Angle-resolved Raman imaging of interlayer rotations and interactions in twisted bilayer graphene

Stacking Engineering toward Giant Second Harmonic Generation in Twisted Graphene Superstructures

The nonlinear optical response in graphene is finding increasing applications in nanophotonic devices. The activation and enhancement of second harmonic generation (SHG) in graphene, which is generally forbidden in monolayer and AB-stacked bilayer graphene due to their centrosymmetry, is of urgent need for nanophotonic applications. Here, we present a comprehensive study of SHG performance of twisted multilayer graphene structures based on stacking engineering. It is found that the modulation of in-plane and out-of-plane SHG susceptibility components by stacking few-layer graphene is essential in producing giant SHG response in twisted multilayer graphene. Giant SHG intensity in twisted multilayer graphene is observed, reaching nearly 10 times that of monolayer MoS2 under 1064 nm excitation, which significantly outperformed graphene structures reported to date. Our findings present a facile and effective approach to enhance SHG in graphene structures, showing promise for future application of graphene in second harmonic nanophotonic devices as well as prospects for the study of SHG among two-dimensional (2D) structures in general.

Nondestructive Single-Atom-Thick Crystallographic Scanner via Sticky-Note-Like van der Waals Assembling-Disassembling

Crystallographic characteristics, including grain boundaries and crystallographic orientation of each grain, are crucial in defining the properties of two-dimensional materials (2DMs). To date, local microstructure analysis of 2DMs, which requires destructive and complex processes, is primarily used to identify unknown 2DM specimens, hindering the subsequent use of characterized samples. Here, a nondestructive large-area 2D crystallographic analytical method through sticky-note-like van der Waals (vdW) assembling-disassembling is presented. By the vdW assembling of veiled polycrystalline graphene (PCG) with a single-atom-thick single-crystalline graphene filter (SCG-filter), detailed crystallographic information of each grain in PCGs is visualized through a 2D Raman signal scan, which relies on the interlayer twist angle. The scanned PCGs are seamlessly separated from the SCG-filter using vdW disassembling, preserving their original condition. The remaining SCG-filter is then reused for additional crystallographic scans of other PCGs. It is believed that the methods can pave the way for advances in the crystallographic analysis of single-atom-thick materials, offering huge implications for the applications of 2DMs.

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".

Resonant Tunneling-Enhanced Photoresponsivity in a Twisted Graphene van der Waals Heterostructure

Leveraging its ultrahigh carrier mobility, zero-bandgap linear dispersion, and extremely short response time, graphene exhibits remarkable potential in ultrafast broad-band photodetection. Nonetheless, the inherently low responsivity of graphene photodetectors, due to the low photogenerated carrier density, significantly impedes the development of practical devices. In this study, we present an improved photoresponse within a graphene-hexagonal boron nitride-graphene vertical tunnel junction device, where the crystallographic orientation of the two graphene electrodes is aligned. Through meticulous device structure design and the adjustment of bias and gate voltages, we observe a 2 orders of magnitude increase in tunneling photocurrent, which is attributed to the momentum-conserving resonant electron tunneling. The enhanced external photoresponsivity is evident across a wide temperature and spectral range and achieves 0.7 A/W for visible light excitation. This characteristic, coupled with the device's negative differential conductance, suggests a novel avenue for highly efficient photodetection and high-frequency, logic-based optoelectronics using van der Waals heterostructures.

Angle-Resolved Optical Imaging of Interlayer Rotations in Twisted Bilayer Graphene

Twisted bilayer graphene (TBG) is a prototypical layered material whose properties are strongly correlated to interlayer coupling. The two stacked graphene layers with distinct orientations are investigated to generate peculiar optical and electronic phenomena. Thus, the rapid, reliable, and nondestructive twist angle identification technique is of essential importance. Here, we integrated the white light reflection spectra (WLRS), the Raman spectroscopy, and the transmission electron microscope (TEM) to propose a facile RGB optical imaging technique that identified the twist angle of the TBG in a large area intuitively with high efficiency. The RGB technique established a robust correlation between the interlayer rotation angle and the contrast difference in the RGB color channels of a standard optical image. The angle-resolved optical behavior is attributed to the absorption resonance matching with the separation of van Hove singularities in the density of states of the TBG. Our study thus developed a route to identify the rotation angle of stacked bilayer graphene by means of a straightforward optical method, which can be further applied in other stacked van der Waals layered materials.

Resonance Raman spectroscopy of twisted interfaces in turbostratic multilayer graphene

Turbostratic multilayer graphene presents a unique system with a large number of twisted interfaces with variable twist angles. In this work, we have systematically studied the laser excitation energy dependence of the Raman modes of turbostratic graphene. The combination of 4 different laser energies is shown to be important to reveal the twist angles ranging from 5∘to 30∘present at the same lateral position of the sample. Rotational or R-modes and D-like modes are observed, which directly arise from additional momentum transfer from the potential of corresponding superlattices. Trends in their dispersion and intensity are discussed. The resonant window for laser excitation indicates lowered positions of the van Hove singularities. Furthermore, an anomalous broadening factor of 0.17-0.265 eV is estimated for the resonance window when compared to the literature on isolated twisted bilayer graphene. Interestingly, a weak dependence of the R-modes on the laser wavelength is also observed. Finally, the dispersion of the 2D modes is also presented.

Probing Interlayer Interactions and Commensurate-Incommensurate Transition in Twisted Bilayer Graphene through Raman Spectroscopy

Twisted 2D layered materials have garnered much attention recently as a class of 2D materials whose interlayer interactions and electronic properties are dictated by the relative rotation/twist angle between the adjacent layers. In this work, we explore a prototype of such a twisted 2D system, artificially stacked twisted bilayer graphene (TBLG), where we probe, using Raman spectroscopy, the changes in the interlayer interactions and electron-phonon scattering pathways as the twist angle is varied from 0° to 30°. The long-range Moiré potential of the superlattice gives rise to additional intravalley and intervalley scattering of the electrons in TBLG, which has been investigated through their Raman signatures. Density functional theory (DFT) calculations of the electronic band structure of the TBLG superlattices were found to be in agreement with the resonant Raman excitations across the van Hove singularities in the valence and conduction bands predicted for TBLG due to hybridization of bands from the two layers. We also observe that the relative rotation between the graphene layers has a marked influence on the second order overtone and combination Raman modes signaling a commensurate-incommensurate transition in TBLG as the twist angle increases. This serves as a convenient and rapid characterization tool to determine the degree of commensurability in TBLG systems.

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.

Fast Twist Angle Mapping of Bilayer Graphene Using Spectroscopic Ellipsometric Contrast Microscopy

Twisted bilayer graphene provides an ideal solid-state model to explore correlated material properties and opportunities for a variety of optoelectronic applications, but reliable, fast characterization of the twist angle remains a challenge. Here we introduce spectroscopic ellipsometric contrast microscopy (SECM) as a tool for mapping twist angle disorder in optically resonant twisted bilayer graphene. We optimize the ellipsometric angles to enhance the image contrast based on measured and calculated reflection coefficients of incident light. The optical resonances associated with van Hove singularities correlate well to Raman and angle-resolved photoelectron emission spectroscopy, confirming the accuracy of SECM. The results highlight the advantages of SECM, which proves to be a fast, nondestructive method for characterization of twisted bilayer graphene over large areas, unlocking process, material, and device screening and cross-correlative measurement potential for bilayer and multilayer materials.

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.

An Atomistic Insight into Moiré Reconstruction in Twisted Bilayer Graphene beyond the Magic Angle

Twisted bilayer graphene exhibits electronic properties strongly correlated with the size and arrangement of moiré patterns. While rigid rotation of the two graphene layers results in a moiré interference pattern, local rearrangements of atoms due to interlayer van der Waals interactions result in atomic reconstruction within the moiré cells. Manipulating these patterns by controlling the twist angle and externally applied strain provides a promising route to tuning their properties. Atomic reconstruction has been extensively studied for angles close to or smaller than the magic angle (θ _m = 1.1°). However, this effect has not been explored for applied strain and is believed to be negligible for high twist angles. Using interpretive and fundamental physical measurements, we use theoretical and numerical analyses to resolve atomic reconstruction in angles above θ _m . In addition, we propose a method to identify local regions within moiré cells and track their evolution with strain for a range of representative high twist angles. Our results show that atomic reconstruction is actively present beyond the magic angle, and its contribution to the moiré cell evolution is significant. Our theoretical method to correlate local and global phonon behavior further validates the role of reconstruction at higher angles. Our findings provide a better understanding of moiré reconstruction in large twist angles and the evolution of moiré cells under the application of strain, which might be potentially crucial for twistronics-based applications.

On the use of Raman spectroscopy to characterize mass-produced graphene nanoplatelets

Raman spectroscopy is one of the most common methods to characterize graphene-related 2D materials, providing information on a wide range of physical and chemical properties. Because of typical sample inhomogeneity, Raman spectra are acquired from several locations across a sample, and analysis is carried out on the averaged spectrum from all locations. This is then used to characterize the "quality" of the graphene produced, in particular the level of exfoliation for top-down manufactured materials. However, these have generally been developed using samples prepared with careful separation of unexfoliated materials. In this work we assess these metrics when applied to non-ideal samples, where unexfoliated graphite has been deliberately added to the exfoliated material. We demonstrate that previously published metrics, when applied to averaged spectra, do not allow the presence of this unexfoliated material to be reliably detected. Furthermore, when a sufficiently large number of spectra are acquired, it is found that by processing and classifying individual spectra, rather than the averaged spectrum, it is possible to identify the presence of this material in the sample, although quantification of the amount remains approximate. We therefore recommend this approach as a robust methodology for reliable characterization of mass-produced graphene-related 2D materials using confocal Raman spectroscopy.

Extraordinary Phonon Displacement and Giant Resonance Raman Enhancement in WSe2/WS2 Moiré Heterostructures

Twisted van der Waals heterostructures are known to induce surprisingly diverse and intriguing phenomena, such as correlated electronic phase and unconventional optical properties. This can be realized by controlled rotation of adjacent atomic planes, which provides an uncommon way to manipulate inelastic light-matter interactions. Here, we discover an extraordinary blue shift of 5-6 wavenumbers for high-frequency phonon modes in WS₂/WSe₂ twisted heterobilayers, captured meticulously using Raman spectroscopy. Phonon spectra displace rapidly over a subtle change in interlayer twist angle owing to heterostrain and atomic reconstruction from the Moiré pattern. First-order linear coefficients of the phonon modes in twisted heterostructures are further found to increase largely compared to their monolayer counterpart and vary immensely with the twist angle. Exceptional and extravagant enhancement of up to 50-fold is observed in the Raman vibrational intensity at a specific twist angle; this is largely influenced by the resonance process derived from a simple critical twist angle model. In addition, we depict how the resonance can be modulated by changing the thermal conditions and also the stacking angle. Therefore, our work further highlights the twist-driven phonon dynamics in pristine two-dimensional heterostructures, adding vital insight into Moiré physics and promoting comprehensive understanding of structural and optical properties in Moiré superlattices.

Design of Multilayered 2D Nanomaterial Composite Structures for EMI Shielding Analysis

It is still very challenging to effectively design nanocomposite microstructures with significantly improved electromagnetic interference shielding effectiveness (EMI SE). Herein, we developed a facile method for fabrication of molybdenum disulfide/graphene nanoplatelets (MoS₂/GNPs) nanocomposites, in which GNPs are utilized as highly effective electrical transport materials, while MoS₂ resolves the agglomeration problem of GNPs. GNPs also serve as an efficient cluster of electrical transport systems and dampen the incoming electromagnetic wave. Two types of samples are synthesized and compared in context of EMI SE values: physically mixed composite and layered samples. The sandwiched MoS₂ between GNP layers showed an EMI SE of ∼24 dB, which was an almost 14% improvement relative to MoS₂/GNPs nanocomposites exhibiting an EMI SE value of ∼21 dB, both containing 0.5 wt % GNPs. This work provides a new strategy for the design of multifunctional nanocomposites using the simple low-cost vacuum filtration method for EMI shielding for future applications.

Twist Angle-Dependent Molecular Intercalation and Sheet Resistance in Bilayer Graphene

Bilayer graphene (BLG) has a two-dimensional (2D) interlayer nanospace that can be used to intercalate molecules and ions, resulting in a significant change of its electronic and magnetic properties. Intercalation of BLG with different materials, such as FeCl₃, MoCl₅, Li ions, and Ca ions, has been demonstrated. However, little is known about how the twist angle of the BLG host affects intercalation. Here, by using artificially stacked BLG with controlled twist angles, we systematically investigated the twist angle dependence of intercalation of metal chlorides. We discovered that BLG with high twist angles of >15° is more favorable for intercalation than BLG with low twist angles. Density functional theory calculations suggested that the weaker interlayer coupling in high twist angle BLG is the key for effective intercalation. Scanning transmission electron microscope observations revealed that co-intercalation of AlCl₃ and CuCl₂ molecules into BLG gives various 2D structures in the confined interlayer nanospace. Moreover, before intercalation we observed a significantly lower sheet resistance in BLG with high twist angles (281 ± 98 Ω/□) than that in AB stacked BLG (580 ± 124 Ω/□). Intercalation further decreased the sheet resistance, reaching values as low as 48 Ω/□, which is the lowest value reported so far for BLG. This work provides a twist angle-dependent phenomenon, in which enhanced intercalation and drastic changes of the electrical properties can be realized by controlling the stacking angle of adjacent graphene layers.

Pressure Tunable van Hove Singularities of Twisted Bilayer Graphene

The giant light-matter interaction induced by van Hove singularities (vHSs) of twisted bilayer graphene (tBLG) is responsible for enhanced optical absorption and strong photoresponse. Here, we investigated the evolution of vHSs in tBLG under pressure by using Raman spectroscopy. Pressure not only induces a blue shift of the G/R band but also tunes the intensity of the G/R band. The blue shift of the G/R band is due to the reduction of the in-plane lattice constant, and the variation of the G/R band intensity is due to the vHSs' shift of tBLG. Moreover, the main band in the absorption spectrum of tBLG is attributed to multiple transitions from valence to conduction bands. Because the ratio of R to G band intensity increases under pressure and the origins of R and G bands are different, we claim that pressure enhances intervalley electron scattering. This study paves the way for pressure engineering of vHS and the corresponding photon-electron-phonon interaction in tBLG.

Using Scalable Graphene via Press-and-Peel: A Robust and Storable Tape

The independent expertise required by the preparation and application of graphene has brought a challenge to the more fluent development of graphene devices. We combine the advantages of chemical vapor deposition and micromechanical exfoliation methods of synthesizing graphene to develop a "graphene tape" for the fast utilization of graphene, which is robust, storable, and user-friendly. Prepared by pretransferring graphene to the surface of a polymer carrier film with weak interfacial adhesion, this graphene tape enables the acquisition, patterning, and layer-by-layer epitaxy of scalable graphene on a target substrate through simple cutting, pressing, and peeling off. Multiple characterizations demonstrate its comparable quality with as-synthesized graphene even after stored for over 30 days, overcoming the time and space limitations of acquiring a graphene sample. We believe that this graphene tape can bridge the current gap between graphene synthesis and applications and promote industrial progress of graphene-based devices in the post-Moore era.

Science of 2.5 dimensional materials: paradigm shift of materials science toward future social innovation

The past decades of materials science discoveries are the basis of our present society - from the foundation of semiconductor devices to the recent development of internet of things (IoT) technologies. These materials science developments have depended mainly on control of rigid chemical bonds, such as covalent and ionic bonds, in organic molecules and polymers, inorganic crystals and thin films. The recent discovery of graphene and other two-dimensional (2D) materials offers a novel approach to synthesizing materials by controlling their weak out-of-plane van der Waals (vdW) interactions. Artificial stacks of different types of 2D materials are a novel concept in materials synthesis, with the stacks not limited by rigid chemical bonds nor by lattice constants. This offers plenty of opportunities to explore new physics, chemistry, and engineering. An often-overlooked characteristic of vdW stacks is the well-defined 2D nanospace between the layers, which provides unique physical phenomena and a rich field for synthesis of novel materials. Applying the science of intercalation compounds to 2D materials provides new insights and expectations about the use of the vdW nanospace. We call this nascent field of science '2.5 dimensional (2.5D) materials,' to acknowledge the important extra degree of freedom beyond 2D materials. 2.5D materials not only offer a new field of scientific research, but also contribute to the development of practical applications, and will lead to future social innovation. In this paper, we introduce the new scientific concept of this science of '2.5D materials' and review recent research developments based on this new scientific concept.

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.

Resonance Raman enhancement by the intralayer and interlayer electron-phonon processes in twisted bilayer graphene

Twisted bilayer graphene is a fascinating system due to the possibility of tuning the electronic and optical properties by controlling the twisting angle \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta$$\end{document}θ between the layers. The coupling between the Dirac cones of the two graphene layers gives rise to van Hove singularities (vHs) in the density of electronic states, whose energies vary with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta$$\end{document}θ. Raman spectroscopy is a fundamental tool to study twisted bilayer graphene (TBG) systems since the Raman response is hugely enhanced when the photons are in resonance with transition between vHs and new peaks appear in the Raman spectra due to phonons within the interior of the Brillouin zone of graphene that are activated by the Moiré superlattice. It was recently shown that these new peaks can be activated by the intralayer and the interlayer electron–phonon processes. In this work we study how each one of these processes enhances the intensities of the peaks coming from the acoustic and optical phonon branches of graphene. Resonance Raman measurements, performed in many different TBG samples with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta$$\end{document}θ between \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4^{\circ }$$\end{document}4∘ and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$16^{\circ }$$\end{document}16∘ and using several different laser excitation energies in the near-infrared (NIR) and visible ranges (1.39–2.71 eV), reveal the distinct enhancement of the different phonons of graphene by the intralayer and interlayer processes. Experimental results are nicely explained by theoretical calculations of the double-resonance Raman intensity in graphene by imposing the momentum conservation rules for the intralayer and the interlayer electron–phonon resonant conditions in TBGs. Our results show that the resonant enhancement of the Raman response in all cases is affected by the quantum interference effect and the symmetry requirements of the double resonance Raman process in 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.

Sequential growth and twisted stacking of chemical-vapor-deposited graphene

Adlayers have been one of the main concerns for controlled synthesis of graphene by the chemical vapor deposition (CVD) method. Here we investigate the CVD growth of graphene adlayers on copper (Cu) using isotope-labeling-based Raman spectroscopy and high-resolution atomic force microscopy (AFM). The results show that, besides conventional simultaneous growth for all the graphene layers, approximately 37% of the adlayers follow a sequential growth which can occur even hours after the nucleation of the first layer. The proportions of AB (Bernal)- and twisted (t)-stacked bilayer graphene (BLG) stacks formed by the two modes are not significantly different. Moreover, in those stacks with both AB- and t-BLG, evidence at the atomic scale demonstrates that they resulted from misoriented domains in their single-crystal-like top layers. We believe that this new understanding of the growth mechanism for graphene adlayers can help pave the way towards the synthesis of large-scale and high-quality graphene with controllable layer numbers.

Micro-photoluminescence of Carbon Dots Deposited on Twisted Double-Layer Graphene Grown by Chemical Vapor Deposition

Carbon-based nanomaterials, such as carbon dots (CDs) and graphene (Gr), feature outstanding optical and electronic properties. Hence, their integration in optoelectronic and photonic devices is easier thanks to their low dimensionality and offers the possibility to reach high-quality performances. In this context, the combination of CDs and Gr into new nanocomposite materials CDs/Gr can further improve their optoelectronic properties and eventually create new ones, paving the way for the development of advanced carbon nanotechnology. In this work, we have thoroughly investigated the structural and emission properties of CDs deposited on single-layer and bilayer graphene lying on a SiO₂/Si substrate. A systematic Raman analysis points out that bilayer (BL) graphene grown by chemical vapor deposition does not always respect the Bernal (AB) stacking, but it is rather a mixture of twisted bilayer (t-BL) featuring domains with different twist angles. Moreover, in-depth micro-photoluminescence measurements, combined with atomic force microscopy (AFM) morphological analysis, show that CD emission efficiency is strongly depleted by the presence of graphene and in particular is dependent on the number of layers as well as on the twist angle of BL graphene. Finally, we propose a model which explains these results on the basis of photoinduced charge-transfer processes, taking into account the energy levels of the hybrid nanosystem formed by coupling CDs with t-BL/SiO₂.

Raman Spectroscopy of Twisted Bilayer Graphene

When two periodic two-dimensional structures are superposed, any mismatch rotation angle between the layers generates a Moiré pattern superlattice, whose size depends on the twisting angle θ. If the layers are composed by different materials, this effect is also dependent on the lattice parameters of each layer. Moiré superlattices are commonly observed in bilayer graphene, where the mismatch angle between layers can be produced by growing twisted bilayer graphene (TBG) samples by CVD or folding the monolayer back upon itself. In TBG, it was shown that the coupling between the Dirac cones of the two layers gives rise to van Hove singularities (vHs) in the density of electronic states, whose energies vary with θ. The understanding of the behavior of electrons and their interactions with phonons in atomically thin heterostructures is crucial for the engineering of novel 2D devices. Raman spectroscopy has been often used to characterize twisted bilayer graphene and graphene heterostructures. Here, we review the main important effects in the Raman spectra of TBG discussing firstly the appearance of new peaks in the spectra associated with phonons with wavevectors within the interior of the Brillouin zone of graphene corresponding to the reciprocal unit vectors of the Moiré superlattice, and that are folded to the center of the reduced Brillouin Zone (BZ) becoming Raman active. Another important effect is the giant enhancement of G band intensity of TBG that occurs only in a narrow range of laser excitation energies and for a given twisting angle. Results show that the vHs in the density of states is not only related to the folding of the commensurate BZ, but mainly associated with the Moiré pattern that does not necessarily have a translational symmetry. Finally, we show that there are two different resonance mechanisms that activate the appearance of the extra peaks: the intralayer and interlayer electron–phonon processes, involving electrons of the same layer or from different layers, respectively. Both effects are observed for twisted bilayer graphene, but Raman spectroscopy can also be used to probe the intralayer process in any kind of graphene-based heterostructure, like in the graphene/h-BN junctions.

Enhanced third-harmonic generation by manipulating the twist angle of bilayer graphene

Twisted bilayer graphene (tBLG) has received substantial attention in various research fields due to its unconventional physical properties originating from Moiré superlattices. The electronic band structure in tBLG modified by interlayer interactions enables the emergence of low-energy van Hove singularities in the density of states, allowing the observation of intriguing features such as increased optical conductivity and photocurrent at visible or near-infrared wavelengths. Here, we show that the third-order optical nonlinearity can be considerably modified depending on the stacking angle in tBLG. The third-harmonic generation (THG) efficiency is found to significantly increase when the energy gap at the van Hove singularity matches the three-photon resonance of incident light. Further study on electrically tuneable optical nonlinearity reveals that the gate-controlled THG enhancement varies with the twist angle in tBLG, resulting in a THG enhanced up to 60 times compared to neutral monolayer graphene. Our results prove that the twist angle opens up a new way to control and increase the optical nonlinearity of tBLG, suggesting rotation-induced tuneable nonlinear optics in stacked two-dimensional material systems.

Misorientation-Controlled Cross-Plane Thermoelectricity in Twisted Bilayer Graphene

The introduction of "twist" or relative rotation between two atomically thin van der Waals membranes gives rise to periodic moiré potential, leading to a substantial alteration of the band structure of the planar assembly. While most of the recent experiments primarily focus on the electronic-band hybridization by probing in-plane transport properties, here we report out-of-plane thermoelectric measurements across the van der Waals gap in twisted bilayer graphene, which exhibits an interplay of twist-dependent interlayer electronic and phononic hybridization. We show that at large twist angles, the thermopower is entirely driven by a novel phonon-drag effect at subnanometer scale, while the electronic component of the thermopower is recovered only when the misorientation between the layers is reduced to <6°. Our experiment shows that cross-plane thermoelectricity at low angles is exceptionally sensitive to the nature of band dispersion and may provide fundamental insights into the coherence of electronic states in twisted bilayer graphene.

Surface functionalization of twisted graphene C32H15 and C104H52 derivatives with alkalis and superalkalis for NLO response; a DFT study

Herein, we present the detailed comparative study on geometric, electronic, optical and non-linear optical response of alkalis and superalkalis doped twisted graphene. The results illustrate that alkali metals and superalkalis interact with the central ring of the twisted graphene through non-covalent interactions which demonstrate the stability of the resultant complexes. NBO charges indicate the transfer of electrons from dopant (alkali metal atoms and superalkalis) towards twisted graphene sheet. Superalkalis doped twisted graphene complexes exhibit higher first hyperpolarizability values compared to alkali metals analogues. Among superalkalis doped complexes, K₃O@C₁₀₄H₅₂ shows the highest β_o value of 1.68 × 10⁵ au. In frequency dependent first hyperpolarizability analysis, strong second harmonic generation (SHG) response of K₃O@C₃₂H₁₅ complex is observed at both selected resonance frequency values (532 nm and1064 nm) whereas EOPE value of K₃O@C₃₂H₁₅ complex shows higher induced response at 1064 nm wavelength. The static hyperpolarizability (β_o) further increases under the influence of applied electric field. Among all complexes, Li₃O@C₃₂H₁₅ graphene complex has the highest β_o value (1.40 × 10⁵ au) under applied electric field along x axis when sheet is in y-z plane. This analysis will be an important guideline for future studies on twisted graphene based NLO materials.

Electronic Raman Scattering in Twistronic Few-Layer Graphene

We study electronic contribution to the Raman scattering signals of two-, three- and four-layer graphene with layers at one of the interfaces twisted by a small angle with respect to each other. We find that the Raman spectra of these systems feature two peaks produced by van Hove singularities in moiré minibands of twistronic graphene, one related to direct hybridization of the Dirac states, and the other resulting from band folding caused by moiré superlattice. The positions of both peaks strongly depend on the twist angle, so that their detection can be used for noninvasive characterization of the twist, even in hBN-encapsulated structures.

Large-Area Single-Crystal Graphene via Self-Organization at the Macroscale

In 1665 Christiaan Huygens first noticed how two pendulums, regardless of their initial state, would synchronize.  It is now known that the universe is full of complex self-organizing systems, from neural networks to correlated materials. Here, graphene flakes, nucleated over a polycrystalline graphene film, synchronize during growth so as to ultimately yield a common crystal orientation at the macroscale. Strain and diffusion gradients are argued as the probable causes for the long-range cross-talk between flakes and the formation of a single-grain graphene layer. The work demonstrates that graphene synthesis can be advanced to control the nucleated crystal shape, registry, and relative alignment between graphene crystals for large area, that is, a single-crystal bilayer, and (AB-stacked) few-layer graphene can been grown at the wafer scale.

Growth of twisted bilayer graphene through two-stage chemical vapor deposition

We investigate growth of twisted bilayer graphene through two-stage chemical vapor deposition (CVD). Exploiting the synergetic nucleation and growth dynamics involving carbon sources from the residual carbon impurities in Cu bulk and gaseous CH_x, sub-millimeter-sized single crystalline graphene grains with multiple merged adlayer grains formed underneath are grown on Cu substrate. The distribution of the twist angles is investigated through a computer algorithm utilizing spectral features from micro-Raman mapping. Besides the more thermodynamically stable AB-stacking (AB-BLG) or large angle (>15°) decoupled bilayer graphene (DC-BLG) configurations, there are some bilayer regions that contain specific twist angles (3-8°, 8-13°, and 11-15°) (termed as TBLG). The statistics show no TBLG formation for BLG with single nucleation center. The formation probability of TBLG is strongly dependent on the relative orientation of merging adlayer grains. Significant defects are found at the grain boundaries formed in AB-DC merging event without creating TBLG domain. The areal fraction of TBLG increases as H₂/CH₄ ratio increases. The growth mechanism of TBLG is discussed in light of the interactions between the second layer grains with consideration of strain generation during merging of adlayers.

Evolution of high-frequency Raman modes and their doping dependence in twisted bilayer MoS2

Twisted van der Waals heterostructures provide a new platform for studying strongly correlated quantum phases. The interlayer coupling in these heterostructures is sensitive to the twist angle (θ) and key to controllably tuning several interesting properties. Here, we demonstrate the systematic evolution of the interlayer coupling strength with twist angle in bilayer MoS₂ using a combination of Raman spectroscopy and classical simulations. At zero doping, we observe a monotonic increase in the separation between the A_1g and E_2g¹ mode frequencies as θ decreases from 10°→ 1°, and the separation approaches that of a bilayer at small twist angles. Furthermore, using doping dependent Raman spectroscopy, we reveal the θ dependent softening and broadening of the A_1g mode, whereas the E_2g¹ mode remains unaffected. Using first principles based simulations, we demonstrate large (weak) electron-phonon coupling for the A_1g (E_2g¹) mode, which explains the experimentally observed trends. Our study provides a non-destructive way to characterize the twist angle and the interlayer coupling and establishes the manipulation of phonons in twisted bilayer MoS₂ (twistnonics).

Second-harmonic imaging microscopy for time-resolved investigations of transition metal dichalcogenides

Two-dimensional transition metal dichalcogenides (TMD) have shown promise for various applications in optoelectronics and so-called valleytronics. Their operation and performance strongly depend on the stacking of individual layers. Here, optical second-harmonic generation in imaging mode is shown to be a versatile tool for systematic time-resolved investigations of TMD monolayers and heterostructures in consideration of the material's structure. Large sample areas can be probed without the need of any mapping or scanning. By means of polarization dependent measurements, the crystalline orientation of monolayers or the stacking angles of heterostructures can be evaluated for the whole field of view. Pump-probe experiments then allow to correlate observed transient changes of the second-harmonic response with the underlying structure. The corresponding time-resolution is virtually limited by the pulse duration of the used laser. As an example, polarization dependent and time-resolved measurements on mono- and multilayer MoS2flakes grown on a SiO2/ Si(001) substrate are presented.

Structural configurations and Raman spectra of carbon nanoscrolls

Three types of carbon nanoscroll (CNS) structures that are formed when scrolling up graphene sheets are investigated using Raman spectroscopy and atomic force microscopy (AFM). The CNSs were produced from exfoliated monolayer graphene deposited on a Si chip by applying a droplet of isopropyl alcohol (IPA) solution. The three types of CNS are classified as single-elliptical-core, double-elliptical-core (both with large internal volumes) and collapsed ribbon-like, based on AFM surface profile measurements. We discuss the structure and formation of CNS with much larger hollow cores than is commonly assumed and relate this to the large effective 2D bending stiffness of graphene in the IPA solution. The large elliptical core structures show Raman spectra similar to those previously reported for CNS and indicate little interaction between the scrolled layers. The Raman spectra from ribbon-like structures show additional features that are similar to that of folded graphene. These new features can be related to layer breathing modes combined with some resonance enhancement at specific regions of the ribbon-like CNSs that are due to specific twist angles produced when the structure folds/collapses.

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.

Effectively modulating vertical tunneling transport by mechanically twisting bilayer graphene within the all-metallic architecture

Bilayer graphene possesses new degrees of freedom for modulating the electronic band structure, which makes it a tempting solution for overcoming the intrinsic absence of sizeable bandgaps in graphene and designing next-generation devices for post-silicon electronics. By twisting bilayer graphene, interlayer hybridized and twist angle-dependent van Hove singularities in the electronic band structure are generated and expected to facilitate the vertical tunneling transport between bilayer graphene. Herein, based on the ab initio quantum transport simulations, we designed a novel all-metallic vertical quantum transport architecture with the twisted bilayer graphene as the transport channel region and Au electrodes as the source/drain contacts to investigate the twist angle-dependent vertical transport properties. Enhancement in the ION/IOFF ratio by 2 orders of magnitude can be achieved by simply twisting the bilayer graphene. Compared to the traditional gate voltage modulation, which tunes the Fermi energy level alone, the current strategy shifts the Fermi energy level of the channel region away from the Dirac cone, moves the Fermi level and the van Hove singularities towards each other and promotes the vertical quantum transport due to the interlayer electronic hybridization. This dual modulation strategy of this novel mechanical gating device thus provides a potential new solution for designing novel vertical transistors.

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 scale epitaxial graphite grown on twin free nickel(111)/spinel substrate

Large scale, single crystalline graphite with millimeter size domain is achieved using a LPCVD process with a temperature below 925 °C.

Polymorphic cobalt diselenide as extremely stable electrocatalyst in acidic media via a phase-mixing strategy

Many platinum group metal-free inorganic catalysts have demonstrated high intrinsic activity for diverse important electrode reactions, but their practical use often suffers from undesirable structural degradation and hence poor stability, especially in acidic media. We report here an alkali-heating synthesis to achieve phase-mixed cobalt diselenide material with nearly homogeneous distribution of cubic and orthorhombic phases. Using water electroreduction as a model reaction, we observe that the phase-mixed cobalt diselenide reaches the current density of 10 milliamperes per square centimeter at overpotential of mere 124 millivolts in acidic electrolyte. The catalyst shows no sign of deactivation after more than 400 h of continuous operation and the polarization curve is well retained after 50,000 potential cycles. Experimental and computational investigations uncover a boosted covalency between Co and Se atoms resulting from the phase mixture, which substantially enhances the lattice robustness and thereby the material stability. The findings provide promising design strategy for long-lived catalysts in acid through crystal phase engineering.

Noble-metal-free catalysts often show stability issues in acidic media due to structural degradation. Here authors show that phase-mixed engineering of cobalt diselenide electrocatalysts can enable greater covalency of Co-Se bonds and improve robustness for catalyzing hydrogen evolution in acid.

Pattern Pick and Place Method for Twisted Bi- and Multi-Layer Graphene

Twisted bi-layer graphene (tBLG) has attracted much attention because of its unique band structure and properties. The properties of tBLG vary with small differences in the interlayer twist angle, but it is difficult to accurately adjust the interlayer twist angle of tBLG with the conventional fabrication method. In this study, we introduce a facile tBLG fabrication method that directly picks up a single-crystalline graphene layer from a growth substrate and places it on another graphene layer with a pre-designed twist angle. Using this approach, we stacked single-crystalline graphene layers with controlled twist angles and thus fabricated tBLG and twisted multi-layer graphene (tMLG). The structural, optical and electrical properties depending on the twist angle and number of layers, were investigated using transmission electron microscopy (TEM), micro–Raman spectroscopy, and gate-dependent sheet resistance measurements. The obtained results show that the pick and place approach enables the direct dry transfer of the top graphene layer on the as-grown graphene to fabricate uniform tBLG and tMLG with minimal interlayer contamination and pre-defined twist angles.

In-plane anisotropy in twisted bilayer graphene probed by Raman spectroscopy

Monolayer graphene has high symmetrical crystal structure and exhibits in-plane isotropic physical properties. However, twisted bilayer graphene (tBLG) is expected to differ physically, due to the broken symmetry introduced by the interlayer coupling between adjacent graphene layers. This symmetry breaking is usually accompanied by in-plane anisotropy in their electrical, optical and thermal properties. However, the existence of in-plane anisotropy in tBLG has remained evasive until now. Here, an unambiguous identification of the in-plane anisotropy in tBLG is established by angle-resolved polarized Raman spectroscopy. It was found that the double-resonant two-dimensional band is anisotropic. The degree of in-plane anisotropy is found to be dependent on the misorientation angles, which is two- and four-fold for tBLG with misorientation angles of 15° and 20°, respectively. This finding adds a new dimension to the properties of graphene, which opens a possibility to the development of graphene-based angle-resolved photonics and electronics.

Twist Angle mapping in layered WS2 by Polarization-Resolved Second Harmonic Generation

Stacked atomically thin transition metal dichalcogenides (TMDs) exhibit fundamentally new physical properties compared to those of the individual layers. The twist angle between the layers plays a crucial role in tuning these properties. Having a tool that provides high-resolution, large area mapping of the twist angle, would be of great importance in the characterization of such 2D structures. Here we use polarization-resolved second harmonic generation (P-SHG) imaging microscopy to rapidly map the twist angle in large areas of overlapping WS₂ stacked layers. The robustness of our methodology lies in the combination of both intensity and polarization measurements of SHG in the overlapping region. This allows the accurate measurement and consequent pixel-by-pixel mapping of the twist angle in this area. For the specific case of 30° twist angle, P-SHG enables imaging of individual layers.

Linear Dichroism Conversion in Quasi-1D Perovskite Chalcogenide

Anisotropic photonic materials with linear dichroism are crucial components in many sensing, imaging, and communication applications. Such materials play an important role as polarizers, filters, and waveplates in photonic devices and circuits. Conventional crystalline materials with optical anisotropy typically show unidirectional linear dichroism over a broad wavelength range. The linear dichroism conversion phenomenon has not been observed in crystalline materials. The investigation of the unique linear dichroism conversion phenomenon in quasi-1D hexagonal perovskite chalcogenide BaTiS₃ is reported. This material shows a record level of optical anisotropy within the visible wavelength range. In contrast to conventional anisotropic optical materials, the linear dichroism polarity in BaTiS₃ makes an orthogonal change at an optical wavelength corresponding to the photon energy of 1.78 eV. First-principles calculations reveal that this anomalous linear dichroism conversion behavior originates from the different selection rules of the parallel energy bands in the BaTiS₃ material. Wavelength-dependent polarized Raman spectroscopy further confirms this phenomenon. Such a material, with linear dichroism conversion properties, could facilitate the sensing and control of the energy and polarization of light, and lead to novel photonic devices such as polarization-wavelength selective detectors and lasers for multispectral imaging, sensing, and optical communication applications.

Interlayer Difference of Bilayer-Stacked MoS2 Structure: Probing by Photoluminescence and Raman Spectroscopy

This work reports the interlayer difference of exciton and phonon performance between the top and bottom layer of a bilayer-stacked two-dimensional materials structure (BSS). Through photoluminescence (PL) and Raman spectroscopy, we find that, compared to that of the bottom layer, the top layer of BSS demonstrates PL redshift, Raman E 2 g 1 mode redshift, and lower PL intensity. Spatial inhomogeneity of PL and Raman are also observed in the BSS. Based on theoretical analysis, these exotic effects can be attributed to substrate-coupling-induced strain and doping. Our findings provide pertinent insight into film-substrate interaction, and are of great significance to researches on bilayer-stacked structures including twisted bilayer structure, Van der Waals hetero- and homo-structure.

Modulating Charge Density Wave Order in a 1T-TaS2/Black Phosphorus Heterostructure

Controllability of collective electron states has been a long-sought scientific and technological goal and promises development of new devices. Herein, we investigate the tuning of charge density wave (CDW) in 1T-TaS₂ via a two-dimensional (2D) van der Waals heterostructure of 1T-TaS₂/BP. Unusual gate-dependent conductance oscillations were observed in 1T-TaS₂ nanoflake supported on BP in transport measurements. Scanning tunneling microscopy study shows that the nearly commensurate (NC) CDW phase survived to 4.5 K in this system, which is substantially lower than the NC to commensurate CDW phase transition temperature of 180 K. A Coulomb blockade model was invoked to explain the conductance oscillations, where the domain walls and domains in NC phase serve as series of quantum dot arrays and tunnelling barriers, respectively. Density functional theory calculations show that a range of interfacial interactions, including strain and charge transfer, influences the CDW stabilities. Our work sheds light on tuning CDW orders via 2D heterostructure stacking and provides new insights on the CDW phase transition and sliding mechanism.

A hidden Markov model for describing turbostratic disorder applied to carbon blacks and graphene

A mathematical framework is presented to represent turbostratic disorder in materials like carbon blacks, smectites and twistedn-layer graphene. In particular, the set of all possible disordered layers, including rotated, shifted and curved layers, forms a stochastic sequence governed by a hidden Markov model. The probability distribution over the set of layer types is treated as an element of a Hilbert space and, using the tools of Fourier analysis and functional analysis, expressions are developed for the scattering cross sections of a broad class of disordered materials.

Stacking angle-tunable photoluminescence from interlayer exciton states in twisted bilayer graphene

Twisted bilayer graphene (tBLG) is a metallic material with two degenerate van Hove singularity transitions that can rehybridize to form interlayer exciton states. Here we report photoluminescence (PL) emission from tBLG after resonant 2-photon excitation, which tunes with the interlayer stacking angle, θ. We spatially image individual tBLG domains at room-temperature and show a five-fold resonant PL-enhancement over the background hot-electron emission. Prior theory predicts that interlayer orbitals mix to create 2-photon-accessible strongly-bound (~0.7 eV) exciton and continuum-edge states, which we observe as two spectral peaks in both PL excitation and excited-state absorption spectra. This peak splitting provides independent estimates of the exciton binding energy which scales from 0.5–0.7 eV with θ = 7.5° to 16.5°. A predicted vanishing exciton-continuum coupling strength helps explain both the weak resonant PL and the slower 1 ps⁻¹ exciton relaxation rate observed. This hybrid metal-exciton behavior electron thermalization and PL emission are tunable with stacking angle for potential enhancements in optoelectronic and fast-photosensing graphene-based applications.

Interlayer electronic states in twisted bilayer graphene are characterized by flat-band regions hosting many-body electronic effects. Here, the authors observe two-photon photoluminescence excitation and excited-state absorption spectra on graphene containing a variety of twist angles to access the dark exciton transitions and estimate the exciton binding energy.