Interlayer Decoupling in 30° Twisted Bilayer Graphene Quasicrystal

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.

The Integration of Two-Dimensional Materials and Ferroelectrics for Device Applications

In recent years, there has been growing interest in functional devices based on two-dimensional (2D) materials, which possess exotic physical properties. With an ultrathin thickness, the optoelectrical and electrical properties of 2D materials can be effectively tuned by an external field, which has stimulated considerable scientific activities. Ferroelectric fields with a nonvolatile and electrically switchable feature have exhibited enormous potential in controlling the electronic and optoelectronic properties of 2D materials, leading to an extremely fertile area of research. Here, we review the 2D materials and relevant devices integrated with ferroelectricity. This review starts to introduce the background about the concerned themes, namely 2D materials and ferroelectrics, and then presents the fundamental mechanisms, tuning strategies, as well as recent progress of the ferroelectric effect on the optical and electrical properties of 2D materials. Subsequently, the latest developments of 2D material-based electronic and optoelectronic devices integrated with ferroelectricity are summarized. Finally, the future outlook and challenges of this exciting field are suggested.

Charge-4e superconductivity and chiral metal in 45°-twisted bilayer cuprates and related bilayers

The material realization of charge-4e/6e superconductivity (SC) is a big challenge. Here, we propose to realize charge-4e SC in maximally-twisted homobilayers, such as 45∘-twisted bilayer cuprates and 30∘-twisted bilayer graphene, referred to as twist-bilayer quasicrystals (TB-QC). When each monolayer hosts a pairing state with the largest pairing angular momentum, previous studies have found that the second-order interlayer Josephson coupling would drive chiral topological SC (TSC) in the TB-QC. Here we propose that, above the Tc of the chiral TSC, either charge-4e SC or chiral metal can arise as vestigial phases, depending on the ordering of the total- and relative-pairing-phase fields of the two layers. Based on a thorough symmetry analysis to get the low-energy effective Hamiltonian, we conduct a combined renormalization-group and Monte-Carlo study and obtain the phase diagram, which includes the charge-4e SC and chiral metal phases.

Moiré Superlattice Structure of Pleated Trilayer Graphene Imaged by 4D Scanning Transmission Electron Microscopy

Moiré superlattices in graphene arise from rotational twists in stacked 2D layers, leading to specific band structures, charge density and interlayer electron and excitonic interactions. The periodicities in bilayer graphene moiré lattices are given by a simple moiré basis vector that describes periodic oscillations in atomic density. The addition of a third layer to form trilayer graphene generates a moiré lattice comprised of multiple harmonics that do not occur in bilayer systems, leading to nontrivial crystal symmetries. Here, we use atomic resolution 4D-scanning transmission electron microscopy to study atomic structure in bilayer and trilayer graphene moiré superlattices and use 4D-STEM to map the electric fields to show subtle variations in the long-range moiré patterns. We show that monolayer graphene folded into an S-bend graphene pleat produces trilayer moiré superlattices with both small (<2°) and larger twist angles (7-30°). Annular in-plane electric field concentrations are detected in high angle bilayers due to overlapping rotated graphene hexagons in each layer. The presence of a third low angle twisted layer in S-bend trilayer graphene, introduces a long-range modulation of the atomic structure so that no real space unit cell is detected. By directly imaging trilayer moiré harmonics that span from picoscale to nanoscale using 4D-STEM, we gain insights into the complex spatial distributions of atomic density and electric fields in trilayer twisted layered materials.

Controllable Synthesis and Growth Mechanism of Interlayer-Coupled Multilayer Graphene

The potential applications of multilayer graphene in many fields, such as superconductivity and thermal conductivity, continue to emerge. However, there are still many problems in the growth mechanism of multilayer graphene. In this paper, a simple control strategy for the preparation of interlayer-coupled multilayer graphene on a liquid Cu substrate was developed. By adjusting the flow rate of a carrier gas in the CVD system, the effect for finely controlling the carbon source supply was achieved. Therefore, the carbon could diffuse from the edge of the single-layer graphene to underneath the layer of graphene and then interlayer-coupled multilayer graphene with different shapes were prepared. Through a variety of characterization methods, it was determined that the stacked mode of interlayer-coupled multilayer graphene conformed to AB-stacking structure. The small multilayer graphene domains stacked under single-layer graphene was first found, and the growth process and growth mechanism of interlayer-coupled multilayer graphene with winged and umbrella shapes were studied, respectively. This study reveals the growth mechanism of multilayer graphene grown by using a carbon source through edge diffusion, paving the way for the controllable preparation of multilayer graphene on a liquid Cu surface.

Recent Advances in Moiré Superlattice Systems by Angle-Resolved Photoemission Spectroscopy

The last decade has witnessed a flourish in 2D materials including graphene and transition metal dichalcogenides (TMDs) as atomic-scale Legos. Artificial moiré superlattices via stacking 2D materials with a twist angle and/or a lattice mismatch have recently become a fertile playground exhibiting a plethora of emergent properties beyond their building blocks. These rich quantum phenomena stem from their nontrivial electronic structures that are effectively tuned by the moiré periodicity. Modern angle-resolved photoemission spectroscopy (ARPES) can directly visualize electronic structures with decent momentum, energy, and spatial resolution, thus can provide enlightening insights into fundamental physics in moiré superlattice systems and guides for designing novel devices. In this review, first, a brief introduction is given on advanced ARPES techniques and basic ideas of band structures in a moiré superlattice system. Then ARPES research results of various moiré superlattice systems are highlighted, including graphene on substrates with small lattice mismatches, twisted graphene/TMD moiré systems, and high-order moiré superlattice systems. Finally, it discusses important questions that remain open, challenges in current experimental investigations, and presents an outlook on this field of research.

Twist angle-dependent work functions in CVD-grown twisted bilayer graphene probed by Kelvin probe force microscopy

Tailoring the interlayer twist angle of bilayer graphene (BLG) significantly affects its electronic properties, including its superconductivity, topological transitions, ferromagnetic states, and correlated insulating states. These exotic electronic properties are sensitive to the work functions of BLG samples. In this study, the twist angle-dependent work functions of chemical vapour deposition-grown twisted bilayer graphene (tBLG) were investigated in detail using Kelvin probe force microscopy (KPFM) in combination with Raman spectroscopy. The thickness-dependent surface potentials of Bernal-stacked multilayer graphene were measured. It is found that with the increase in the number of layers, the work function decreases and tends to saturate. Bernal-stacked BLG and tBLG were determined via KPFM due to their twist angle-specific surface potentials. The detailed relationship between the twist angle and surface potential was determined via in situ KPFM and Raman spectral measurements. With the increase in the twist angle, the work function of tBLG will increase rapidly and then increase slowly when it is greater than 5°. The thermal stability of tBLG was investigated through a controlled annealing process. tBLG will become Bernal-stacked BLG after annealing at 350 °C. Our work provides the twist angle-dependent surface potentials of tBLG and provides the relevant conditions for the stability of the twist angle, which lays the foundation for further exploration of its twist angle-dependent electronic properties.

One Dimensional Twisted Van der Waals Structures Constructed by Self-Assembling Graphene Nanoribbons on Carbon Nanotubes

Twisted van der Waals heterostructures were recently found to possess unique physical properties, such as superconductivity in magic angle bilayer graphene. Owing to the nonhomogeneous stacking, the energy of twisted van der Waals heterostructures are often higher than their AA or AB stacking counterpart, therefore, fabricating such structures remains a great challenge in experiments. On the other hand, one dimensional (1D) coaxial van der Waals structures has less freedom to undergo phase transition, thus offer opportunity for fabricating the 1D cousin of twisted bilayer graphene. In this work, we show by molecular dynamic simulations that graphene nanoribbons can self-assemble onto the surface of carbon nanotubes driven by van der Waals interactions. By modifying the size of the carbon nanotubes or graphene nanoribbons, the resultant configurations can be controlled. Of particular interest is the formation of twisted double walled carbon nanotubes whose chiral angle difference can be tuned, including the 1.1° magic angle. Upon the longitudinal unzipping of such structures, twisted bilayer graphene nanoribbons can be obtained. As the longitudinal unzipping of carbon nanotubes is a mature technique, we expect the strategy proposed in this study to stimulate experimental efforts and promote the fast growing research in twistronics.

Enhanced Chemical Stability in the Twisted Dodecagonal Stacking of Two-Dimensional Copper Nanocluster Assemblies

Deterministic chemical stacking of two-dimensional materials with controlled symmetry is a synthetic chemistry challenge that deserves attention. It is plausible that depending on the angle of stacking the material properties of the assembly could be tuned. Herein, we report 30° twisted stacking of two-dimensional nanosheets of a hexagonal assembly of organic ligand-stabilized Cu nanoclusters formed through a Zn²⁺-mediated complexation reaction. Electron diffraction in transmission electron microscopy revealed the presence of regions of dodecagonal symmetry with the apparent loss of translation symmetry. Photoluminescence measurements indicated the formation of the stacked assembly in the liquid medium. The as-synthesized twisted stacking structure exhibited superior delayed photoluminescence and chemical stability─in the presence of molecular iodine─as compared to the hexagonal crystal. The discovery can lead to a bright future in exploring new chemical and physical properties through the design of stacked assemblies of luminescent or other materials.

Moiré-Induced Transport in CVD-Based Small-Angle Twisted Bilayer Graphene

To realize the applicative potential of 2D twistronic devices, scalable synthesis and assembly techniques need to meet stringent requirements in terms of interface cleanness and twist-angle homogeneity. Here, we show that small-angle twisted bilayer graphene assembled from separated CVD-grown graphene single-crystals can ensure high-quality transport properties, determined by a device-scale-uniform moiré potential. Via low-temperature dual-gated magnetotransport, we demonstrate the hallmarks of a 2.4°-twisted superlattice, including tunable regimes of interlayer coupling, reduced Fermi velocity, large interlayer capacitance, and density-independent Brown-Zak oscillations. The observation of these moiré-induced electrical transport features establishes CVD-based twisted bilayer graphene as an alternative to "tear-and-stack" exfoliated flakes for fundamental studies, while serving as a proof-of-concept for future large-scale assembly.

Interlayer electron flow and field shielding in twisted trilayer graphene quantum dots

While multilayer graphene (MLG) possesses excellent intralayer electron mobility, its interlayer electrical conductance exhibits great diversity that results in exotic phenomena and various applications in electronic devices. Driven by a vertical electric field, electron flow occurs across the layers, and its current is tunable by controlling the interlayer stacking and distance, disc size and field strength. The electron rearrangement induced by the external field is appropriately described by the polarizability that measures the electronic response against the applied field. Based on the field-induced electron density variations computed with a first-principles approach, a polarizability decomposition scheme is developed in this work to isolate the inter- and intra-layer contributions from the total polarizability of twisted trilayer graphene (TTG) quantum dots. The inter- and intra-layer counterparts reflect the charge transfer (CT) and field shielding effects among the layers, respectively. Shielded by the top and bottom layers, the middle layer is particularly effective in bridging, switching and promoting the interlayer electron flow. Large CT and shielding effects occur not only in the strongly coupled Bernal stacking, but also in the structures misorientating from the full-AAA stacking by a small twist angle. Moreover, both effects vary with the twist angle and disc size, indicating a controllable conductive/dielectric conversion in the vertical direction. In light of inter- and intralayer polarizability, our study addresses the precise modulation of interlayer conductance for TTG quantum dots, which is required in the microstructure design and performance manipulation of MLG-based electronic devices.

Developing Graphene-Based Moiré Heterostructures for Twistronics

Graphene-based moiré heterostructures are strongly correlated materials, and they are considered to be an effective platform to investigate the challenges of condensed matter physics. This is due to the distinct electronic properties that are unique to moiré superlattices and peculiar band structures. The increasing research on strongly correlated physics via graphene-based moiré heterostructures, especially unconventional superconductors, greatly promotes the development of condensed matter physics. Herein, the preparation methods of graphene-based moiré heterostructures on both in situ growth and assembling monolayer 2D materials are discussed. Methods to improve the quality of graphene and optimize the transfer process are presented to mitigate the limitations of low-quality graphene and damage caused by the transfer process during the fabrication of graphene-based moiré heterostructures. Then, the topological properties in various graphene-based moiré heterostructures are reviewed. Furthermore, recent advances regarding the factors that influence physical performances via a changing twist angle, the exertion of strain, and regulation of the dielectric environment are presented. Moreover, various unique physical properties in graphene-based moiré heterostructures are demonstrated. Finally, the challenges faced during the preparation and characterization of graphene-based moiré heterostructures are discussed. An outlook for the further development of moiré heterostructures is also presented.

Recent progress in the synthesis of novel two-dimensional van der Waals materials

The last decade has witnessed the significant progress of physical fundamental research and great success of practical application in two-dimensional (2D) van der Waals (vdW) materials since the discovery of graphene in 2004. To date, vdW materials is still a vibrant and fast-expanding field, where tremendous reports have been published covering topics from cutting-edge quantum technology to urgent green energy, and so on. Here, we briefly review the emerging hot physical topics and intriguing materials, such as 2D topological materials, piezoelectric materials, ferroelectric materials, magnetic materials and twistronic heterostructures. Then, various vdW material synthetic strategies are discussed in detail, concerning the growth mechanisms, preparation conditions and typical examples. Finally, prospects and further opportunities in the booming field of 2D materials are addressed.

Engineering of Numerous Moiré Superlattices in Twisted Multilayer Graphene for Twistronics and Straintronics Applications

Because of their unique atomic structure, 2D materials are able to create an up-to-date paradigm in fundamental science and technology on the way to engineering the band structure and electronic properties of materials on the nanoscale. One of the simplest methods along this path is the superposition of several 2D nanomaterials while simultaneously specifying the twist angle between adjacent layers (θ), which leads to the emergence of Moiré superlattices. The key challenge in 2D nanoelectronics is to obtain a nanomaterial with numerous Moiré superlattices in addition to a high carrier mobility in a stable and easy-to-fabricate material. Here, we demonstrate the possibility of synthesizing twisted multilayer graphene (tMLG) with a number of monolayers N_L = 40-250 and predefined narrow ranges of θ = 3-8°, θ = 11-15°, and θ = 26-30°. A 2D nature of the electron transport is observed in the tMLG, and its carrier mobilities are close to those of twisted bilayer graphene (tBLG) (with θ = 30°) between h-BN layers. We demonstrate an undoubtful presence of numerous Moiré superlattices simultaneously throughout the entire tMLG thickness, while the periods of these superlattices are rather close to each other. This offers a challenge of producing a next generation of devices for nanoelectronics, twistronics, and neuromorphic computing for large data applications.

Interferometric 4D-STEM for Lattice Distortion and Interlayer Spacing Measurements of Bilayer and Trilayer 2D Materials

Van der Waals materials composed of stacks of individual atomic layers have attracted considerable attention due to their exotic electronic properties that can be altered by, e.g., manipulating the twist angle of bilayer materials or the stacking sequence of trilayer materials. To fully understand and control the unique properties of these few-layer materials, a technique that can provide information about their local in-plane structural deformations, twist direction, and out-of-plane structure is needed. In principle, interference in overlap regions of Bragg disks originating from separate layers of a material encodes 3D information about the relative positions of atoms in the corresponding layers. Here, an interferometric 4D scanning transmission electron microscopy technique is described that utilizes this phenomenon to extract precise structural information from few-layer materials with nm-scale resolution. It is demonstrated how this technique enables measurement of local pm-scale in-plane lattice distortions as well as twist direction and average interlayer spacings in bilayer and trilayer graphene, and therefore provides a means to better understand the interplay between electronic properties and precise structural arrangements of few-layer 2D materials.

Trigonal quasicrystalline states in [Formula: see text] rotated double moiré superlattices

We study the lattice configuration and electronic structure of a double moiré superlattice, which is composed of a graphene layer encapsulated by two other layers in a way such that the two hexagonal moiré patterns are arranged in a dodecagonal quasicrystalline configuration. We show that there are between 0 and 4 such configurations depending on the lattice mismatch between graphene and the encapsulating layer. We then reveal the resonant interaction, which is distinct from the conventional 2-, 3-, 4-wave mixing of moiré superlattices, that brings together and hybridizes twelve degenerate Bloch states of monolayer graphene. These states do not fully satisfy the dodecagonal quasicrystalline rotational symmetry due to the symmetry of the wave vectors involved. Instead, their wave functions exhibit trigonal quasicrystalline order, which lacks inversion symmetry, at the energies much closer to the charge neutrality point of graphene.

Hetero-site nucleation for growing twisted bilayer graphene with a wide range of twist angles

Twisted bilayer graphene (tBLG) has recently attracted growing interest due to its unique twist-angle-dependent electronic properties. The preparation of high-quality large-area bilayer graphene with rich rotation angles would be important for the investigation of angle-dependent physics and applications, which, however, is still challenging. Here, we demonstrate a chemical vapor deposition (CVD) approach for growing high-quality tBLG using a hetero-site nucleation strategy, which enables the nucleation of the second layer at a different site from that of the first layer. The fraction of tBLGs in bilayer graphene domains with twist angles ranging from 0° to 30° was found to be improved to 88%, which is significantly higher than those reported previously. The hetero-site nucleation behavior was carefully investigated using an isotope-labeling technique. Furthermore, the clear Moiré patterns and ultrahigh room-temperature carrier mobility of 68,000 cm² V^-1 s^-1 confirmed the high crystalline quality of our tBLG. Our study opens an avenue for the controllable growth of tBLGs for both fundamental research and practical applications.

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.

Opportunities and Challenges in Twisted Bilayer Graphene: A Review

Two-dimensional (2D) materials exhibit enhanced physical, chemical, electronic, and optical properties when compared to those of bulk materials. Graphene demands significant attention due to its superior physical and electronic characteristics among different types of 2D materials. The bilayer graphene is fabricated by the stacking of the two monolayers of graphene. The twisted bilayer graphene (tBLG) superlattice is formed when these layers are twisted at a small angle. The presence of disorders and interlayer interactions in tBLG enhances several characteristics, including the optical and electrical properties. The studies on twisted bilayer graphene have been exciting and challenging thus far, especially after superconductivity was reported in tBLG at the magic angle. This article reviews the current progress in the fabrication techniques of twisted bilayer graphene and its twisting angle-dependent properties.

30°-Twisted Bilayer Graphene Quasicrystals from Chemical Vapor Deposition

The artificial stacking of atomically thin crystals suffers from intrinsic limitations in terms of control and reproducibility of the relative orientation of exfoliated flakes. This drawback is particularly severe when the properties of the system critically depends on the twist angle, as in the case of the dodecagonal quasicrystal formed by two graphene layers rotated by 30°. Here we show that large-area 30°-rotated bilayer graphene can be grown deterministically by chemical vapor deposition on Cu, eliminating the need of artificial assembly. The quasicrystals are easily transferred to arbitrary substrates and integrated in high-quality hexagonal boron nitride-encapsulated heterostructures, which we process into dual-gated devices exhibiting carrier mobility up to 10⁵ cm²/(V s). From low-temperature magnetotransport, we find that the graphene quasicrystals effectively behave as uncoupled graphene layers, showing 8-fold degenerate quantum Hall states. This result indicates that the Dirac cones replica detected by previous photoemission experiments do not contribute to the electrical transport.