Graphene bilayer with a twist: electronic structure

Controlled Folding of Single Crystal Graphene

Folded graphene in which two layers are stacked with a twist angle between them has been predicted to exhibit unique electronic, thermal, and magnetic properties. We report the folding of a single crystal monolayer graphene film grown on a Cu(111) substrate by using a tailored substrate having a hydrophobic region and a hydrophilic region. Controlled film delamination from the hydrophilic region was used to prepare macroscopic folded graphene with good uniformity on the millimeter scale. This process was used to create many folded sheets each with a defined twist angle between the two sheets. By identifying the original lattice orientation of the monolayer graphene on Cu foil, or establishing the relation between the fold angle and twist angle, this folding technique allows for the preparation of twisted bilayer graphene films with defined stacking orientations and may also be extended to create folded structures of other two-dimensional nanomaterials.

Phonons and thermal transport in graphene and graphene-based materials

A discovery of the unusual thermal properties of graphene stimulated experimental, theoretical and computational research directed at understanding phonon transport and thermal conduction in two-dimensional material systems. We provide a critical review of recent results in the graphene thermal field focusing on phonon dispersion, specific heat, thermal conductivity, and comparison of different models and computational approaches. The correlation between the phonon spectrum in graphene-based materials and the heat conduction properties is analyzed in details. The effects of the atomic plane rotations in bilayer graphene, isotope engineering, and relative contributions of different phonon dispersion branches are discussed. For readers' convenience, the summaries of main experimental and theoretical results on thermal conductivity as well as phonon mode contributions to thermal transport are provided in the form of comprehensive annotated tables.

Helical edge states and fractional quantum Hall effect in a graphene electron-hole bilayer

Helical 1D electronic systems are a promising route towards realizing circuits of topological quantum states that exhibit non-Abelian statistics. Here, we demonstrate a versatile platform to realize 1D systems made by combining quantum Hall (QH) edge states of opposite chiralities in a graphene electron-hole bilayer at moderate magnetic fields. Using this approach, we engineer helical 1D edge conductors where the counterpropagating modes are localized in separate electron and hole layers by a tunable electric field. These helical conductors exhibit strong non-local transport signals and suppressed backscattering due to the opposite spin polarizations of the counterpropagating modes. Unlike other approaches used for realizing helical states, the graphene electron-hole bilayer can be used to build new 1D systems incorporating fractional edge states. Indeed, we are able to tune the bilayer devices into a regime hosting fractional and integer edge states of opposite chiralities, paving the way towards 1D helical conductors with fractional quantum statistics.

Incommensurate Graphene Foam as a High Capacity Lithium Intercalation Anode

Graphite’s capacity of intercalating lithium in rechargeable batteries is limited (theoretically, 372 mAh g⁻¹) due to low diffusion within commensurately-stacked graphene layers. Graphene foam with highly enriched incommensurately-stacked layers was grown and applied as an active electrode in rechargeable batteries. A 93% incommensurate graphene foam demonstrated a reversible specific capacity of 1,540 mAh g⁻¹ with a 75% coulombic efficiency, and an 86% incommensurate sample achieves above 99% coulombic efficiency exhibiting 930 mAh g⁻¹ specific capacity. The structural and binding analysis of graphene show that lithium atoms highly intercalate within weakly interacting incommensurately-stacked graphene network, followed by a further flexible rearrangement of layers for a long-term stable cycling. We consider lithium intercalation model for multilayer graphene where capacity varies with N number of layers resulting Li_N+1C_2N stoichiometry. The effective capacity of commonly used carbon-based rechargeable batteries can be significantly improved using incommensurate graphene as an anode material.

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.

Strain-Gradient Modulated Exciton Emission in Bent ZnO Wires Probed by Cathodoluminescence

Photoelectrical properties of semiconductor nanostructures are expected to be improved significantly by strain engineering. Besides the local strain, the strain gradient is promising to tune the luminescence properties by modifying the crystal symmetry. Here, we report the investigation of strain-gradient induced symmetry-breaking effect on excitonic states in pure bending ZnO microwires by high spatial-resolved cathodoluminescence at low temperature of 80 K. In addition to the local-strain induced light emission peak shift, the bound exciton emission photon energy shows an extraordinary jump of ∼16.6 meV at a high strain-gradient of 1.22% μm^-1, which is ascribed to the strain gradient induced symmetry-breaking. Such a symmetry-breaking lifts the energy degeneracy of the electronic band structures, which significantly modifies the electron-hole interactions and the fine structures of the bound exciton states. These results provide a further understanding of the strain gradient effect on the excitonic states and possess a potential for the applications in optoelectronic devices.

Broken-Symmetry Quantum Hall States in Twisted Bilayer Graphene

Twisted bilayer graphene offers a unique bilayer two-dimensional-electron system where the layer separation is only in sub-nanometer scale. Unlike Bernal-stacked bilayer, the layer degree of freedom is disentangled from spin and valley, providing eight-fold degeneracy in the low energy states. We have investigated broken-symmetry quantum Hall (QH) states and their transitions due to the interplay of the relative strength of valley, spin and layer polarizations in twisted bilayer graphene. The energy gaps of the broken-symmetry QH states show an electron-hole asymmetric behaviour, and their dependence on the induced displacement field are opposite between even and odd filling factor states. These results strongly suggest that the QH states with broken valley and spin symmetries for individual layer become hybridized via interlayer tunnelling, and the hierarchy of the QH states is sensitive to both magnetic field and displacement field due to charge imbalance between layers.

Quasi-Flat Plasmonic Bands in Twisted Bilayer Graphene

The charge susceptibility of twisted bilayer graphene is investigated in the Dirac cone, respectively, random-phase approximation. For small enough twist angles θ ≲ 2°, we find weakly Landau damped interband plasmons, that is, collective excitonic modes that exist in the undoped material with an almost constant energy dispersion. In this regime, the loss function can be described as a Fano resonance, and we argue that these excitations arise from the interaction of quasi-localized states with the incident light field. These predictions can be tested by nanoinfrared imaging and possible applications include a "perfect" lens without the need of left-handed materials.

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.

Twisted Bilayer Graphene: Moiré with a Twist

A multiscale model is developed to predict the equilibrium structure of twisted bilayer graphene (tBLG). Two distinct, modified Moiré structures are observed. The breathing mode, stable at large twist angle, has small amplitude (opposite sign) buckling of the two layers. The bending mode is characterized by large amplitude (same sign) buckling of the layers. The latter gives rise to a distorted Moiré pattern consisting of a twisted dislocation structure. The relaxation of the Moiré structure reduces the symmetry and increases the period of the tBLG. On the basis of these results, we derive a quantitative analytical model for the angle dependence of the tBLG energy.

Superlattice-Induced Insulating States and Valley-Protected Orbits in Twisted Bilayer Graphene

Twisted bilayer graphene (TBLG) is one of the simplest van der Waals heterostructures, yet it yields a complex electronic system with intricate interplay between moiré physics and interlayer hybridization effects. We report on electronic transport measurements of high mobility small angle TBLG devices showing clear evidence for insulating states at the superlattice band edges, with thermal activation gaps several times larger than theoretically predicted. Moreover, Shubnikov-de Haas oscillations and tight binding calculations reveal that the band structure consists of two intersecting Fermi contours whose crossing points are effectively unhybridized. We attribute this to exponentially suppressed interlayer hopping amplitudes for momentum transfers larger than the moiré wave vector.

Coherent commensurate electronic states at the interface between misoriented graphene layers

Graphene and layered materials in general exhibit rich physics and application potential owing to their exceptional electronic properties, which arise from the intricate π-orbital coupling and the symmetry breaking in twisted bilayer systems. Here, we report room-temperature experiments to study electrical transport across a bilayer graphene interface with a well-defined rotation angle between the layers that is controllable in situ. This twisted interface is artificially created in mesoscopic pillars made of highly oriented pyrolytic graphite by mechanical actuation. The overall measured angular dependence of the conductivity is consistent with a phonon-assisted transport mechanism that preserves the electron momentum of conduction electrons passing the interface. The most intriguing observations are sharp conductivity peaks at interlayer rotation angles of 21.8° and 38.2°. These angles correspond to a commensurate crystalline superstructure leading to a coherent two-dimensional (2D) electronic interface state. Such states, predicted by theory, form the basis for a new class of 2D weakly coupled bilayer systems with hitherto unexplored properties and applications.

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.

Tunneling spectra of graphene on copper unraveled

Scanning tunneling spectroscopy is often employed to study two-dimensional (2D) materials on conductive growth substrates, in order to gain information on the electronic structures of the 2D material-substrate systems, which can lead to insight into 2D material-substrate interactions, growth mechanisms, etc. The interpretation of the spectra can be complicated, however. Specifically for graphene grown on copper, there have been conflicting reports of tunneling spectra. A clear understanding of the mechanisms behind the variability is desired. In this work, we have revealed that the root cause of the variability in tunneling spectra is the variation in graphene-substrate coupling under various experimental conditions, providing a salutary perspective on the important role of 2D material-substrate interactions. The conclusions are drawn from measured data and theoretical calculations for monolayer, AB-stacked bilayer, and twisted bilayer graphene coexisting on the same substrates in areas with and without intercalated oxygen, demonstrating a high degree of consistency. The Van Hove singularities of the twisted graphene unambiguously indicate the Dirac energy between them, lending strong evidence to our assignment of the spectral features. In addition, we have discovered an O-Cu superstructure that has never been observed before.

NanoARPES of twisted bilayer graphene on SiC: absence of velocity renormalization for small angles

The structural and electronic properties of twisted bilayer graphene (TBG) on SiC(000) grown by Si flux-assisted molecular beam epitaxy were investigated using scanning tunneling microscopy (STM) and angle-resolved photoelectron spectroscopy with nanometric spatial resolution. STM images revealed a wide distribution of twist angles between the two graphene layers. The electronic structure recorded in single TBG grains showed two closely-spaced Dirac π bands associated to the two stacked layers with respective twist angles in the range 1–3°. The renormalization of velocity predicted in previous theoretical calculations for small twist angles was not observed.

Chiral atomically thin films

Chiral materials possess left- and right-handed counterparts linked by mirror symmetry. These materials are useful for advanced applications in polarization optics, stereochemistry and spintronics. In particular, the realization of spatially uniform chiral films with atomic-scale control of their handedness could provide a powerful means for developing nanodevices with novel chiral properties. However, previous approaches based on natural or grown films, or arrays of fabricated building blocks, could not offer a direct means to program intrinsic chiral properties of the film on the atomic scale. Here, we report a chiral stacking approach, where two-dimensional materials are positioned layer-by-layer with precise control of the interlayer rotation (θ) and polarity, resulting in tunable chiral properties of the final stack. Using this method, we produce left- and right-handed bilayer graphene, that is, a two-atom-thick chiral film. The film displays one of the highest intrinsic ellipticity values (6.5 deg μm(-1)) ever reported, and a remarkably strong circular dichroism (CD) with the peak energy and sign tuned by θ and polarity. We show that these chiral properties originate from the large in-plane magnetic moment associated with the interlayer optical transition. Furthermore, we show that we can program the chiral properties of atomically thin films layer-by-layer by producing three-layer graphene films with structurally controlled CD spectra.

Interaction driven quantum Hall effect in artificially stacked graphene bilayers

The honeycomb lattice structure of graphene gives rise to its exceptional electronic properties of linear dispersion relation and its chiral nature of charge carriers. The exceptional electronic properties of graphene stem from linear dispersion relation and chiral nature of charge carries, originating from its honeycomb lattice structure. Here, we address the quantum Hall effect in artificially stacked graphene bilayers and single layer graphene grown by chemical vapor deposition. The quantum Hall plateaus started to appear more than 3 T and became clearer at higher magnetic fields up to 9 T. Shubnikov-de Hass oscillations were manifestly observed in graphene bilayers texture. These unusual plateaus may have been due to the layers interaction in artificially stacked graphene bilayers. Our study initiates the understanding of interactions between artificially stacked graphene layers.

Polytypism and unexpected strong interlayer coupling in two-dimensional layered ReS2

Anisotropic two-dimensional (2D) van der Waals (vdW) layered materials, with both scientific interest and application potential, offer one more dimension than isotropic 2D materials to tune their physical properties. Various physical properties of 2D multi-layer materials are modulated by varying their stacking orders owing to significant interlayer vdW coupling. Multilayer rhenium disulfide (ReS2), a representative anisotropic 2D material, was expected to be randomly stacked and lack interlayer coupling. Here, we demonstrate two stable stacking orders, namely isotropic-like (IS) and anisotropic-like (AI) N layer (NL, N > 1) ReS2 are revealed by ultralow- and high-frequency Raman spectroscopy, photoluminescence and first-principles density functional theory calculation. Two interlayer shear modes are observed in AI-NL-ReS2 while only one shear mode appears in IS-NL-ReS2, suggesting anisotropic- and isotropic-like stacking orders in IS- and AI-NL-ReS2, respectively. This explicit difference in the observed frequencies identifies an unexpected strong interlayer coupling in IS- and AI-NL-ReS2. Quantitatively, the force constants of them are found to be around 55-90% of those of multilayer MoS2. The revealed strong interlayer coupling and polytypism in multi-layer ReS2 may stimulate future studies on engineering physical properties of other anisotropic 2D materials by stacking orders.

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.

Copper-Vapor-Assisted Rapid Synthesis of Large AB-Stacked Bilayer Graphene Domains on Cu-Ni Alloy

The synergic effects of Cu85Ni15 and the copper vapor evaporated from copper foil enabled the fast growth of a ≈300 μm bilayer graphene in ≈10 minutes. The copper vapor reduces the growth rate of the first graphene layer while the carbon dissolved in the alloy boosts the growth of the subsequently developed second graphene layer with an AB-stacking order.

Nitrogen-Doped Graphene and Twisted Bilayer Graphene via Hyperthermal Ion Implantation with Depth Control

We investigate hyperthermal ion implantation (HyTII) as a means for substitutionally doping layered materials such as graphene. In particular, this systematic study characterizes the efficacy of substitutional N-doping of graphene using HyTII over an N(+) energy range of 25-100 eV. Scanning tunneling microscopy results establish the incorporation of N substituents into the graphene lattice during HyTII processing. We illustrate the differences in evolution of the characteristic Raman peaks following incremental doses of N(+). We use the ratios of the integrated D and D' peaks, I(D)/I(D') to assess the N(+) energy-dependent doping efficacy, which shows a strong correlation with previously reported molecular dynamics (MD) simulation results and a peak doping efficiency regime ranging between approximately 30 and 50 eV. We also demonstrate the inherent monolayer depth control of the HyTII process, thereby establishing a unique advantage over other less-specific methods for doping. We achieve this by implementing twisted bilayer graphene (TBG), with one layer of isotopically enriched (13)C and one layer of natural (12)C graphene, and modify only the top layer of the TBG sample. By assessing the effects of N-HyTII processing, we uncover dose-dependent shifts in the transfer characteristics consistent with electron doping and we find dose-dependent electronic localization that manifests in low-temperature magnetotransport measurements.

van der Waals Heterostructures with High Accuracy Rotational Alignment

We describe the realization of van der Waals (vdW) heterostructures with accurate rotational alignment of individual layer crystal axes. We illustrate the approach by demonstrating a Bernal-stacked bilayer graphene formed using successive transfers of monolayer graphene flakes. The Raman spectra of this artificial bilayer graphene possess a wide 2D band, which is best fit by four Lorentzians, consistent with Bernal stacking. Scanning tunneling microscopy reveals no moiré pattern on the artificial bilayer graphene, and tunneling spectroscopy as a function of gate voltage reveals a constant density of states, also in agreement with Bernal stacking. In addition, electron transport probed in dual-gated samples reveals a band gap opening as a function of transverse electric field. To illustrate the applicability of this technique to realize vdW heterostructuctures in which the functionality is critically dependent on rotational alignment, we demonstrate resonant tunneling double bilayer graphene heterostructures separated by hexagonal boron-nitride dielectric.

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.

Friedel oscillation near a van Hove singularity in two-dimensional Dirac materials

We consider Friedel oscillation in the two-dimensional Dirac materials when the Fermi level is near the van Hove singularity. Twisted graphene bilayer and the surface state of topological crystalline insulator are the representative materials which show low-energy saddle points that are feasible to probe by gating. We approximate the Fermi surface near saddle point with a hyperbola and calculate the static Lindhard response function. Employing a theorem of Lighthill, the induced charge density [Formula: see text] due to an impurity is obtained and the algebraic decay of [Formula: see text] is determined by the singularity of the static response function. Although a hyperbolic Fermi surface is rather different from a circular one, the static Lindhard response function in the present case shows a singularity similar with the response function associated with circular Fermi surface, which leads to the [Formula: see text] at large distance R. The dependences of charge density on the Fermi energy are different. Consequently, it is possible to observe in twisted graphene bilayer the evolution that [Formula: see text] near Dirac point changes to [Formula: see text] above the saddle point. Measurements using scanning tunnelling microscopy around the impurity sites could verify the prediction.

Large-Area Growth of Turbostratic Graphene on Ni(111) via Physical Vapor Deposition

Single-layer graphene has demonstrated remarkable electronic properties that are strongly influenced by interfacial bonding and break down for the lowest energy configuration of stacked graphene layers (AB Bernal). Multilayer graphene with relative rotations between carbon layers, known as turbostratic graphene, can effectively decouple the electronic states of adjacent layers, preserving properties similar to that of SLG. While the growth of AB Bernal graphene through chemical vapor deposition has been widely reported, we investigate the growth of turbostratic graphene on heteroepitaxial Ni(111) thin films utilizing physical vapor deposition. By varying the carbon deposition temperature between 800 –1100 °C, we report an increase in the graphene quality concomitant with a transition in the size of uniform thickness graphene, ranging from nanocrystallites to thousands of square microns. Combination Raman modes of as-grown graphene within the frequency range of 1650 cm⁻¹ to 2300 cm⁻¹, along with features of the Raman 2D mode, were employed as signatures of turbostratic graphene. Bilayer and multilayer graphene were directly identified from areas that exhibited Raman characteristics of turbostratic graphene using high-resolution TEM imaging. Raman maps of the pertinent modes reveal large regions of turbostratic graphene on Ni(111) thin films at a deposition temperature of 1100 °C.

Structural characterization of individual graphene sheets formed by arc discharge and their growth mechanisms

Two types of arc graphene sheets with different morphology and crystal structures are found, and further probed by Raman spectroscopy. Moreover, a new growth mechanism responsible for the difference of arc graphene is proposed.

The stacking dependent electronic structure and optical properties of bilayer black phosphorus

The optical excitations of bilayer black phosphorus with four different stacking patterns.

Nonlinear optical effects in nitrogen-doped graphene

The band structure of graphene can be adjusted by incorporating other elements or functional groups, correspondingly, the response to an external light field will also be changed.

Graphene Dynamic Synapse with Modulatable Plasticity

The synaptic activities in the nervous system is the basis of memory and learning behaviors, and the concept of biological synapse has also spurred the development of neuromorphic engineering. In recent years, the hardware implementation of the biological synapse has been achieved based on CMOS circuits, resistive switching memory, and field effect transistors with ionic dielectrics. However, the artificial synapse with regulatable plasticity has never been realized of the device level. Here, an artificial dynamic synapse based on twisted bilayer graphene is demonstrated with tunable plasticity. Due to the ambipolar conductance of graphene, both behaviors of the excitatory synapse and the inhibitory synapse could be realized in a single device. Moreover, the synaptic plasticity could also be modulated by tuning the carrier density of graphene. Because the artificial synapse here could be regulated and inverted via changing the bottom gate voltage, the whole process of synapse development could be imitated. Hence, this work would offer a broad new vista for the 2D material electronics and guide the innovation of neuro-electronics fundamentally.

Spectroscopic characterization of charge carrier anisotropic motion in twisted few-layer graphene

Graphene, a layer of carbon atoms in a honeycomb lattice, captures enormous interest as probably the most promising component of future electronics thanks to its mechanical robustness, flexibility, and unique charge carrier quasiparticles propagating like massless high energy Dirac fermions. If several graphene layers form a stack, the interaction between them is, on the one hand, weak, allowing realization of various registries between the layers and, on the other hand, strong enough for a wide range tuning of the electronic properties. Here we grow few layer graphene with various number of layers and twist configurations and address the electronic properties of individual atomic layers in single microscopic domains using angle-resolved photoelectron spectromicroscopy. The dependence of the interlayer coupling on the twist angle is analyzed and, in the domains with tri-layers and more, if different rotations are present, the electrons in weaker coupled adjacent layers are shown to have different properties manifested by coexisting van Hove singularities, moiré superlattices with corresponding superlattice Dirac points, and charge carrier group velocity renormalizations. Moreover, pronounced anisotropy in the charge carrier motion, opening a possibility to transform strongly coupled graphene bilayers into quasi one-dimensional conductors, is observed.

Electromechanical oscillations in bilayer graphene

Nanoelectromechanical systems constitute a class of devices lying at the interface between fundamental research and technological applications. Realizing nanoelectromechanical devices based on novel materials such as graphene allows studying their mechanical and electromechanical characteristics at the nanoscale and addressing fundamental questions such as electron-phonon interaction and bandgap engineering. In this work, we realize electromechanical devices using single and bilayer graphene and probe the interplay between their mechanical and electrical properties. We show that the deflection of monolayer graphene nanoribbons results in a linear increase in their electrical resistance. Surprisingly, we observe oscillations in the electromechanical response of bilayer graphene. The proposed theoretical model suggests that these oscillations arise from quantum mechanical interference in the transition region induced by sliding of individual graphene layers with respect to each other. Our work shows that bilayer graphene conceals unexpectedly rich and novel physics with promising potential in applications based on nanoelectromechanical systems.

van Hove Singularity Enhanced Photochemical Reactivity of Twisted Bilayer Graphene

Twisted bilayer graphene (tBLG) exhibits van Hove singularities (VHSs) in the density of states that can be tuned by changing the twist angle (θ), sparking various novel physical phenomena. Much effort has been devoted to investigate the θ-dependent physical properties of tBLG. Yet, the chemical properties of tBLG with VHSs, especially the chemical reactivity, remain unexplored. Here we report the first systematic study on the chemistry of tBLG through the photochemical reaction between graphene and benzoyl peroxide. Twisted bilayer graphene exhibits θ-dependent reactivity, and remarkably enhanced reactivity is obtained when the energy of incident laser matches with the energy interval of the VHSs of tBLG. This work provides an insight on the chemistry of tBLG, and the successful enhancement of chemical reactivity derived from VHS is highly beneficial for the controllable chemical modification of tBLG as well as the development of tBLG based devices.

Nitrogen Doping Enables Covalent-Like π-π Bonding between Graphenes

The neighboring layers in bilayer (and few-layer) graphenes of both AA and AB stacking motifs are known to be separated at a distance corresponding to van der Waals (vdW) interactions. In this Letter, we present for the first time a new aspect of graphene chemistry in terms of a special chemical bonding between the giant graphene "molecules". Through rigorous theoretical calculations, we demonstrate that the N-doped graphenes (NGPs) with various doping levels can form an unusual two-dimensional (2D) π-π bonding in bilayer NGPs bringing the neighboring NGPs to significantly reduced interlayer separations. The interlayer binding energies can be enhanced by up to 50% compared to the pristine graphene bilayers that are characterized by only vdW interactions. Such an unusual chemical bonding arises from the π-π overlap across the vdW gap while the individual layers maintain their in-plane π-conjugation and are accordingly planar. The existence of the resulting interlayer covalent-like bonding is corroborated by electronic structure calculations and crystal orbital overlap population (COOP) analyses. In NGP-based graphite with the optimal doping level, the NGP layers are uniformly stacked and the 3D bulk exhibits metallic characteristics both in the in-plane and along the stacking directions.

Control of layer stacking in CVD graphene under quasi-static condition

The type of layer stacking in bilayer graphene has a significant influence on its electronic properties because of the contrast nature of layer coupling. Herein, different geometries of the reaction site for the growth of bilayer graphene by the chemical vapor deposition (CVD) technique and their effects on the nature of layer stacking are investigated. Micro-Raman mapping and curve fitting analysis confirmed the type of layer stacking for the CVD grown bilayer graphene. The samples grown with sandwiched structure such as quartz/Cu foil/quartz along with a spacer, between the two quartz plates to create a sealed space, resulted in Bernal or AB stacked bilayer graphene while the sample sandwiched without a spacer produced the twisted bilayer graphene. The contrast difference in the layer stacking is a consequence of the difference in the growth mechanism associated with different geometries of the reaction site. The diffusion dominated process under quasi-static control is responsible for the growth of twisted bilayer graphene in sandwiched geometry while surface controlled growth with ample and continual supply of carbon in sandwiched geometry along with a spacer, leads to AB stacked bilayer graphene. Through this new approach, an efficient technique is presented to control the nature of layer stacking.

The Hide-and-Seek of Grain Boundaries from Moiré Pattern Fringe of Two-Dimensional Graphene

Grain boundaries (GBs) commonly exist in crystalline materials and affect various properties of materials. The facile identification of GBs is one of the significant requirements for systematical study of polycrystalline materials including recently emerging two-dimensional materials. Previous observations of GBs have been performed by various tools including high resolution transmission electron microscopy. However, a method to easily identify GBs, especially in the case of low-angle GBs, has not yet been well established. In this paper, we choose graphene bilayers with a GB as a model system and investigate the effects of interlayer rotations to the identification of GBs. We provide a critical condition between adjacent moiré fringe spacings, which determines the possibility of GB recognition. In addition, for monolayer graphene with a grain boundary, we demonstrate that low-angle GBs can be distinguished easily by inducing moiré patterns deliberately with an artificial reference overlay.

Interface Coupling in Twisted Multilayer Graphene by Resonant Raman Spectroscopy of Layer Breathing Modes

Raman spectroscopy is the prime nondestructive characterization tool for graphene and related layered materials. The shear (C) and layer breathing modes (LBMs) are due to relative motions of the planes, either perpendicular or parallel to their normal. This allows one to directly probe the interlayer interactions in multilayer samples. Graphene and other two-dimensional (2d) crystals can be combined to form various hybrids and heterostructures, creating materials on demand with properties determined by the interlayer interaction. This is the case even for a single material, where multilayer stacks with different relative orientations have different optical and electronic properties. In twisted multilayer graphene there is a significant enhancement of the C modes due to resonance with new optically allowed electronic transitions, determined by the relative orientation of the layers. Here we show that this applies also to the LBMs, which can be now directly measured at room temperature. We find that twisting has a small effect on LBMs, quite different from the case of the C modes. This implies that the periodicity mismatch between two twisted layers mostly affects shear interactions. Our work shows that ultralow-frequency Raman spectroscopy is an ideal tool to uncover the interface coupling of 2d hybrids and heterostructures.

Study on the diffusion mechanism of graphene grown on copper pockets

A correlation between graphene domains grown on the outer and the inner surfaces of Cu pockets is found, which discloses a new graphene growth mechanism based on the fast diffusion of carbon atoms through the 25 micro-meter-thick Cu foil, confirmed by isotopic labeling. Subsequently, on the outer surface of the Cu pocket, bilayer graphene with a coverage of about 78% is grown.

Strain-induced conduction gap in vertical devices made of misoriented graphene layers

We investigate the effects of uniaxial strain on the transport properties of vertical devices made of two misoriented (or twisted) graphene layers, which partially overlap each other. We find that because of the different orientations of the two graphene lattices, their Dirac points can be displaced and separated in the k-space by the effects of strain. Hence, a finite conduction gap as large as a few hundred meV can be obtained in the device with a small strain of only a few percent. The dependence of this conduction gap on the strain magnitude, strain direction, channel orientation and twist angle are clarified and presented. On this basis, the strong modulation of conductance and significant improvement of Seebeck coefficient are shown. The suggested devices therefore may be very promising for improving applications of graphene, e.g., as transistors or strain and thermal sensors.

Magneto-optical Kramers-Kronig analysis

We describe a simple magneto-optical experiment and introduce a magneto-optical Kramers-Kronig analysis (MOKKA) that together allow extracting the complex dielectric function for left- and right-handed circular polarizations in a broad range of frequencies without actually generating circularly polarized light. The experiment consists of measuring reflectivity and Kerr rotation, or alternatively transmission and Faraday rotation, at normal incidence using only standard broadband polarizers without retarders or quarter-wave plates. In a common case, where the magneto-optical rotation is small (below ∼0.2 rad), a fast measurement protocol can be realized, where the polarizers are fixed at 45(∘) with respect to each other. Apart from the time-effectiveness, the advantage of this protocol is that it can be implemented at ultra-high magnetic fields and in other situations, where an in-situ polarizer rotation is difficult. Overall, the proposed technique can be regarded as a magneto-optical generalization of the conventional Kramers-Kronig analysis of reflectivity on bulk samples and the Kramers-Kronig constrained variational analysis of more complex types of spectral data. We demonstrate the application of this method to the textbook semimetals bismuth and graphite and also use it to obtain handedness-resolved magneto-absorption spectra of graphene on SiC.

Origin of band gaps in graphene on hexagonal boron nitride

Recent progress in preparing well-controlled two-dimensional van der Waals heterojunctions has opened up a new frontier in materials physics. Here we address the intriguing energy gaps that are sometimes observed when a graphene sheet is placed on a hexagonal boron nitride substrate, demonstrating that they are produced by an interesting interplay between structural and electronic properties, including electronic many-body exchange interactions. Our theory is able to explain the observed gap behaviour by accounting first for the structural relaxation of graphene’s carbon atoms when placed on a boron nitride substrate, and then for the influence of the substrate on low-energy π-electrons located at relaxed carbon atom sites. The methods we employ can be applied to many other van der Waals heterojunctions.

Graphene doesn’t usually have a bandgap but one can appear when the two-dimensional material is placed on a hexagonal boron nitride substrate. Jung et al. now develop a theory that indicates that this occurs because the graphene’s carbon atoms structurally relax when placed on boron nitride.

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.

Superlattice structures in twisted bilayers of folded graphene

The electronic properties of bilayer graphene strongly depend on relative orientation of the two atomic lattices. Whereas Bernal-stacked graphene is most commonly studied, a rotational mismatch between layers opens up a whole new field of rich physics, especially at small interlayer twist. Here we report on magnetotransport measurements on twisted graphene bilayers, prepared by folding of single layers. These reveal a strong dependence on the twist angle, which can be estimated by means of sample geometry. At small rotation, superlattices with a wavelength in the order of 10 nm arise and are observed by friction atomic force microscopy. Magnetotransport measurements in this small-angle regime show the formation of satellite Landau fans. These are attributed to additional Dirac singularities in the band structure and discussed with respect to the wide range of interlayer coupling models.

The properties of bilayer graphene can be tuned by twisting the layers relative to one another. Schmidt et al. now demonstrate the twist angle dependence of magnetotransport in this material system and uncover the formation of satellite Landau fans in the small-angle regime because of superlattice formation

Thermal conductivity of twisted bilayer graphene

We have investigated experimentally the thermal conductivity of suspended twisted bilayer graphene. The measurements were performed using an optothermal Raman technique. It was found that the thermal conductivity of twisted bilayer graphene is lower than that of monolayer graphene and the reference, Bernal stacked bilayer graphene in the entire temperature range examined (∼300-700 K). This finding indicates that the heat carriers - phonons - in twisted bilayer graphene do not behave in the same manner as that observed in individual graphene layers. The decrease in the thermal conductivity found in twisted bilayer graphene was explained by the modification of the Brillouin zone due to plane rotation and the emergence of numerous folded phonon branches that enhance the phonon Umklapp and normal scattering. The results obtained are important for understanding thermal transport in two-dimensional systems.

Superlubricity of two-dimensional fluorographene/MoS2 heterostructure: a first-principles study

The atomic-scale friction of the fluorographene (FG)/MoS2 heterostructure is investigated using first-principles calculations. Due to the intrinsic lattice mismatch and formation of periodic Moiré patterns, the potential energy surface of the FG/MoS2 heterostructure is ultrasmooth and the interlayer shear strength is reduced by nearly two orders of magnitude, compared with both FG/FG and MoS2/MoS2 bilayers, entering the superlubricity regime. The size dependency of superlubricity is revealed as being based on the relationship between the emergence of Moiré patterns and the lattice mismatch ratio for heterostructures.