Large scale synthesis of single layer graphene (SLG) by chemical vapor deposition (CVD) has received a lot of attention recently. However, CVD synthesis of AB stacked bi-layer graphene (BLG) is still a challenging work. Here we report synthesis of BLG homogeneously in large area by thermal CVD. The 2D Raman band of CVD BLG splits into four components, suggesting splitting of electronic bands due to strong interlayer coupling. The splitting of electronic bands in CVD BLG is further evidenced by the study of near infrared (NIR) absorption and carrier dynamics probed by transient absorption spectroscopy. Ultraviolet photoelectron spectroscopy invesigation also indiates CVD BLG possesses different electronic structures from those of CVD SLG. The growth mechanism of BLG is found to be related to catalystic activity of copper (Cu)surface, which is determined by purity of Cu foils employed in CVD process. Our work showsthat strongly coupled or even AB stacked BLG can be grown on Cu foils in large scale, which isof particular importance for device applications based on their split electronic bands
The crystallographic stacking order in multilayer graphene plays an important role in determining its electronic structure. In trilayer graphene, rhombohedral stacking (ABC) is particularly intriguing, exhibiting a flat band with an electric-field tunable band gap. Such electronic structure is distinct from simple hexagonal stacking (AAA) or typical Bernal stacking (ABA), and is promising for nanoscale electronics, optoelectronics applications. So far clean experimental electronic spectra on the first two stackings are missing because the samples are usually too small in size (um or nm scale) …
Few-layer graphene (FLG) has been predicted to exist in various crystallographic stacking sequences, which can strongly influence the electronic properties of FLG. We demonstrate an accurate and efficient method to characterize stacking order in FLG using the distinctive features of the Raman 2D-mode. Raman imaging allows us to visualize directly the spatial distribution of Bernal (ABA) and rhombohedral (ABC) stacking in tri- and tetra-layer graphene. We find that 15% of exfoliated graphene tri- and tetra-layers is comprised of micron-sized domains of rhombohedral stacking, rather than of usua…
The Seebeck coefficient in multilayer graphene is investigated within the density-functional theory, using the semiclassical Boltzmann equations and interpolating the bands in a maximally-localized Wannier functions basis set. We compare various graphene stackings (AA, AB and ABC) both free-standing and deposited on a $4H$-SiC(0001) C-terminated substrate. We find that the presence of the SiC substrate can significantly affect the thermopower properties of graphene layers, depending on the stacking, providing a promising way to tailor efficient graphene-based devices.
Different stacking sequences of graphene are investigated using a combination of experimental and theoretical methods. The high-resolution transmission electron microscopy (HRTEM) of the stacking sequence of several layers of graphene, formed on the C-terminated 4H-SiC(0001) surface, was used to determine the stacking sequence and the interlayer distances. These data prove that the three metastable configurations exist: ABAB, AAAA, ABCA. In accordance to these, findings those three cases were considered theoretically, using Density Functional Theory calculations comparing graphene sheets, free…
The optical conductivities of graphene layers are strongly dependent on their stacking orders. Our first-principle calculations show that while the optical conductivities of single layer graphene (SLG) and bilayer graphene (BLG) with Bernal stacking are almost frequency independent in the visible region, the optical conductivity of twisted bilayer graphene (TBG) is frequency dependent, giving rise to additional absorption features due to the band folding effect. Experimentally, we obtain from contrast spectra the optical conductivity profiles of BLG with different stacking geometries. Some TBG…
We examine the stacking order of multilayer graphene grown on the SiC$(000\bar{1})$ surface using low-energy electron diffraction and surface X-ray diffraction. We show that the films contain a high density of rotational stacking faults caused by three types of rotated graphene: sheets rotated $30^\circ$ and $\pm 2.20^\circ$ relative to the SiC substrate. These angles are unique because they correspond to commensurate phases of layered graphene, both with itself and with the SiC substrate. {\it Ab intio} calculations show that these rotational phases electronically decouple adjacent graphene l…
Bilayer graphene (BLG) with a tunable bandgap appears interesting as an alternative to graphene for practical applications, thus its transport properties are being actively pursued. Using density functional theory and perturbation analysis, we investigated, under an external electric field, the electronic properties of BLGs in various stackings relevant to recently observed complex structures. We established the first phase diagram summarizing the stacking-dependent gap openings of BLGs for a given field. We further identified high-density midgap states, localized on grain boundaries, even und…
Strain, both naturally occurring and deliberately engineered, can have a considerable effect on the structural and electronic properties of 2D and layered materials. Uniaxial or biaxial heterostrain modifies the stacking arrangement of bilayer graphene (BLG) which subsequently influences the electronic structure of the bilayer. Here, we use Density Functional Theory (DFT) calculations to investigate the interplay between an external applied heterostrain and the resulting stacking in BLG. We determine how a strain applied to one layer is transferred to a second, 'free' layer and at what critica…
The electronic structure of few-layer graphene (FLG) samples with crystalline order was investigated experimentally by infrared absorption spectroscopy for photon energies ranging from 0.2 - 1 eV. Distinct optical conductivity spectra were observed for different samples having precisely the same number of layers. The different spectra arise from the existence of two stable polytypes of FLG, namely, Bernal (AB) stacking and rhombohedral (ABC) stacking. The observed absorption features, reflecting the underlying symmetry of the two polytypes and the nature of the associated van Hone singularitie…
We investigate the behaviour of the $π$-electrons under compression and the effect of the stacking order of graphene layers. First we find that electrons can hardly be squeezed through the $sp^2$ network, regardless of the stacking order. The largely deformed electronic orbitals (mainly those of $π$-electrons) under compression along the $\textit{c}$-axis increase interlayer interaction between graphene layers as expected, but surprisingly in a similar way for the A-A and Bernal stacking. On the other hand, the large out-of-plane compression shifts the in-plane phonon frequencies of A-A stacke…
We present a compositional and structural investigation of silicene, germanene, and stanene bilayers from first-principles. Due to the staggering of the individual layers, several stacking patterns are possible, most of which are not available to the bilayer graphene. This structural variety, in conjunction with the presence of the spin-orbit coupling, unveil a diversity of the electronic properties, with the appearance of distinct band features, including orbital hybridization and band inversion. We show that for particular cases, the intrinsic spin Hall response exhibits signatures of non-tr…
Graphene, defined as a single atomic plane of graphite, is a semimetal with small overlap between the valence and the conduction bands. The stacking of graphene up to several atomic layers can produce diverse physical properties, depending on the stacking way. The bilayer graphene is also a semimetal, adopting the AB-stacked (or Bernal-stacked) structure or the rare AA-stacked structure. The trilayer or a few layer graphene (FLG) can be semimetal or semiconductor, depending on whether it takes Bernal (ABA) stacking or rhombohedral (ABC) stacking. We will give a perspective on the recent two mi…
We present an \textit{ab initio} study based on density-functional theory of first- and second-order Raman spectra of graphene-based materials with different stacking arrangements and numbers of layers. Going from monolayer and bilayer graphene to periodic graphitic structures, we investigate the behavior of the first-order G-band and of the second-order 2D-band excited by the same set of photon energies. The former turns out to be very similar in all considered graphene-based materials, while in the latter we find the signatures of individual structures. With a systematic analysis of the seco…
Multilayer graphene (MLG) grown by chemical vapor deposition (CVD) is a promising material for electronic and optoelectronic devices. Understanding the stacking configuration and interlayer coupling of MLGs is technologically relevant and of importance for the device applications. Here, we reported a kind of twisted MLGs (tMLGs), which are formed by stacking one graphene monolayer on the top of AB-stacked MLG by rotating a certain angle between them. The twist angle of tMLGs are identified by the twist-related modes, R and R'. With increasing the total layer number of N, the observed interlaye…
First-principles calculation has been performed to investigate the stability and electronic properties of double-layer graphene heterostructure (DLGH). In this system, two graphene layers are separated by hexagonal boron-nitride (h-BN) layers which work as a insulating barrier. Our results show that the stability of the system is determined by the atomistic configurations between graphene and its adjacent h-BN layer. Among different stacking sequences, Ab-stacking is most stable. Since the inserted h-BN layers modulate the on-site energies for carbon atoms of graphene layers, the electronic st…
The crystal structure of a material plays an important role in determining its electronic properties. Changing from one crystal structure to another involves a phase transition which is usually controlled by a state variable such as temperature or pressure. In the case of trilayer graphene, there are two common stacking configurations (Bernal and rhombohedral) which exhibit very different electronic properties. In graphene flakes with both stacking configurations, the region between them consists of a localized strain soliton where the carbon atoms of one graphene layer shift by the carbon-car…
We carry out a computational study on the geometric and electronic properties of multi-layers of silicene in different stacking configurations using a state-of-art abinitio density functional theory based calculations. In this work we investigate the evolution of these properties with increasing number of layers (n) ranging from 1 to 10. Though, mono-layer of silicene possesses properties similar to those of graphene, our results show that the geometric and electronic properties of multi-layers of silicene are strikingly different from those of multi-layers of graphene. We observe that there e…
A broad variety of defects has been observed in two-dimensional materials. Many of these defects can be created by top-down methods such as electron irradiation or chemical etching, while a few of them are created along bottom-up processes, in particular during the growth of the material, in which case avoiding their formation can be challenging. This occurs e.g. with dislocations, Stone-Wales defects, or atomic vacancies in graphene. Here we address a defect that has been observed repeatedly since 2007 in epitaxial graphene on metal surfaces like Ru(0001) and Re(0001), but whose nature has re…
Heterostructures made of stacked 2D materials with different electronic properties are studied for their potential in creating multifunctional devices. Graphene (G) and hexagonal boron nitride (h-BN) van der Waals (vdW) systems have been extensively researched, including recent studies on synthesizing h-BN on graphene/SiC(0001) templates. These studies suggest that h-BN encapsulation could occur in addition to vdW epitaxy. This work presents theoretical research on G/h-BN heterostructures on SiC(0001) with a carbon buffer layer. The results show an energetic preference for h-BN encapsulation b…
The diffusion, penetration and intercalation of metallic atomic dopants is an important question for various graphite applications in engineering and nanotechnology. We have performed systematic first-principles calculations of the behaviour of ruthenium nanoclusters on a graphene monolayer and intercalated into a bilayer. Our computational results show that at a sufficiently high density of single Ru atom interstitials, intercalated atoms can shear the surrounding lattice to an AA stacking configuration, an effect which weakens with increasing cluster size. Moreover, the interlayer stacking c…
The stacking faults (deviates from Bernal) will break the translational symmetry of multilayer graphenes and modify their electronic and optical behaviors to the extent depending on the interlayer coupling strength. This paper addresses the stacking-induced band splitting and folding effect on the electronic band structure of twisted bilayer graphene. Based on the first-principles density functional theory study, we predict that the band folding effect of graphene layers may enable the G band Raman double resonance in the visible excitation range. Such prediction is confirmed experimentally wi…
In van der Waals heterostructures, the periodic potential from the Moiré superlattice can be used as a control knob to modulate the electronic structure of the constituent materials. Here we present a nanoscale angle-resolved photoemission spectroscopy (Nano-ARPES) study of transferred graphene/h-BN heterostructures with two different stacking angles of 2.4° and 4.3° respectively. Our measurements reveal six replicas of graphene Dirac cones at the superlattice Brillouin zone (SBZ) centers. The size of the SBZ and its relative rotation angle to the graphene BZ are in good agreement with Moiré s…
We show that the origin of the universal optical conductivity in a normal $N$-layer graphene multilayer is an emergent chiral symmetry which guarantees that $σ(ω)=Nσ_{uni}$ in both low and high frequency limits. [$σ_{uni}=(π/2) e^2/h$]. We use this physics to relate intermediate frequency conductivity trends to qualitative characteristics of the multilayer stacking sequence.
Nitrogenated holey graphene (NHG) has attracted much attention because of its semiconducting properties. However, the stacking orders and defect properties have not been investigated. In this letter, the structural and stacking properties of NHG are first investigated. We obtain the most stable stacking structure. Then, the band structures for bulk and multilayer NHG are studied. Impact of the strain on the band gaps and bond characteristics is discuss. In addition, we investigate formation mechanism of native defects of carbon vacancy (VC), carbon interstitial (Ci), nitrogen vacancy (VN), and…
We investigate the electronic and transport properties of gated bilayer graphene with one corrugated layer, which results in a stacking AB/BA boundary. When a gate voltage is applied to one layer, topologically protected gap states appear at the corrugation, which reveal as robust transport channels along the stacking boundary. With increasing size of the corrugation, more localized, quantum-well-like states emerge. These finite-size states are also conductive along the fold, but in contrast to the stacking boundary states, which are gapless, they present a gap. We have also studied periodic c…
We derive a general relation between the stacking vector ${\bf u}$ describing the relative shift of two layers of bilayer graphene and the Chern index. We find $C = ν- \text{sign}\left(|V_{AB}|-|V_{BA}|\right)$, where $ν$ is a valley index and $|V_{αβ}|$ the absolute value of stacking potentials that depend on ${\bf u}$ and that uniquely determine the interlayer interaction; AA stacking plays no role in the topological character. With this expression we show that while ideal and relaxed minimally twisted bilayer graphene appear so distinct as to be almost different materials, their Chern index…
Graphene, as an atomic-thick ultrasoft membrane, almost has no resistance against out-of-plane deformations and, therefore, it is always wrinkled to a certain degree. Recently, corrugated structures and their effects on the electronic properties of monolayer graphene have been studied extensively. However, similar experimental studies in bilayer graphene have yet to be reported. Here, we show that corrugations in bilayer graphene can generate incommensurate stacking solitons (domain walls) between commensurate Bernal-stacked domains. By using scanning tunneling microscopy, we microscopically s…
We use a tight-binding model and the random-phase approximation to study the Coulomb excitations in simple-hexagonal-stacking multilayer graphene and discuss the field effects. The calculation results include the energy bands, the response functions, and the plasmon dispersions. A perpendicular electric field is predicted to induce significant charge transfer and thus capable of manipulating the energy, intensity, and the number of plasmon modes. This could be further validated by inelastic light scattering or electron-energy-loss spectroscopy.
Correct defect quantification in graphene samples is crucial both for fundamental and applied re-search. Raman spectroscopy represents the most widely used tool to identify defects in graphene. However, despite its extreme importance the relation between the Raman features and the amount of defects in multilayered graphene samples has not been experimentally verified. In this study we intentionally created defects in single layer graphene, turbostratic bilayer graphene and Bernal stacked bilayer graphene by oxygen plasma. By employing isotopic labelling, our study reveals substantial differenc…
Trilayer graphene (TLG) exhibits rich novel electronic properties and extraordinary quantum Hall phenomena owning to enhanced electronic interactions and tunable chirality of its quasiparticles. Here, we report direct observation of chirality transition of quasiparticles at stacking solitons of TLG via spatial-resolved Landau level spectroscopy. The one-dimensional stacking solitons with width of the order of 10 nm separate adjacent Bernal-stacked TLG and rhombohedral-stacked TLG. By using high field tunneling spectra of scanning tunneling microscopy, we measured Landau quantization in both th…
We combine experimental observations by scanning tunneling microscopy (STM) and density functional theory (DFT) to reveal the most stable edge structures of graphene on Ni(111) as well as the role of stacking-driven activation and suppression of edge reconstruction. Depending on the position of the outermost carbon atoms relative to hollow and on-top Ni sites, zigzag edges have very different energies. Triangular graphene nanoislands are exclusively bound by the more stable zigzag hollow edges. In hexagonal nanoislands, which are constrained by geometry to alternate zigzag hollow and zigzag to…
We present a theoretical study on the electron transmission through the AB-BA stacking boundary in multilayer graphene. Using the tight-binding model and the transfer matrix method, we calculate the electron transmission probability through the boundary as a function of electron Fermi energy in multilayers from bilayer to five-layer. We find that the transmission is strongly suppressed particularly near the band touching point, suggesting that the electronic conductivity in general multilayer graphenes is significantly interfered by stacking fault. The conductivity suppression by stacking faul…
The electronic properties and optical excitations are investigated in the geometry- and field-modulated bilayer graphene systems, respectively, by using the tight-binding model and Kubo formula. The stacking symmetry of bilayer graphene can be manipulated by varying the width and position of domain wall (DW) within two normally stacked graphene. All the layer-dependent atomic interactions are taken into consideration under external fields. The modulation of stacking configuration gives rise to significant effects of zone folding on energy subbands, subenvelope wave functions, density of states…
Graphene on silicon carbide (SiC) bears great potential for future graphene electronic applications because it is available on the wafer-scale and its properties can be custom-tailored by inserting various atoms into the graphene/SiC interface. It remains unclear, however, how atoms can cross the impermeable graphene layer during this widely used intercalation process. Here we demonstrate that, in contrast to the current consensus, graphene layers on SiC are not homogeneous, but instead composed of domains of different crystallographic stacking. We show that these domains are intrinsically for…
Since the strong interlayer interaction of AB-stacked graphene in bulk form degrades the superior property of single-layer graphene, formation of randomly stacked graphene is required to apply the high performances of graphene to macroscopic devices. However, conventional methods to obtain bulk-scale graphene suffer from a low crystallinity and/or the formation of a thermodynamically stable AB-stacked structure. This study develops a novel approach to produce bulk-scale graphene with a high crystallinity and high fractions of random stacking by utilizing the porous morphology of a graphene oxi…
We investigate the magnetotransport properties of quasi-free standing epitaxial graphene bilayer on SiC, grown by atmospheric pressure graphitization in Ar, followed by H$_2$ intercalation. At the charge neutrality point the longitudinal resistance shows an insulating behavior, which follows a temperature dependence consistent with variable range hopping transport in a gapped state. In a perpendicular magnetic field, we observe quantum Hall states (QHSs) both at filling factors ($ν$) multiple of four ($ν=4, 8, 12$), as well as broken valley symmetry QHSs at $ν=0$ and $ν=6$. These results unamb…
The quantum Hall effects in the sliding bilayer graphene and AAB-stacked trilayer system are investigated by the Kubo formula and the generalized tight-binding model. The various stacking configurations can greatly diversify the magnetic quantization and thus create the rich and unique transport properties. The quantum conductivities are very sensitive to the Fermi energy and magnetic-field strength. The diverse features cover the specific non-integer conductivities, the integer conductivities with the distinct steps, the splitting-created reduction and complexity of quantum conductivity, a va…
It is well established that some kinds of lattice deformations in graphene monolayer, which change electron hopping in sublattice and affect in-plane motion of electrons, may induce out-of-plane pseudo-magnetic fields as large as 100 T. Here, we demonstrate that stacking misorientation in graphene bilayers mimics the effect of huge in-plane pseudo-magnetic fields greater than 1000 T on the interlayer hopping of electrons. As well as addressing the similarity between the effect of in-plane pseudo-magnetic fields and twisting on the electronic band structure of Bernal graphene bilayer, we point …
Novel systems of layered graphene are attracting interest for theories and applications. The stability, band structures of few-layer graphite films, and their dependence on electric field applied along the c-axis are examined within the density functional theory. We predict that those of Bernal type and also rhombohedral type tri- and tetra-layer graphite films exhibit stability. The rhombohedral-type systems including AB-bilayer, show variable band gap induced by perpendicular electric field, whereas the other systems such as the Bernal-type films stay semi-metallic.
The evolution of electronic structure of graphene nanoribbons (GNRs) as a function of the number of layers stacked together is investigated using \textit{ab initio} density functional theory (DFT) including interlayer van der Waals interactions. Multilayer armchair GNRs (AGNRs), similar to single-layer AGNRs, exhibit three classes of band gaps depending on their width. In zigzag GNRs (ZGNRs), the geometry relaxation resulting from interlayer interactions plays a crucial role in determining the magnetic polarization and the band structure. The antiferromagnetic (AF) interlayer coupling is more …
Terrace-sized, single-orientation graphene can be grown on top of a carbon buffer layer on silicon carbide by thermal decomposition. Despite its homogeneous appearance, a surprisingly large variation in electron transport properties is observed. Here, we employ Aberration-Corrected Low-Energy Electron Microscopy (AC-LEEM) to study a possible cause of this variability. We characterize the morphology of stacking domains between the graphene and the buffer layer of high-quality samples. Similar to the case of twisted bilayer graphene, the lattice mismatch between the graphene layer and the buffer…
Recently, the rhombohedral trilayer graphene (r-TLG) has attracted much attention because of its low-energy flat bands, which are predicted to result in many strongly correlated phenomena. Here, we demonstrate that it is possible to probe the stacking order and electronic spectrum of the r-TLG directly with a scanning tunneling microscopy around a monoatomic step edge of the top graphene layer. The tunneling spectra of the r-TLG exhibit four adjacent peaks, which are generated by the low-energy flat bands, flanking the charge neutrality point. Based on these spectra, the true energy gap and th…
The crystallographic symmetries and spatial distribution of stacking domains in graphene films on SiC have been studied by low energy electron diffraction (LEED) and dark field imaging in a low energy electron microscope (LEEM). We find that the graphene diffraction spots from 2 and 3 atomic layers of graphene have 3-fold symmetry consistent with AB (Bernal) stacking of the layers. On the contrary, graphene diffraction spots from the buffer layer and monolayer graphene have apparent 6-fold symmetry, although the 3-fold nature of the satellite spots indicates a more complex periodicity in the g…
The field of two-dimensional (2D) materials has expanded to multilayered systems where electronic, optical, and mechanical properties change-often dramatically-with stacking order, thickness, twist, and interlayer spacing [1-5]. For transition metal dichalcogenides (TMDs), bond coordination within a single van der Waals layer changes the out-of-plane symmetry that can cause metal-insulator transitions [1, 6] or emergent quantum behavior [7]. Discerning these structural order parameters is often difficult using real-space measurements, however, we show 2D materials have distinct, conspicuous th…
Stacking two-dimensional layered materials such as graphene and transitional metal dichalcogenides with nonzero interlayer twist angles has recently become attractive because of the emergence of novel physical properties. Stacking of one-dimensional nanomaterials offers the lateral stacking offset as an additional parameter for modulating the resulting material properties. Here, we report that the edge states of twisted bilayer zigzag graphene nanoribbons (TBZGNRs) can be tuned with both the twist angle and the stacking offset. Strong edge state variations in the stacking region are first reve…
Combining atomically-thin van der Waals materials into heterostructures provides a powerful path towards the creation of designer electronic devices. The interaction strength between neighboring layers, most easily controlled through their interlayer separation, can have significant influence on the electronic properties of these composite materials. Here, we demonstrate unprecedented control over interlayer interactions by locally modifying the interlayer separation between graphene and boron nitride, which we achieve by applying pressure with a scanning tunneling microscopy tip. For the spec…
Graphene nano-electro-mechanical switches are promising components due to their excellent switching performance such as low pull-in voltage and low contact resistance. Mass fabrication with an appropriate counter electrode remains challenging. In this work, we report the stacking of nanocrystalline graphene (NCG) with a 70-nm dielectric separation layer. The buried NCG layer is contacted through the formation of vias and acts as actuation electrode. After metallization, the top 7.5-nm thin NCG layer is patterned to form double-clamped beams, and the structure is released by hydrofluoric acid e…
The 1+1 layer folded graphene sheets that deviate from AB stacking are successfully fabricated and their electronic structures are investigated by Raman spectroscopy. Significant blue shift of the 2D band of folded graphene compared to that of single layer graphene (SLG) is observed. This is attributed to SLG-like electronic structure of folded graphene but with slowing down of Fermi velocity (as much as ~5.6%). Different amount of blue shift of 2D band is observed for different folded graphenes, which may correspond to the different twist angle and/or separation between the two layers, result…
$α$-graphyne is a two-dimensional sheet of $sp$-$sp^2$ hybridized carbon atoms in a honeycomb lattice. While the geometrical structure is similar to that of graphene, the hybridized triple bonds give rise to electronic structure that is different from that of graphene. Similar to graphene, $α$-graphyne can be stacked in bilayers with two stable configurations, but the different stackings have very different electronic structures: one is predicted to have gapless parabolic bands and the other a tunable band gap which is attractive for applications. In order to realize applications, it is crucia…
In two-dimensional van der Waals (vdWs) materials, the relative twist angle between adjacent layers not only controls their electronic properties, but also determines their stacking energy. This effect makes it much easier to realize energetically favorable configurations of the vdWs materials, for example, Bernal-stacked structure of bilayer graphene. Here we demonstrate that we can controllably tailor adhesive energy landscape of graphene nanostructures on graphene and stabilize the system with tunable twist angle by using a one-dimensional tilt grain boundary (GB). The area ratio with diffe…
We report the synthesis efficiency of few-layer graphene (FLG) in an external magnetic field modulated DC carbon arc in different non-reactive buffer gases. The effects of buffer gases on the anode erosion rate and the cathode deposit (CD) formation rate have been investigated during the synthesis of FLG. The constituents of the as-synthesized CDs were investigated using transmission electron microscopy, selected area electron diffraction, Raman spectroscopy and X-ray diffraction analysis. A plausible growth mechanism of such FLG is predicted. The results indicate that, under a parametrically …
In a multi-layer electronic system, stacking order provides a rarely-explored degree of freedom for tuning its electronic properties. Here we demonstrate the dramatically different transport properties in trilayer graphene (TLG) with different stacking orders. At the Dirac point, ABA-stacked TLG remains metallic while the ABC counterpart becomes insulating. The latter exhibits a gap-like dI/dV characteristics at low temperature and thermally activated conduction at higher temperatures, indicating an intrinsic gap ~6 meV. In magnetic fields, in addition to an insulating state at filling factor …
Small-twist-angle bilayer graphene supports strongly correlated insulating states and superconductivity. Twisted few-layer graphene systems are likely to open up new directions for strong correlation physics in moiré superlattices. We derive and study moiré band models that describe the electronic structure of graphene trilayers in which one of the three layers is twisted by a small angle relative to perfect AAA, ABA, or ABC stacking arrangements. We find that the electronic structure depends very strongly on the starting stackings arrangement and on which layer is twisted. We identify ABA sta…
