects for opportunities of strained twisted 2D materials, discussions on existing challenges, and an outlook on the intriguing emerging field, namely "strain-twistronics".

In-plane anisotropic two-dimensional materials for twistronics

In-plane anisotropic two-dimensional (2D) materials exhibit in-plane orientation-dependent properties. The anisotropic unit cell causes these materials to show lower symmetry but more diverse physical properties than in-plane isotropic 2D materials. In addition, the artificial stacking of in-plane anisotropic 2D materials can generate new phenomena that cannot be achieved in in-plane isotropic 2D materials. In this perspective we provide an overview of representative in-plane anisotropic 2D materials and their properties, such as black phosphorus, group IV monochalcogenides, group VI transition metal dichalcogenides with 1T' and Tdphases, and rhenium dichalcogenides. In addition, we discuss recent theoretical and experimental investigations of twistronics using in-plane anisotropic 2D materials. Both in-plane anisotropic 2D materials and their twistronics hold considerable potential for advancing the field of 2D materials, particularly in the context of orientation-dependent optoelectronic devices.

Stacking engineering in layered homostructures: transitioning from 2D to 3D architectures

Artificial materials, characterized by their distinctive properties and customized functionalities, occupy a central role in a wide range of applications including electronics, spintronics, optoelectronics, catalysis, and energy storage. The emergence of atomically thin two-dimensional (2D) materials has driven the creation of artificial heterostructures, harnessing the potential of combining various 2D building blocks with complementary properties through the art of stacking engineering. The promising outcomes achieved for heterostructures have spurred an inquisitive exploration of homostructures, where identical 2D layers are precisely stacked. This perspective primarily focuses on the field of stacking engineering within layered homostructures, where precise control over translational or rotational degrees of freedom between vertically stacked planes or layers is paramount. In particular, we provide an overview of recent advancements in the stacking engineering applied to 2D homostructures. Additionally, we will shed light on research endeavors venturing into three-dimensional (3D) structures, which allow us to proactively address the limitations associated with artificial 2D homostructures. We anticipate that the breakthroughs in stacking engineering in 3D materials will provide valuable insights into the mechanisms governing stacking effects. Such advancements have the potential to unlock the full capability of artificial layered homostructures, propelling the future development of materials, physics, and device applications.

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.

Stacking Order Engineering of Two-Dimensional Materials and Device Applications

Stacking orders in 2D van der Waals (vdW) materials dictate the relative sliding (lateral displacement) and twisting (rotation) between atomically thin layers. By altering the stacking order, many new ferroic, strongly correlated and topological orderings emerge with exotic electrical, optical and magnetic properties. Thanks to the weak vdW interlayer bonding, such highly flexible and energy-efficient stacking order engineering has transformed the design of quantum properties in 2D vdW materials, unleashing the potential for miniaturized high-performance device applications in electronics, spintronics, photonics, and surface chemistry. This Review provides a comprehensive overview of stacking order engineering in 2D vdW materials and their device applications, ranging from the typical fabrication and characterization methods to the novel physical properties and the emergent slidetronics and twistronics device prototyping. The main emphasis is on the critical role of stacking orders affecting the interlayer charge transfer, orbital coupling and flat band formation for the design of innovative materials with on-demand quantum properties and surface potentials. By demonstrating a correlation between the stacking configurations and device functionality, we highlight their implications for next-generation electronic, photonic and chemical energy conversion devices. We conclude with our perspective of this exciting field including challenges and opportunities for future stacking order engineering research.

Non-volatile electrical polarization switching via domain wall release in 3R-MoS2 bilayer

Understanding the nature of sliding ferroelectricity is of fundamental importance for the discovery and application of two-dimensional ferroelectric materials. In this work, we investigate the phenomenon of switchable polarization in a bilayer MoS2 with natural rhombohedral stacking, where the spontaneous polarization is coupled with excitonic effects through asymmetric interlayer coupling. Using optical spectroscopy and imaging techniques, we observe how a released domain wall switches the polarization of a large single domain. Our results highlight the importance of domain walls in the polarization switching of non-twisted rhombohedral transition metal dichalcogenides and open new opportunities for the non-volatile control of their optical response.

A 2D ferroelectric vortex pattern in twisted BaTiO3 freestanding layers

The wealth of complex polar topologies1-10 recently found in nanoscale ferroelectrics results from a delicate balance between the intrinsic tendency of the materials to develop a homogeneous polarization and the electric and mechanical boundary conditions imposed on them. Ferroelectric-dielectric interfaces are model systems in which polarization curling originates from open circuit-like electric boundary conditions, to avoid the build-up of polarization charges through the formation of flux-closure11-14 domains that evolve into vortex-like structures at the nanoscale15-17 level. Although ferroelectricity is known to couple strongly with strain (both homogeneous18 and inhomogeneous19,20), the effect of mechanical constraints21 on thin-film nanoscale ferroelectrics has been comparatively less explored because of the relative paucity of strain patterns that can be implemented experimentally. Here we show that the stacking of freestanding ferroelectric perovskite layers with controlled twist angles provides an opportunity to tailor these topological nanostructures in a way determined by the lateral strain modulation associated with the twisting. Furthermore, we find that a peculiar pattern of polarization vortices and antivortices emerges from the flexoelectric coupling of polarization to strain gradients. This finding provides opportunities to create two-dimensional high-density vortex crystals that would enable us to explore previously unknown physical effects and functionalities.

Twisted-layer boron nitride ceramic with high deformability and strength

Moiré superlattices formed by twisted stacking in van der Waals materials have emerged as a new platform for exploring the physics of strongly correlated materials and other emergent phenomena1-5. However, there remains a lack of research on the mechanical properties of twisted-layer van der Waals materials, owing to a lack of suitable strategies for making three-dimensional bulk materials. Here we report the successful synthesis of a polycrystalline boron nitride bulk ceramic with high room-temperature deformability and strength. This ceramic, synthesized from an onion-like boron nitride nanoprecursor with conventional spark plasma sintering and hot-pressing sintering, consists of interlocked laminated nanoplates in which parallel laminae are stacked with varying twist angles. The compressive strain of this bulk ceramic can reach 14% before fracture, about one order of magnitude higher compared with traditional ceramics (less than 1% in general), whereas the compressive strength is about six times that of ordinary hexagonal boron nitride layered ceramics. The exceptional mechanical properties are due to a combination of the elevated intrinsic deformability of the twisted layering in the nanoplates and the three-dimensional interlocked architecture that restricts deformation from propagating across individual nanoplates. The advent of this twisted-layer boron nitride bulk ceramic opens a gate to the fabrication of highly deformable bulk ceramics.

Optical properties and plasmons in moiré structures

The discoveries of numerous exciting phenomena in twisted bilayer graphene (TBG) are stimulating significant investigations on moiré structures that possess a tunable moiré potential. Optical response can provide insights into the electronic structures and transport phenomena of non-twisted and twisted moiré structures. In this article, we review both experimental and theoretical studies of optical properties such as optical conductivity, dielectric function, non-linear optical response, and plasmons in moiré structures composed of graphene, hexagonal boron nitride (hBN), and/or transition metal dichalcogenides. Firstly, a comprehensive introduction to the widely employed methodology on optical properties is presented. After, moiré potential induced optical conductivity and plasmons in non-twisted structures are reviewed, such as single layer graphene-hBN, bilayer graphene-hBN and graphene-metal moiré heterostructures. Next, recent investigations of twist-angle dependent optical response and plasmons are addressed in twisted moiré structures. Additionally, we discuss how optical properties and plasmons could contribute to the understanding of the many-body effects and superconductivity observed in moiré structures.

Nanotube Slidetronics

One-dimensional slidetronics is predicted for double-walled boron-nitride nanotubes. Local electrostatic polarization patterns along the body of the nanotube are found to be determined by the nature of the two nanotube walls, their relative configuration, and circumferential faceting modulation during coaxial interwall sliding. By careful choice of chiral indices, chiral polarization patterns can emerge that spiral around the nanotube circumference. The potential usage of the discovered slidetronic effect for low-dimensional nanogenerators is briefly discussed.

Multiresistance states in ferro- and antiferroelectric trilayer boron nitride

Stacking two atomic layers together can induce interlayer (sliding) ferroelectricity that is absent in their naturally occurring crystal forms. With the flexibility of two-dimensional materials, more layers could be assembled to give rise to even richer polarization states. Here, we show that three-layer boron nitride can host ferro- and antiferroelectric domains in the same sample. When used as a tunneling junction, the polarization of these domains could be switched in a layer-by-layer procedure, producing multiple resistance states. Theoretical investigation reveals an important role played by the interaction between the trilayer boron nitride and graphene substrate. These findings reveal the great potential and unique properties of 2D sliding ferroelectric materials.

Electrostatic moiré potential from twisted hexagonal boron nitride layers

Moiré superlattices host a rich variety of correlated electronic phases. However, the moiré potential is fixed by interlayer coupling, and it is dependent on the nature of carriers and valleys. In contrast, it has been predicted that twisted hexagonal boron nitride (hBN) layers can impose a periodic electrostatic potential capable of engineering the properties of adjacent functional layers. Here, we show that this potential is described by a theory of electric polarization originating from the interfacial charge redistribution, validated by its dependence on supercell sizes and distance from the twisted interfaces. This enables controllability of the potential depth and profile by controlling the twist angles between the two interfaces. Employing this approach, we further demonstrate how the electrostatic potential from a twisted hBN substrate impedes exciton diffusion in semiconductor monolayers, suggesting opportunities for engineering the properties of adjacent functional layers using the surface potential of a twisted hBN substrate.

Moiré synaptic transistor with room-temperature neuromorphic functionality

Moiré quantum materials host exotic electronic phenomena through enhanced internal Coulomb interactions in twisted two-dimensional heterostructures1-4. When combined with the exceptionally high electrostatic control in atomically thin materials5-8, moiré heterostructures have the potential to enable next-generation electronic devices with unprecedented functionality. However, despite extensive exploration, moiré electronic phenomena have thus far been limited to impractically low cryogenic temperatures9-14, thus precluding real-world applications of moiré quantum materials. Here we report the experimental realization and room-temperature operation of a low-power (20 pW) moiré synaptic transistor based on an asymmetric bilayer graphene/hexagonal boron nitride moiré heterostructure. The asymmetric moiré potential gives rise to robust electronic ratchet states, which enable hysteretic, non-volatile injection of charge carriers that control the conductance of the device. The asymmetric gating in dual-gated moiré heterostructures realizes diverse biorealistic neuromorphic functionalities, such as reconfigurable synaptic responses, spatiotemporal-based tempotrons and Bienenstock-Cooper-Munro input-specific adaptation. In this manner, the moiré synaptic transistor enables efficient compute-in-memory designs and edge hardware accelerators for artificial intelligence and machine learning.

Mechanical, electronic, optical, piezoelectric and ferroic properties of strained graphene and other strained monolayers and multilayers: an update

This is an update of a previous review (Naumiset al2017Rep. Prog. Phys.80096501). Experimental and theoretical advances for straining graphene and other metallic, insulating, ferroelectric, ferroelastic, ferromagnetic and multiferroic 2D materials were considered. We surveyed (i) methods to induce valley and sublattice polarisation (P) in graphene, (ii) time-dependent strain and its impact on graphene's electronic properties, (iii) the role of local and global strain on superconductivity and other highly correlated and/or topological phases of graphene, (iv) inducing polarisationPon hexagonal boron nitride monolayers via strain, (v) modifying the optoelectronic properties of transition metal dichalcogenide monolayers through strain, (vi) ferroic 2D materials with intrinsic elastic (σ), electric (P) and magnetic (M) polarisation under strain, as well as incipient 2D multiferroics and (vii) moiré bilayers exhibiting flat electronic bands and exotic quantum phase diagrams, and other bilayer or few-layer systems exhibiting ferroic orders tunable by rotations and shear strain. The update features the experimental realisations of a tunable two-dimensional Quantum Spin Hall effect in germanene, of elemental 2D ferroelectric bismuth, and 2D multiferroic NiI2. The document was structured for a discussion of effects taking place in monolayers first, followed by discussions concerning bilayers and few-layers, and it represents an up-to-date overview of exciting and newest developments on the fast-paced field of 2D materials.

Distinguishing Different Stackings in Layered Materials via Luminescence Spectroscopy

Despite its simple crystal structure, layered boron nitride features a surprisingly complex variety of phonon-assisted luminescence peaks. We present a combined experimental and theoretical study on ultraviolet-light emission in hexagonal and rhombohedral bulk boron nitride crystals. Emission spectra of high-quality samples are measured via cathodoluminescence spectroscopy, displaying characteristic differences between the two polytypes. These differences are explained using a fully first-principles computational technique that takes into account radiative emission from "indirect," finite-momentum excitons via coupling to finite-momentum phonons. We show that the differences in peak positions, number of peaks, and relative intensities can be qualitatively and quantitatively explained, once a full integration over all relevant momenta of excitons and phonons is performed.

Substrate Ferroelectric Proximity Effects Have a Strong Influence on Charge Carrier Lifetime in Black Phosphorus

By stacking monolayer black phosphorus (MBP) with nonpolarized and ferroelectric polarized bilayer hexagonal boron nitride (h-BN), we demonstrate that ferroelectric proximity effects have a strong influence on the charge carrier lifetime of MBP using nonadiabatic (NA) molecular dynamics simulations. Through enhancing the motion of phosphorus atoms, ferroelectric polarization enhances the overlap of electron-hole wave functions that improves NA coupling and decreases the bandgap, resulting in a rapid electron-hole recombination completing within a quarter of nanoseconds, which is two times shorter than that in nonpolarized stackings. In addition to the dominant in-plane Ag2 mode in free-standing MBP, the out-of-plane high-frequency Ag1 and low-frequency interlayer breathing modes presented in the heterojunctions drive the recombination. Notably, the resonance between the breathing mode within bilayer h-BN and the B1u mode of MBP provides an additional nonradiative channel in ferroelectric stackings, further accelerating charge recombination. These findings are crucial for charge dynamics manipulation in two-dimensional materials via substrate ferroelectric proximity effects.

Non-Linear Optics at Twist Interfaces in h-BN/SiC Heterostructures

Understanding the emergent electronic structure in twisted atomically thin layers has led to the exciting field of twistronics. However, practical applications of such systems are challenging since the specific angular correlations between the layers must be precisely controlled and the layers have to be single crystalline with uniform atomic ordering. Here, an alternative, simple, and scalable approach is suggested, where nanocrystallinetwo-dimensional (2D) film on 3D substrates yields twisted-interface-dependent properties. Ultrawide-bandgap hexagonal boron nitride (h-BN) thin films are directly grown on high in-plane lattice mismatched wide-bandgap silicon carbide (4H-SiC) substrates to explore the twist-dependent structure-property correlations. Concurrently, nanocrystalline h-BN thin film shows strong non-linear second-harmonic generation and ultra-low cross-plane thermal conductivity at room temperature, which are attributed to the twisted domain edges between van der Waals stacked nanocrystals with random in-plane orientations. First-principles calculations based on time-dependent density functional theory manifest strong even-order optical nonlinearity in twisted h-BN layers. This work unveils that directly deposited 2D nanocrystalline thin film on 3D substrates could provide easily accessible twist-interfaces, therefore enabling a simple and scalable approach to utilize the 2D-twistronics integrated in 3D material devices for next-generation nanotechnology.

Strain-Induced Quasi-1D Channels in Twisted Moiré Lattices

We study the effects of strain in moiré systems composed of honeycomb lattices. We elucidate the formation of almost perfect one-dimensional moiré patterns in twisted bilayer systems. The formation of such patterns is a consequence of an interplay between twist and strain which gives rise to a collapse of the reciprocal space unit cell. As a criterion for such collapse we find a simple relation between the two quantities and the material specific Poisson ratio. The induced one-dimensional behavior is characterized by two, usually incommensurate, periodicities. Our results offer explanations for the complex patterns of one-dimensional channels observed in low angle twisted bilayer graphene systems and twisted bilayer dicalcogenides. Our findings can be applied to any hexagonal twisted moiré pattern and can be easily extended to other geometries.

Visualizing moiré ferroelectricity via plasmons and nano-photocurrent in graphene/twisted-WSe2 structures

Ferroelectricity, a spontaneous and reversible electric polarization, is found in certain classes of van der Waals (vdW) materials. The discovery of ferroelectricity in twisted vdW layers provides new opportunities to engineer spatially dependent electric and optical properties associated with the configuration of moiré superlattice domains and the network of domain walls. Here, we employ near-field infrared nano-imaging and nano-photocurrent measurements to study ferroelectricity in minimally twisted WSe2. The ferroelectric domains are visualized through the imaging of the plasmonic response in a graphene monolayer adjacent to the moiré WSe2 bilayers. Specifically, we find that the ferroelectric polarization in moiré domains is imprinted on the plasmonic response of the graphene. Complementary nano-photocurrent measurements demonstrate that the optoelectronic properties of graphene are also modulated by the proximal ferroelectric domains. Our approach represents an alternative strategy for studying moiré ferroelectricity at native length scales and opens promising prospects for (opto)electronic devices.

Ferroelectric Switching at Symmetry-Broken Interfaces by Local Control of Dislocations Networks

Semiconducting ferroelectric materials with low energy polarization switching offer a platform for next-generation electronics such as ferroelectric field-effect transistors. Recently discovered interfacial ferroelectricity in bilayers of transition metal dichalcogenide films provides an opportunity to combine the potential of semiconducting ferroelectrics with the design flexibility of 2D material devices. Here, local control of ferroelectric domains in a marginally twisted WS2 bilayer is demonstrated with a scanning tunneling microscope at room temperature, and their observed reversible evolution is understood using a string-like model of the domain wall network (DWN). Two characteristic regimes of DWN evolution are identified: (i) elastic bending of partial screw dislocations separating smaller domains with twin stackings due to mutual sliding of monolayers at domain boundaries and (ii) merging of primary domain walls into perfect screw dislocations, which become the seeds for the recovery of the initial domain structure upon reversing electric field. These results open the possibility to achieve full control over atomically thin semiconducting ferroelectric domains using local electric fields, which is a critical step towards their technological use.

Atypical Sliding and Moiré Ferroelectricity in Pure Multilayer Graphene

Most nonferroelectric two-dimensional materials can be endowed with so-called sliding ferroelectricity via nonequivalent homobilayer stacking, which is not applicable to monoelement systems like pure graphene bilayer with inversion symmetry at any sliding vector. Herein, we show first-principles evidence that multilayer graphene with N>3 can all be ferroelectric, where the polarizations of polar states stem from the symmetry breaking in stacking configurations of across layer instead of adjacent layer, which are electrically switchable via interlayer sliding. The nonpolar states can also be electrically driven to polar states via sliding, and more diverse states with distinct polarizations will emerge in more layers. In contrast to the ferroelectric moiré domains with opposite polarization directions in twisted bilayers reported previously, the moiré pattern in some multilayer graphene systems (e.g., twisted monolayer-trilayer graphene) possess nonzero net polarizations with domains of the same direction separated by nonpolar regions, which can be electrically reversed upon interlayer sliding. The distinct moiré bands of two polar states should facilitate electrical detection of such sliding moiré ferroelectricity during switching.

Operando electron microscopy investigation of polar domain dynamics in twisted van der Waals homobilayers

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.

Excitons in mesoscopically reconstructed moiré heterostructures

Moiré effects in vertical stacks of two-dimensional crystals give rise to new quantum materials with rich transport and optical phenomena that originate from modulations of atomic registries within moiré supercells. Due to finite elasticity, however, the superlattices can transform from moiré-type to periodically reconstructed patterns. Here we expand the notion of such nanoscale lattice reconstruction to the mesoscopic scale of laterally extended samples and demonstrate rich consequences in optical studies of excitons in MoSe₂-WSe₂ heterostructures with parallel and antiparallel alignments. Our results provide a unified perspective on moiré excitons in near-commensurate semiconductor heterostructures with small twist angles by identifying domains with exciton properties of distinct effective dimensionality, and establish mesoscopic reconstruction as a compelling feature of real samples and devices with inherent finite size effects and disorder. Generalized to stacks of other two-dimensional materials, this notion of mesoscale domain formation with emergent topological defects and percolation networks will instructively expand the understanding of fundamental electronic, optical and magnetic properties of van der Waals heterostructures.

High-Performance Sliding Ferroelectric Transistor Based on Schottky Barrier Tuning

Sliding ferroelectricity associated with interlayer translation is an excellent candidate for ferroelectric device miniaturization. However, the weak polarization gives rise to the poor performance of sliding ferroelectric transistors with a low on/off ratio and a narrow memory window, which restricts its practical application. To address the issue, we propose a facile strategy by regulating the Schottky barrier in sliding ferroelectric semiconductor transistors based on γ-InSe, in which a high performance with a large on/off ratio (10⁶) and a wide memory window (4.5 V) was ultimately acquired. Additionally, the memory window of the device can be further modulated by electrostatic doping or light excitation. These results open up new ways for designing novel ferroelectric devices based on emerging sliding ferroelectricity.

Every-other-layer dipolar excitons in a spin-valley locked superlattice

Monolayer semiconducting transition metal dichalcogenides possess broken inversion symmetry and strong spin-orbit coupling, leading to a unique spin-valley locking effect. In 2H stacked pristine multilayers, spin-valley locking yields an electronic superlattice structure, where alternating layers correspond to barriers and quantum wells depending on the spin-valley indices. Here we show that the spin-valley locked superlattice hosts a kind of dipolar exciton with the electron and hole constituents separated in an every-other-layer configuration: that is, either in two even or two odd layers. Such excitons become optically bright via hybridization with intralayer excitons. This effect is also manifested by the presence of multiple anti-crossing patterns in the reflectance spectra, as the dipolar exciton is tuned through the intralayer resonance by an electric field. The reflectance spectra further reveal an excited state orbital of the every-other-layer exciton, pointing to a sizable binding energy in the same order of magnitude as the intralayer exciton. As layer thickness increases, the dipolar exciton can form a one-dimensional Bose-Hubbard chain displaying layer number-dependent fine spectroscopy structures.

Complex Strain Scapes in Reconstructed Transition-Metal Dichalcogenide Moiré Superlattices

We investigate the intrinsic strain associated with the coupling of twisted MoS₂/MoSe₂ heterobilayers by combining experiments and molecular dynamics simulations. Our study reveals that small twist angles (between 0 and 2°) give rise to considerable atomic reconstructions, large moiré periodicities, and high levels of local strain (with an average value of ∼1%). Moreover, the formation of moiré superlattices is assisted by specific reconstructions of stacking domains. This process leads to a complex strain distribution characterized by a combined deformation state of uniaxial, biaxial, and shear components. Lattice reconstruction is hindered with larger twist angles (>10°) that produce moiré patterns of small periodicity and negligible strains. Polarization-dependent Raman experiments also evidence the presence of an intricate strain distribution in heterobilayers with near-0° twist angles through the splitting of the E_2g¹ mode of the top (MoS₂) layer due to atomic reconstruction. Detailed analyses of moiré patterns measured by AFM unveil varying degrees of anisotropy in the moiré superlattices due to the heterostrain induced during the stacking of monolayers.

Local dielectric function of hBN-encapsulated WS2flakes grown by chemical vapor deposition

Hexagonal boron nitride (hBN), sometimes referred to as white graphene, receives growing interest in the scientific community, especially when combined into van der Waals (vdW) homo- and heterostacks, in which novel and interesting phenomena may arise. hBN is also commonly used in combination with two-dimensional (2D) semiconducting transition metal dichalcogenides (TMDCs). The realization of hBN-encapsulated TMDC homo- and heterostacks can indeed offer opportunities to investigate and compare TMDC excitonic properties in various stacking configurations. In this work, we investigate the optical response at the micrometric scale of mono- and homo-bilayer WS₂grown by chemical vapor deposition and encapsulated between two single layers of hBN. Imaging spectroscopic ellipsometry is exploited to extract the local dielectric functions across one single WS₂flake and detect the evolution of excitonic spectral features from monolayer to bilayer regions. Exciton energies undergo a redshift by passing from hBN-encapsulated single layer to homo-bilayer WS₂, as also confirmed by photoluminescence spectra. Our results can provide a reference for the study of the dielectric properties of more complex systems where hBN is combined with other 2D vdW materials into heterostructures and are stimulating towards the investigation of the optical response of other technologically-relevant heterostacks.

General Theory for Bilayer Stacking Ferroelectricity

Two-dimensional (2D) ferroelectrics, which are rare in nature, enable high-density nonvolatile memory with low energy consumption. Here, we propose a theory of bilayer stacking ferroelectricity (BSF), in which two stacked layers of the same 2D material, with different rotation and translation, exhibit ferroelectricity. By performing systematic group theory analysis, we find all the possible BSF in all 80 layer groups (LGs) and discover the rules about the creation and annihilation of symmetries in the bilayer. Our general theory can not only explain all the previous findings (including sliding ferroelectricity), but also provide a new perspective. Interestingly, the direction of the electric polarization of the bilayer could be totally different from that of the single layer. In particular, the bilayer could become ferroelectric after properly stacking two centrosymmetric nonpolar monolayers. By means of first-principles simulations, we predict that the ferroelectricity and thus multiferroicity can be introduced to the prototypical 2D ferromagnetic centrosymmetric material CrI_{3} by stacking. Furthermore, we find that the out-of-plane electric polarization in bilayer CrI_{3} is interlocked with the in-plane electric polarization, suggesting that the out-of-plane polarization can be manipulated in a deterministic way through the application of an in-plane electric field. The present BSF theory lays a solid foundation for designing a large number of bilayer ferroelectrics and thus colorful platforms for fundamental studies and applications.

Orbital distortion and electric field control of sliding ferroelectricity in a boron nitride bilayer

Recent experiments confirm that two-dimensional boron nitride (BN) films possess room-temperature out-of-plane ferroelectricity when each BN layer is sliding with respect to each other. This ferroelectricity is attributed to the interlayered orbital hybridization or interlayer charge transfer in previous work. In this work, we attempt to understand the sliding ferroelectricity from the perspective of orbital distortion of long-pair electrons. Using the maximally localized Wannier function method and first-principles calculations, the out-of-planep_zorbitals of BN are investigated. Our results indicate that the interlayer van der Waals interaction causes the distortion of the Np_zorbitals. Based on the picture of out-of-plane orbital distortion, we propose a possible mechanism to tune the ferroelectric polarization by external fields, including electric field and stress field. It is found that both the polarization intensity and direction can be modulated under the electric field. The polarization intensity of the system can also be controlled by stress field perpendicular to the plane. This study will provide theoretical help in the device design based on sliding ferroelectrics.

Polar meron-antimeron networks in strained and twisted bilayers

Out-of-plane polar domain structures have recently been discovered in strained and twisted bilayers of inversion symmetry broken systems such as hexagonal boron nitride. Here we show that this symmetry breaking also gives rise to an in-plane component of polarization, and the form of the total polarization is determined purely from symmetry considerations. The in-plane component of the polarization makes the polar domains in strained and twisted bilayers topologically non-trivial, forming a network of merons and antimerons (half-skyrmions and half-antiskyrmions). For twisted systems, the merons are of Bloch type whereas for strained systems they are of Néel type. We propose that the polar domains in strained or twisted bilayers may serve as a platform for exploring topological physics in layered materials and discuss how control over topological phases and phase transitions may be achieved in such systems.

Preparation, properties and applications of two-dimensional superlattices

As a combination concept of a 2D material and a superlattice, two-dimensional superlattices (2DSs) have attracted increasing attention recently. The natural advantages of 2D materials in their properties, dimension, diversity and compatibility, and their gradually improved technologies for preparation and device fabrication serve as solid foundations for the development of 2DSs. Compared with the existing 2D materials and even their heterostructures, 2DSs relate to more materials and elaborate architectures, leading to novel systems with more degrees of freedom to modulate material properties at the nanoscale. Here, three typical types of 2DSs, including the component, strain-induced and moiré superlattices, are reviewed. The preparation methods, properties and state-of-the-art applications of each type are summarized. An outlook of the challenges and future developments is also presented. We hope that this work can provide a reference for the development of 2DS-related research.

Piezocatalytic Techniques in Environmental Remediation

As a consequence of rapid industrialization throughout the world, various environmental pollutants have begun to accumulate in water, air, and soil. This endangers the ecological environment of the earth, and environmental remediation has become an immediate priority. Among various environmental remediation techniques, piezocatalytic techniques, which uniquely take advantage of the piezoelectric effect, have attracted much attention. Piezoelectric effects allow pollutant degradation directly, while also enhancing photocatalysis by reducing the recombination of photogenerated carriers. In this Review, we provide a comprehensive summary of recent developments in piezocatalytic techniques for environmental remediation. The origin of the piezoelectric effect as well as classification of piezoelectric materials and their application in environmental remediation are systematically summarized. We also analyze the potential underlying mechanisms. Finally, urgent problems and the future development of piezocatalytic techniques are discussed.

Engineering Grain Boundaries in Two-Dimensional Electronic Materials

Engineering the boundary structures in 2D materials provides an unprecedented opportunity to program the physical properties of the materials with extensive tunability and realize innovative devices with advanced functionalities. However, structural engineering technology is still in its infancy, and creating artificial boundary structures with high reproducibility remains difficult. In this review, various emergent properties of 2D materials with different grain boundaries, and the current techniques to control the structures, are introduced. The remaining challenges for scalable and reproducible structure control and the outlook on the future directions of the related techniques are also discussed.

Interlayer Registry Dictates Interfacial 2D Material Ferroelectricity

We discover that the complex ferroelectric response of layered materials toward interlayer sliding is fully dictated by the interlayer lattice registry. Importantly, the entire sliding polarization landscape of two-dimensional (2D) layered material interfaces is fully described via a simple and intuitive geometric measure, termed the polarization registry index (PRI), that quantifies the degree of interlayer commensurability. Beyond the understanding of the fundamental origin of 2D ferroelectricity, the developed tool also provides highly efficient characterization and rationalization of existing experimental and computational evidence of 2D interfacial ferroelectricity, as well as the prediction of emergent controllable polarization in new noncentrosymmetric layered systems.