Stacking-dependent optical conductivity of bilayer graphene

The Rise of Xene Hybrids

Xenes, mono-elemental atomic sheets, exhibit Dirac/Dirac-like quantum behavior. When interfaced with other 2D materials such as boron nitride, transition metal dichalcogenides, and metal carbides/nitrides/carbonitrides, it enables them with unique physicochemical properties, including structural stability, desirable bandgap, efficient charge carrier injection, flexibility/breaking stress, thermal conductivity, chemical reactivity, catalytic efficiency, molecular adsorption, and wettability. For example, BN acts as an anti-oxidative shield, MoS2 injects electrons upon laser excitation, and MXene provides mechanical flexibility. Beyond precise compositional modulations, stacking sequences, and inter-layer coupling controlled by parameters, achieving scalability and reproducibility in hybridization is crucial for implementing these quantum materials in consumer applications. However, realizing the full potential of these hybrid materials faces challenges such as air gaps, uneven interfaces, and the formation of defects and functional groups. Advanced synthesis techniques, a deep understanding of quantum behaviors, precise control over interfacial interactions, and awareness of cross-correlations among these factors are essential. Xene-based hybrids show immense promise for groundbreaking applications in quantum computing, flexible electronics, energy storage, and catalysis. In this timely perspective, recent discoveries of novel Xenes and their hybrids are highlighted, emphasizing correlations among synthetic parameters, structure, properties, and applications. It is anticipated that these insights will revolutionize diverse industries and technologies.

Waveguide-integrated twisted bilayer graphene photodetectors

Graphene photodetectors have exhibited high bandwidth and capability of being integrated with silicon photonics (SiPh), holding promise for future optical communication devices. However, they usually suffer from a low photoresponsivity due to weak optical absorption. In this work, we have implemented SiPh-integrated twisted bilayer graphene (tBLG) detectors and reported a responsivity of 0.65 A W-1 for telecom wavelength 1,550 nm. The high responsivity enables a 3-dB bandwidth of >65 GHz and a high data stream rate of 50 Gbit s-1. Such high responsivity is attributed to the enhanced optical absorption, which is facilitated by van Hove singularities in the band structure of high-mobility tBLG with 4.1o twist angle. The uniform performance of the fabricated photodetector arrays demonstrates a fascinating prospect of large-area tBLG as a material candidate for heterogeneous integration with SiPh.

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.

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.

Controlled light energy and perfect absorption in twisted bilayer graphene

We theoretically study the components of the dynamical optical conductivity tensor and associated finite-frequency dielectric response of bilayer graphene (BLG), where one graphene layer can slide in-plane or commensurably twist on top of the other. Our results reveal that even slight deviations from the conventional AA, AB, or AC stacking orders yield a finite transverse conductivity. Upon calculating the optical conductivity of the BLG at any arbitrary interlayer displacement, Δ, and chemical potential, µ, it is utilized for a layered device with an epsilon-near-zero (ENZ) insert and metallic back plate. We find that both Δ and µ can effectively control the polarization, energy flow direction, and absorptivity of linearly polarized incident light. By appropriately tailoring Δ and µ, near-perfect absorption and tunable dissipation can be accessible through particular angles of incidence and a broad range of ENZ layer thicknesses. Our findings can be applied to the design of programmable optoelectronics devices.

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.

High throughput calculations for a dataset of bilayer materials

Bilayer materials made of 2D monolayers are emerging as new systems creating diverse opportunities for basic research and applications in optoelectronics, thermoelectrics, and topological science among others. Herein, we present a computational bilayer materials dataset containing 760 structures with their structural, electronic, and transport properties. Different stacking patterns of each bilayer have been framed by analyzing their monolayer symmetries. Density functional theory calculations including van der Waals interactions are carried out for each stacking pattern to evaluate the corresponding ground states, which are correctly identified for experimentally synthesized transition metal dichalcogenides, graphene, boron nitride, and silicene. Binding energies and interlayer charge transfer are evaluated to analyze the interlayer coupling strength. Our dataset can be used for materials screening and data-assisted modeling for desired thermoelectric or optoelectronic applications.

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.

Emerging Two-Dimensional Tellurene and Tellurides for Broadband Photodetectors

As with all stylish 2D functional materials, tellurene and tellurides possessing excellent physical and chemical properties such as high environmental stability, tunable narrow bandgap, and lower thermal conductivity, have aroused the great interest of the researchers. These properties of such materials also form the basis for relatively newfangled scholarly fields involving advanced topics, especially for broadband photodetectors. Integrating the excellent properties of many 2D materials, tellurene/telluride-based photodetectors show great flexibility, higher frequency response or faster time response, high signal-to-noise ratio, and so on, which make them leading the frontier of photodetector research. To fully understand the excellent properties of tellurene/tellurides and their optoelectronic applications, the recent advances in tellurene/telluride-based photodetectors are maximally summarized. Benefiting from the solid research in this field, the challenges and opportunities of tellurene/tellurides for future optoelectronic applications are also discussed in this review, which might provide possibilities for the realization of state-of-the-art high-performance tellurene/telluride-based devices.

Theoretical Model of a Plasmonically Enhanced Tunable Spectrally Selective Infrared Photodetector Based on Intercalation-Doped Nanopatterned Multilayer Graphene

We showed in past work that nanopatterned monolayer graphene (NPG) can be used for realizing an ultrafast (∼100 ns) and spectrally selective mid-infrared (mid-IR) photodetector based on the photothermoelectric effect and working in the 8-12 μm regime. In later work, we showed that the absorption wavelength of NPG can be extended to the 3-8 μm regime. Further extension to shorter wavelengths would require a smaller nanohole size that is not attainable with current technology. Here, we show by means of a theoretical model that nanopatterned multilayer graphene intercalated with FeCl₃ (NPMLG-FeCl₃) overcomes this problem by substantially extending the detection wavelength into the range from λ = 1.3 to 3 μm. We present a proof of concept for a spectrally selective infrared (IR) photodetector based on NPMLG-FeCl₃ that can operate from λ = 1.3 to 12 μm and beyond. The localized surface plasmons (LSPs) on the graphene sheets in NPMLG-FeCl₃ allow for electrostatic tuning of the photodetection wavelength. Most importantly, the LSPs along with an optical cavity increase the absorbance from about N × 2.6% for N-layer graphene-FeCl₃ (without patterning) to nearly 100% for NPMLG-FeCl₃, where the strong absorbance occurs locally inside the graphene sheets only. Our IR detection scheme relies on the photothermoelectric effect induced by asymmetric patterning of the multilayer graphene (MLG) sheets. The LSPs on the nanopatterned side create hot carriers that give rise to the Seebeck effect at room temperature, achieving a responsivity of R=6.15×103 V/W, a detectivity of D* = 2.3 × 10⁹ Jones, and an ultrafast response time of the order of 100 ns. Our theoretical results can be used to develop graphene-based photodetection, optical IR communication, IR color displays, and IR spectroscopy over a wide IR range.

Angle-resolved one and Two-Photon absorption spectrum in twisted bilayer graphene quantum dots

In this paper, one-photon absorption (OPA) spectrum and two-photon absorption (TPA) spectrum and its electronic excitation, charge transfer, partial density of states (PDOS) and magnetic induction current density of zigzag edge twisted bilayer graphene quantum dots (Z-TwBLG-QDs) with different twisted angles which were divide into two pattern of Moiré superlatrate (MS) are qualitativly and quantitativly analyed by using density functional theory (DFT), excited state wave function, single electron approximation, and gauge-invariant atomic orbital (GIAO) method. The inter-layer local excitation in the electronic transition and intra-layer charge transfer dominated by MS and anti-symmetric electron-hole pair density induced by PDOS are discussed. The twisted angle is decisive to the absorption spectrum, large twisted angle will lead to the red shift of the absorption spectrum. The two-photon transition shows that the twisted angle can regulate the TPA cross section and the boundary effect of Z-TwBLG-QDs in a specific wavelength range. The edge effect of two-step transition can be enhanced by MS with specific twisted angles. The physical mechanism of twisted angle regulating electron transition behavior is revealed by magnetic induction current density analysis.

First-principles study of borophene/phosphorene heterojunction as anode material for lithium-ion batteries

It is urgent to explore high-capacity and efficient anode materials for rechargeable lithium-ion batteries. For borophene and phosphorene, two configurations are considered to form a heterojunction: twist angles of 0° (I) and 90° (II). There is a less degree of mismatch and larger formation energy in the formation of a B/P heterojunction, implying that borophene and phosphorene form the stable heterojunction. The heterojunctions of these two configurations demonstrate good conductivity, and the electrons near the Fermi level are mainly provided by borophene. Very importantly, the low energy barrier for interlayer migration of Li is observed in configuration I (0.14eV) and II (0.06 eV), and the migration of Li on the borophene and phosphorene side of the heterojunction still maintains its original energy barrier in bare monolayer. Moreover, the two configurations show the theoretical capacity as high as 738.69 and 721.86 mA h g^-1, respectively, which is comparable to bare phosphorene. Furthermore, compared with bare phosphorene, the average voltage is greatly reduced after the formation of heterojunction. Hence, the overall electrochemical properties of the B/P heterojunction have been enhanced by combining the advantages of the individual phosphorene and borophene monolayers, which guarantees the B/P heterojunction as a good candidate for the anode material used in Li-ion batteries.

Refractive index of graphene AA and AB stacked bilayers under the influence of relative planar twisting

The optical properties of graphene in monolayer and bilayer structure is essential for the development of optical devices viz surface plasmon resonance (SPR) based bio-sensors. The band structure of the twisted bilayer graphene (BLG) is remarkably different than the normal AA or AB stacking. This provides an opportunity to control the optical and electrical properties of BLG by applying an in-plane twist to one of the layer relative to other in a BLG system. Here, we calculated the refractive index (RI) of AA and AB stacking of BLG system using density functional theory. Though the spectrum for AA stacking shows some similarity with that of monolayer graphene, the spectrum for AB stacking was found to be remarkably different. The spectrum of AB stacked layer is red-shifted and the absorption peaks in low energy regime increases nearly by three-folds. A large dependency of the twist angle on RI of twisted BLG were found. Based on the calculation, a schematic of phase diagram showing material behavior of such twisted BLG systems as a function of twist angle and photon energy was constructed. The twisted AA stacked BLG shows largely dielectric behavior whereas the twisted AB stacked BLG shows predominately semimetallic and semiconducting behavior. This study presents a RI landscape of twisted BLG dependent on important parameters viz photon energy and inplane relative twist angle. Our studies will be very useful for the design and development of optical devices employing BLG systems particularly SPR based bio-sensors which essentially measures change in RI due to adsorption of analytes.

Twist dependent magneto-optical response in twisted bilayer graphene

By employing a linearised Boltzmann equation, we calculate the magneto-optical properties of twisted bilayer graphene using non-magnetic wave functions. Both transverse and longitudinal responses are calculated up to the second order in applied magnetic field with their twist angle and Fermi level dependence examined. We find that increasing the twist angle increases the transverse metallic response so long as the Fermi level remains below the upper conduction band. Interlayer transitions provide an appreciable enhancement when the Fermi level traverses the gap between the two conduction bands. Interlayer transitions are also responsible for a nonzero anomalous Hall conductivity in this model. As the Fermi level moves towards zero, the longitudinal response begins to dominate and a highly anisotropic negative magneto-resistance is observed.

Photonic spin Hall effect in twisted bilayer graphene

Here, we investigate the photonic spin Hall effect in twisted bilayer graphene. The optical conductivities for several rotation angles of twisted bilayer graphene are calculated by first principles, based on which a theoretical framework is established to describe the light-matter interaction. To enhance the photonic spin Hall effect, twisted bilayer graphene is placed on a BK7 glass substrate and a Gaussian beam is launched near the Brewster angle. The spin splitting as well as Goos-Hänchen shifts are investigated, which are associated, respectively, with the imaginary and real parts of the surface conductivities of the twisted bilayer graphene. These findings provide a deeper understanding of the photonic spin Hall effect in two-dimensional materials and have potential application in characterizing bilayer graphene.

Electronic Structures of Twisted Bilayer InSe/InSe and Heterobilayer Graphene/InSe

Building vertical van der Waals heterojunctions between two-dimensional layered materials has become a promising strategy for modulating the properties of two-dimensional materials. Herein, we investigate the electronic structures of non-twisted/twisted bilayer InSe/InSe and heterobilayer graphene/InSe (Gr/InSe) by employing density functional theory calculations. For twisted bilayer InSe/InSes, their interlayer distances and band gaps are almost identical but a bit larger than those of the AB-stacking one due to the spontaneous polarization. Differently, the band gaps of twisted Gr/InSe are found to vary with the rotation angles. Our results provide an effective way to tune the electronic properties of two-dimensional materials.

Strain-controlled electronic and magnetic properties of tVS2/hVS2 van der Waals heterostructures

The structural, electronic and magnetic properties of the T-phase and H-phase of the VS₂ monolayer and their heterobilayers are studied by means of first-principles calculations. We find that the two phases of the VS₂ monolayer are both ferromagnetic (FM) semiconductors and that these two monolayers form a typical van der Waals (vdW) heterostructure with a weak interlayer interaction. By comparing the energy of different magnetic configurations, the FM state of the tVS₂/hVS₂ heterostructure is found to be in the ground state under normal conditions or biaxial strains. Under compressive strains, the anti-FM (AFM) and FM states degenerate. Based on the band structure obtained and the work function, it is found that the T-phase and H-phase are capable of forming an efficient p-n heterostructure. Due to spontaneous charge transfer at the interface, a gapless semiconductor is formed in our HSE06 calculations. We also find that the twist angle between the monolayers has a negligible impact on the band structure of the heterostructure in its spin-down channel. Moreover, the tVS₂/hVS₂ heterostructure is found to switch from a gapless semiconductor to a metal or a half-metal under some given biaxial or uniaxial strains. Therefore, the heterostructure could be a half-metallic property with strains, realizing 100% polarization at the Fermi level. Our study provides the possibility of realizing 100% spin-polarization at the Fermi level in these FM vdW heterostructures, which is significant for further spin transport exploration.

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.

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.

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.

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

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

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.

MXene/Graphene Heterostructures as High-Performance Electrodes for Li-Ion Batteries

Recently, MXene/graphene heterostructures have been successfully fabricated and found to exhibit outstanding performance as electrodes for Li-ion batteries. However, insights into the mechanism behind the encouraging experimental results are missing. We use first-principles calculations to systematically investigate the electrochemical properties of MXene/graphene heterostructures, choosing Ti₂CX₂ (X = F, O, and OH) as representative MXenes. Our calculations disclose that the presence of graphene not only avoids restacking effects of MXene layers but also enhances the electric conductivity, Li adsorption strength (while maintaining a high Li mobility), and mechanical stiffness. These favorable attributes collectively lead to the excellent performance of MXene/graphene electrodes observed experimentally. While the Ti₂CO₂/graphene heterostructure is proposed to be the most promising candidate within the studied materials, the developed comprehensive understanding is of significance also for the future rational design of MXene-based electrodes.

Work Function Variations in Twisted Graphene Layers

By combining optical imaging, Raman spectroscopy, kelvin probe force microscopy (KFPM), and photoemission electron microscopy (PEEM), we show that graphene’s layer orientation, as well as layer thickness, measurably changes the surface potential (Φ). Detailed mapping of variable-thickness, rotationally-faulted graphene films allows us to correlate Φ with specific morphological features. Using KPFM and PEEM we measure ΔΦ up to 39 mV for layers with different twist angles, while ΔΦ ranges from 36–129 mV for different layer thicknesses. The surface potential between different twist angles or layer thicknesses is measured at the KPFM instrument resolution of ≤ 200 nm. The PEEM measured work function of 4.4 eV for graphene is consistent with doping levels on the order of 10¹²cm⁻². We find that Φ scales linearly with Raman G-peak wavenumber shift (slope = 22.2 mV/cm⁻¹) for all layers and twist angles, which is consistent with doping-dependent changes to graphene’s Fermi energy in the ‘high’ doping limit. Our results here emphasize that layer orientation is equally important as layer thickness when designing multilayer two-dimensional systems where surface potential is considered.

Real-Space Imaging of the Tailored Plasmons in Twisted Bilayer Graphene

We report a systematic plasmonic study of twisted bilayer graphene (TBLG)-two graphene layers stacked with a twist angle. Through real-space nanoimaging of TBLG single crystals with a wide distribution of twist angles, we find that TBLG supports confined infrared plasmons that are sensitively dependent on the twist angle. At small twist angles, TBLG has a plasmon wavelength comparable to that of single-layer graphene. At larger twist angles, the plasmon wavelength of TBLG increases significantly with apparently lower damping. Further analysis and modeling indicate that the observed twist-angle dependence of TBLG plasmons in the Dirac linear regime is mainly due to the Fermi-velocity renormalization, a direct consequence of interlayer electronic coupling. Our work unveils the tailored plasmonic characteristics of TBLG and deepens our understanding of the intriguing nano-optical physics in novel van der Waals coupled two-dimensional materials.

Robust quasi-ohmic contact against angle rotation in noble transition-metal-dichalcogenide/graphene heterobilayers

Small Schottky barriers appear in PtS₂/graphene and PdS₂/graphene against interlayer rotation angles.

Oxidation-assisted graphene heteroepitaxy on copper foil

We propose an innovative, easy-to-implement approach to synthesize aligned large-area single-crystalline graphene flakes by chemical vapor deposition on copper foil. This method doubly takes advantage of residual oxygen present in the gas phase. First, by slightly oxidizing the copper surface, we induce grain boundary pinning in copper and, in consequence, the freezing of the thermal recrystallization process. Subsequent reduction of copper under hydrogen suddenly unlocks the delayed reconstruction, favoring the growth of centimeter-sized copper (111) grains through the mechanism of abnormal grain growth. Second, the oxidation of the copper surface also drastically reduces the nucleation density of graphene. This oxidation/reduction sequence leads to the synthesis of aligned millimeter-sized monolayer graphene domains in epitaxial registry with copper (111). The as-grown graphene flakes are demonstrated to be both single-crystalline and of high quality.

Stranski-Krastanov and Volmer-Weber CVD Growth Regimes To Control the Stacking Order in Bilayer Graphene

Aside from unusual properties of monolayer graphene, bilayer has been shown to have even more interesting physics, in particular allowing bandgap opening with dual gating for proper interlayer symmetry. Such properties, promising for device applications, ignited significant interest in understanding and controlling the growth of bilayer graphene. Here we systematically investigate a broad set of flow rates and relative gas ratio of CH₄ to H₂ in atmospheric pressure chemical vapor deposition of multilayered graphene. Two very different growth windows are identified. For relatively high CH₄ to H₂ ratios, graphene growth is relatively rapid with an initial first full layer forming in seconds upon which new graphene flakes nucleate then grow on top of the first layer. The stacking of these flakes versus the initial graphene layer is mostly turbostratic. This growth mode can be likened to Stranski-Krastanov growth. With relatively low CH₄ to H₂ ratios, growth rates are reduced due to a lower carbon supply rate. In addition bi-, tri-, and few-layer flakes form directly over the Cu substrate as individual islands. Etching studies show that in this growth mode subsequent layers form beneath the first layer presumably through carbon radical intercalation. This growth mode is similar to that found with Volmer-Weber growth and was shown to produce highly oriented AB-stacked materials. These systematic studies provide new insight into bilayer graphene formation and define the synthetic range where gapped bilayer graphene can be reliably produced.

Building Large-Domain Twisted Bilayer Graphene with van Hove Singularity

Twisted bilayer graphene (tBLG) with van Hove Singularity (VHS) has exhibited novel twist-angle-dependent chemical and physical phenomena. However, scalable production of high-quality tBLG is still in its infancy, especially lacking the angle controlled preparation methods. Here, we report a facile approach to prepare tBLG with large domain sizes (>100 μm) and controlled twist angles by a clean layer-by-layer transfer of two constituent graphene monolayers. The whole process without interfacial polymer contamination in two monolayers guarantees the interlayer interaction of the π-bond electrons, which gives rise to the existence of minigaps in electronic structures and the consequent formation of VHSs in density of state. Such perturbation on band structure was directly observed by angle-resolved photoemission spectroscopy with submicrometer spatial resolution (micro-ARPES). The VHSs lead to a strong light-matter interaction and thus introduce ∼20-fold enhanced intensity of Raman G-band, which is a characteristic of high-quality tBLG. The as-prepared tBLG with strong light-matter interaction was further fabricated into high-performance photodetectors with selectively enhanced photocurrent generation (up to ∼6 times compared with monolayer in our device).

Effect of interlayer interactions on exciton luminescence in atomic-layered MoS2 crystals

The atomic-layered semiconducting materials of transition metal dichalcogenides are considered effective light sources with both potential applications in thin and flexible optoelectronics and novel functionalities. In spite of the great interest in optoelectronic properties of two-dimensional transition metal dichalcogenides, the excitonic properties still need to be addressed, specifically in terms of the interlayer interactions. Here, we report the distinct behavior of the A and B excitons in the presence of interlayer interactions of layered MoS2 crystals. Micro-photoluminescence spectroscopic studies reveal that on the interlayer interactions in double layer MoS2 crystals, the emission quantum yield of the A exciton is drastically changed, whereas that of the B exciton remains nearly constant for both single and double layer MoS2 crystals. First-principles density functional theory calculations confirm that a significant charge redistribution occurs in the double layer MoS2 due to the interlayer interactions producing a local electric field at the interfacial region. Analogous to the quantum-confined Stark effect, we suggest that the distinct behavior of the A and B excitons can be explained by a simplified band-bending model.

High-Precision Twist-Controlled Bilayer and Trilayer Graphene

Twist-controlled bilayer graphene (tBLG) and double-twisted trilayer graphene (DTTG) with high precision are fabricated and their controllable optoelectronic properties are investigated for the first time. The successful fabrication of tBLG and DTTG with designated θ provides an attractive starting point for systematic studies of interlayer coupling in misoriented few-layer graphene systems with well-defined geometry.

Selectively enhanced photocurrent generation in twisted bilayer graphene with van Hove singularity

Graphene with ultra-high carrier mobility and ultra-short photoresponse time has shown remarkable potential in ultrafast photodetection. However, the broad and weak optical absorption (∼2.3%) of monolayer graphene hinders its practical application in photodetectors with high responsivity and selectivity. Here we demonstrate that twisted bilayer graphene, a stack of two graphene monolayers with an interlayer twist angle, exhibits a strong light–matter interaction and selectively enhanced photocurrent generation. Such enhancement is attributed to the emergence of unique twist-angle-dependent van Hove singularities, which are directly revealed by spatially resolved angle-resolved photoemission spectroscopy. When the energy interval between the van Hove singularities of the conduction and valance bands matches the energy of incident photons, the photocurrent generated can be significantly enhanced (up to ∼80 times with the integration of plasmonic structures in our devices). These results provide valuable insight for designing graphene photodetectors with enhanced sensitivity for variable wavelength.

Graphene has the high carrier mobility and short photoresponse time required for efficient photodetection, but broad and weak optical absorption are severe drawbacks. Here, the authors show that twisted bilayer graphene with van Hove singularities exhibits a strong light-matter interaction and selectively enhanced photocurrent generation.

Optical phonons in twisted bilayer graphene with gate-induced asymmetric doping

Twisted bilayer graphene (tBLG) devices with ion gel gate dielectrics are studied using Raman spectroscopy in the twist angle regime where a resonantly enhanced G band can be observed. We observe prominent splitting and intensity quenching on the G Raman band when the carrier density is tuned away from charge neutrality. This G peak splitting is attributed to asymmetric charge doping in the two graphene layers, which reveals individual phonon self-energy renormalization of the two weakly coupled layers of graphene. We estimate the effective interlayer capacitance at low doping density of tBLG using an interlayer screening model. The anomalous intensity quenching of both G peaks is ascribed to the suppression of resonant interband transitions between the two saddle points (van Hove singularities) that are displaced in the momentum space by gate-tuning. In addition, we observe a softening (hardening) of the R Raman band, a superlattice-induced phonon mode in tBLG, in electron (hole) doping. Our results demonstrate that gate modulation can be used to control the optoelectronic and vibrational properties in tBLG devices.

Epitaxial graphene on SiC{0001}: advances and perspectives

We review here recent progress on epitaxial graphene grown on a SiC substrate. Epitaxial graphene can be easily grown by heating the SiC single crystal in a high vacuum or in an inert gas atmosphere. The SiC surfaces used for graphene growth contain Si- and C-terminated faces. On the Si-face, homogeneous and clean graphene can be grown with a controlled number of layers, and the carrier mobility reaches as high as several m(2) V s(-1), although this is reduced by the presence of the substrate steps. On the C-face, although the number of layers is not homogeneous, twisted bilayer graphene can be grown, which is expected to be the technique of choice to modify the electronic structure of graphene. From the application point of view, graphene on SiC will be the platform used to fabricate high-speed electronic devices and dense graphene nanoribbon arrays, which will be used to introduce a bandgap.

Layer-dependent optical conductivity in atomic thin WS₂ by reflection contrast spectroscopy

Optical conductivity, which originates from the interband transition due to electron-phonon interaction, is one of the powerful tools used for studying the electronic states in layered transition metal dichalcogenides (TMDCs). Here, we report for the first time the optical conductivity of WS2, one of the emerging classes of TMDCs, prepared directly on SiO2/Si substrate using reflection contrast spectroscopy. The measured optical conductivity at direct excitonic transition point K of the Brillouin zone for monolayer WS2 shows a value of 0.37 e(2)/πℏ in the visible range of the energy spectrum. Our results reveal that the optical conductivity of WS2 layers is frequency-dependent and show additional features in the conductivity spectra for bilayer to bulk counterparts, signifying a transition from direct band gap to indirect band gap with the evolution of layer numbers as predicted by our calculations.

How to reliably determine the complex refractive index (RI) of graphene by using two independent measurement constraints

Reliable determination of the complex refractive index (RI) of graphene inherently requires two independent measurement realizations for two independent unknowns of the real (n_G) and imaginary (k_G) components, i.e., RI = n_G + ik_G. Thus, any single set of measurement realization provides only one constraint that is insufficient to uniquely determine the complex RI of graphene. Tandem uses of two independent measurement techniques, namely the surface plasmon resonance (SPR) angle detection and the attenuated total reflection (ATR) intensity measurement, allow for the unique determination of the complex RI of CVD-synthesized graphene. The presently measured graphene RI is determined to be 2.65 + 1.27i for the E-field oscillating parallel to graphene at 634 nm wavelength, with variations for different numbers of L (1, 3 and 5) remaining within ±3%. Thus, our demonstration results for the specified wavelength serve as an impetus to suggest the need for two independent measurement techniques in determining both the real and imaginary RI values for graphene. Additional efforts have been made to characterize graphene layers using the density function theory (DFT): this calculation provides RI_G = 2.71 + 1.41i.

Van Hove singularities and excitonic effects in the optical conductivity of twisted bilayer graphene

We report a systematic study of the optical conductivity of twisted bilayer graphene (tBLG) across a large energy range (1.2-5.6 eV) for various twist angles, combined with first-principles calculations. At previously unexplored high energies, our data show signatures of multiple van Hove singularities (vHSs) in the tBLG bands as well as the nonlinearity of the single layer graphene bands and their electron-hole asymmetry. Our data also suggest that excitonic effects play a vital role in the optical spectra of tBLG. Including electron-hole interactions in first-principles calculations is essential to reproduce the shape of the conductivity spectra, and we find evidence of coherent interactions between the states associated with the multiple vHSs in tBLG.

Bilayer Phosphorene: Effect of Stacking Order on Bandgap and Its Potential Applications in Thin-Film Solar Cells

Phosphorene, a monolayer of black phosphorus, is promising for nanoelectronic applications not only because it is a natural p-type semiconductor but also because it possesses a layer-number-dependent direct bandgap (in the range of 0.3 to 1.5 eV). On basis of the density functional theory calculations, we investigate electronic properties of the bilayer phosphorene with different stacking orders. We find that the direct bandgap of the bilayers can vary from 0.78 to 1.04 eV with three different stacking orders. In addition, a vertical electric field can further reduce the bandgap to 0.56 eV (at the field strength 0.5 V/Å). More importantly, we find that when a monolayer of MoS2 is superimposed with the p-type AA- or AB-stacked bilayer phosphorene, the combined trilayer can be an effective solar-cell material with type-II heterojunction alignment. The power conversion efficiency is predicted to be ∼18 or 16% with AA- or AB-stacked bilayer phosphorene, higher than reported efficiencies of the state-of-the-art trilayer graphene/transition metal dichalcogenide solar cells.

Rotational disorder in twisted bilayer graphene

Conventional means of stacking two-dimensional (2D) crystals inevitably leads to imperfections. To examine the ramifications of these imperfections, rotational disorder and strain are quantified in twisted bilayer graphene (TBG) using a combination of Raman spectroscopic and low-energy electron diffraction imaging. The twist angle between TBG layers varies on the order of 2° within large (50-100 μm) single-crystalline grains, resulting in changes of the emergent Raman response by over an order of magnitude. Rotational disorder does not evolve continuously across the large grains but rather comes about by variations in the local twist angles between differing contiguous subgrains, ∼ 1 μm in size, that themselves exhibit virtually no twist angle variation (ΔΘ ∼ 0.1°). Owing to weak out-of-plane van der Waals bonding between azimuthally rotated graphene layers, these subgrains evolve in conjunction with the 0.3% strain variation observed both within and between the atomic layers. Importantly, the emergent Raman response is altered, but not removed, by these extrinsic perturbations. Interlayer interactions are therefore resilient to strain and rotational disorder, a fact that gives promise to the prospect of designer 2D solid heterostructures created via transfer processes.

Large hexagonal bi- and trilayer graphene single crystals with varied interlayer rotations

Bi- and trilayer graphene have attracted intensive interest due to their rich electronic and optical properties, which are dependent on interlayer rotations. However, the synthesis of high-quality large-size bi- and trilayer graphene single crystals still remains a challenge. Here, the synthesis of 100 μm pyramid-like hexagonal bi- and trilayer graphene single-crystal domains on Cu foils using chemical vapor deposition is reported. The as-produced graphene domains show almost exclusively either 0° or 30° interlayer rotations. Raman spectroscopy, transmission electron microscopy, and Fourier-transformed infrared spectroscopy were used to demonstrate that bilayer graphene domains with 0° interlayer stacking angles were Bernal stacked. Based on first-principle calculations, it is proposed that rotations originate from the graphene nucleation at the Cu step, which explains the origin of the interlayer rotations and agrees well with the experimental observations.

Twisted bi-layer graphene: microscopic rainbows

Blue, pink, and yellow colorations appear from twisted bi-layer graphene (tBLG) when transferred to a SiO2 /Si substrate (SiO2 = 100 nm-thick). Raman and electron microscope studies reveal that these colorations appear for twist angles in the 9-15° range. Optical contrast simulations confirm that the observed colorations are related to the angle-dependent electronic properties of tBLG combined with the reflection that results from the layered structure tBLG/100 nm-thick SiO2 /Si.

Observation of low energy Raman modes in twisted bilayer graphene

Two new Raman modes below 100 cm(-1) are observed in twisted bilayer graphene grown by chemical vapor deposition. The two modes are observed in a small range of twisting angle at which the intensity of the G Raman peak is strongly enhanced, indicating that these low energy modes and the G Raman mode share the same resonance enhancement mechanism, as a function of twisting angle. The ~94 cm(-1) mode (measured with a 532 nm laser excitation) is assigned to the fundamental layer breathing vibration (ZO' mode) mediated by the twisted bilayer graphene lattice, which lacks long-range translational symmetry. The dependence of this mode's frequency and line width on the rotational angle can be explained by the double resonance Raman process that is different from the previously identified Raman processes activated by twisted bilayer graphene superlattice. The dependence also reveals the strong impact of electronic-band overlaps of the two graphene layers. Another new mode at ~52 cm(-1), not observed previously in the bilayer graphene system, is tentatively attributed to a torsion mode in which the bottom and top graphene layers rotate out-of-phase in the plane.

Hyperspectral imaging of structure and composition in atomically thin heterostructures

Precise vertical stacking and lateral stitching of two-dimensional (2D) materials, such as graphene and hexagonal boron nitride (h-BN), can be used to create ultrathin heterostructures with complex functionalities, but this diversity of behaviors also makes these new materials difficult to characterize. We report a DUV-vis-NIR hyperspectral microscope that provides imaging and spectroscopy at energies of up to 6.2 eV, allowing comprehensive, all-optical mapping of chemical composition in graphene/h-BN lateral heterojunctions and interlayer rotations in twisted bilayer graphene (tBLG). With the addition of transmission electron microscopy, we obtain quantitative structure-property relationships, confirming the formation of interfaces in graphene/h-BN lateral heterojunctions that are abrupt on a micrometer scale, and a one-to-one relationship between twist angle and interlayer optical resonances in tBLG. Furthermore, we perform similar hyperspectral imaging of samples that are supported on a nontransparent silicon/SiO2 substrate, enabling facile fabrication of atomically thin heterostructure devices with known composition and structure.

Free radical reactions in two dimensions: a case study on photochlorination of graphene

Graphene, a two-dimensional giant-molecule of sp(2) -bonded carbon atoms, provides a perfect platform for studying free radical reaction chemistry in two-dimensions, which holds promise to control the chemical functionality of graphene. Free-radical photochlorination of graphene is used as an example to investigate the thickness, stacking order, and single- and double-side dependent reactivity in graphene. Anomalously low reactivity is observed in the photochlorination of AB-stacked bilayer graphene in comparison with that of few-layer graphene. Double-sided chlorination of graphene shows higher reactivity and chlorine coverage than single-sided reaction. It is also experimentally and theoretically demonstrated that chlorine free radicals at low coverage prefer to form a stable charge-transfer complex with graphene, which highly enhances graphene's conductivity and simultaneously generates a pseudo-bandgap through noninvasive doping. Moreover, the initial accumulation of chlorine radicals is considered as the rate-determining step of photochlorination of graphene.

Twisting bilayer graphene superlattices

Bilayer graphene is an intriguing material in that its electronic structure can be altered by changing the stacking order or the relative twist angle, yielding a new class of low-dimensional carbon system. Twisted bilayer graphene can be obtained by (i) thermal decomposition of SiC; (ii) chemical vapor deposition (CVD) on metal catalysts; (iii) folding graphene; or (iv) stacking graphene layers one atop the other, the latter of which suffers from interlayer contamination. Existing synthesis protocols, however, usually result in graphene with polycrystalline structures. The present study investigates bilayer graphene grown by ambient pressure CVD on polycrystalline Cu. Controlling the nucleation in early stage growth allows the constituent layers to form single hexagonal crystals. New Raman active modes are shown to result from the twist, with the angle determined by transmission electron microscopy. The successful growth of single-crystal bilayer graphene provides an attractive jumping-off point for systematic studies of interlayer coupling in misoriented few-layer graphene systems with well-defined geometry.

Terahertz conductivity of twisted bilayer graphene

Using terahertz time-domain spectroscopy, the real part of optical conductivity [σ(1)(ω)] of twisted bilayer graphene was obtained at different temperatures (10-300 K) in the frequency range 0.3-3 THz. On top of a Drude-like response, we see a strong peak in σ(1)(ω) at ~2.7 THz. We analyze the overall Drude-like response using a disorder-dependent (unitary scattering) model, then attribute the peak at 2.7 THz to an enhanced density of states at that energy, which is caused by the presence of a van Hove singularity arising from a commensurate twisting of the two graphene layers.