The growth, atomic structure, and electronic property of trilayer graphene (TLG) on Ru(0001) were studied by low temperature scanning tunneling microscopy and spectroscopy in combined with tight-binding approximation (TBA) calculations. TLG on Ru(0001) shows a flat surface with a hexagonal lattice due to the screening effect of the bottom two layers and the AB-stacking in the top two layers. The coexistence of AA- and AB-stacking in the bottom two layers leads to three different stacking orders of TLG, namely, ABA-, ABC-, and ABB-stacking. STS measurements combined with TBA calculations reveal that the density of states of TLG with ABC- and ABB-stacking is characterized by one and two sharp peaks near to the Fermi level, respectively, in contrast to the V-shaped feature of TLG with ABA-stacking. Our work demonstrates that TLG on Ru(0001) might be an ideal platform for exploring stacking-dependent electronic properties of graphene.
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) …
Recently, three different magnetic states were observed experimentally in trilayer CrI3 under pressure,including ferromagnetic (FM)-upupup, FM-downupdown and FM-upupdown. To reveal the nature of the observed three magnetic states, we studied the magnetic properties of four possible stacking structures in trilayer CrI3: I (rhombohedral), II (monoclinic), III (hexagonal) and IV (triclinic). We find that all four stacking structures possess the FM-upupup ground state. After applying a few strains, the FM-downupdown becomes the ground state in II and III structures, and the FM-upupdown is preferre…
The hexagonal-2H crystal phase of Ge recently emerged as a promising direct bandgap semiconductor in the mid-infrared range providing new prospects of additional optoelectronic functionalities of group-IV semiconductors (Ge and SiGe). The controlled synthesis of such hexagonal (2H) Ge phase is a challenge that can be overcome by using wurtzite GaAs nanowires as a template. However, depending on growth conditions, unusual basal stacking faults (BSFs) of I$_3$-type are formed in the metastable 2H structure. The growth of such core/shell heterostructures is observed in situ and in real-time by me…
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…
The effect of the number of stacking layers and the type of stacking on the electronic and optical properties of bilayer and trilayer black phosphorus are investigated by using first principles calcula- tions within the framework of density functional theory. We find that inclusion of many body effects (i.e., electron-electron and electron-hole interactions) modifies strongly both the electronic and opti- cal properties of black phosphorus. While trilayer black phosphorus with a particular stacking type is found to be a metal by using semilocal functionals, it is predicted to have an electroni…
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…
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…
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 …
The lower-symmetry trilayer AAB-stacked graphene exhibits rich electronic properties and thus diverse Coulomb excitations. Three pairs of unusual valence and conduction bands create nine available interband excitations for the undoped case, in which the imaginary (real) part of the polarizability shows 1D square root asymmetric peaks and 2D shoulder structures (pairs of antisymmetric peaks and logarithm type symmetric peaks). Moreover, the low frequency acoustic plasmon, being revealed as a prominent peak in the energy loss spectrum, can survive in a narrow gap system with the large-density-of…
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…
In this work, we have presented a first principle simulation study on the electronic properties of MoS2/MX2/MoS2 (M=Mo or W; X=S or Se) trilayer heterostrcuture. We have investigated the effect of stacking configuration, bi-axial compressive and tensile strain on the electronic properties of the trilayer heterostructures. In our study, it is found that, under relaxed condition all the trilayer heterostructures at different stacking configurations show semiconducting nature. The nature of the bandgap however depends on the inserted TMDC monolayer between the top and bottom MoS2 layers and their…
We report a nano-infrared (IR) imaging study of trilayer graphene (TLG) with both ABA (Bernal) and ABC (rhombohedral) stacking orders using the scattering-type scanning near-field optical microscope (s-SNOM). With s-SNOM operating in the mid-IR region, we mapped in real space the surface plasmon polaritons (SPPs) of ABA-TLG and ABC-TLG, which are tunable with electrical gating. Through quantitative modeling of the plasmonic imaging data, we found that the plasmon wavelength of ABA-TLG is significantly larger than that of ABC-TLG, resulting in a sizable impedance mismatch and hence a strong pla…
Using ab initio calculations, we study the electronic and structural properties of vacancies and hydrogen adsorbates on trilayer graphene. Those defects are found to share similar low-energy electronic features, since they both remove a pz electron from the honeycomb lattice and induce a defect level near the Fermi energy. However, a vacancy also leaves unpaired $σ$ electrons on the lattice, which lead to important structural differences and also contribute to magnetism. We explore both ABA and ABC stackings and compare properties such as formation energies, magnetic moments, spin density and …
A striking feature of bilayer graphene is the induction of a significant band gap in the electronic states by the application of a perpendicular electric field. Thicker graphene layers are also highly attractive materials. The ability to produce a band gap in these systems is of great fundamental and practical interest. Both experimental and theoretical investigations of graphene trilayers with the typical ABA layer stacking have, however, revealed the lack of any appreciable induced gap. Here we contrast this behavior with that exhibited by graphene trilayers with ABC crystallographic stackin…
From monolayers composed of different atoms, we can build structures with spontaneous vertical polarization by conveniently stacking multiple layers. We have studied, using first-principles methods and based on modern polarization theory, a system composed of three layers of hexagonal Boron-Nitride(h-BN) in all possible stackings. We obtain for each of the configurations how charge transfers between the layers and how it impacts on the polarization of the system. In addition, we studied a system of three layers, one of them rotated, and we found that not only did the magnitude of the polarizat…
The zero energy modes induced by vacancies in ABC stacked trilayer graphene are investigated. Depending on the position of the vacancy, a new zero energy solution is realised, different from those obtained in multilayer compounds with Bernal stacking. The electronic modification induced in the sample by the new vacancy states is characterised by computing the local density of states and their localisation properties are studied by the inverse participation ratio. We also analyse the situation in the presence of a gap in the spectrum due to a perpendicular electric field.
Electronic structures and their Landau quantizations in twisted graphene bilayer and trilayer are investigated using scanning tunnelling microscopy and spectroscopy. In the twisted trilayer, the top graphene layer and second layer are AB (Bernal) stacking and there is a stacking misorientation between the second layer and third layer. Both the twisted bilayer and trilayer exhibit two pronounced low-energy van Hove singularities (VHSs) in their spectra. Below the VHSs, the observed Landau level quantization in the twisted bilayer is identical to that of massless Dirac fermion in graphene monola…
The N=0 Landau levels of ABC and ABA trilayer graphene both have approximate 12-fold degeneracies that are lifted by interactions to produce strong quantum Hall effects (QHE) at all integer filling factors between nu=-6 and nu=6. We discuss similarities and differences between the strong-magnetic-field weak-disorder physics of the two trilayer cases, and between trilayer and bilayer cases. These differences can be used to identify the stacking order of high-quality trilayer samples by studying their quantum Hall effects.
We study the energetic stability and the local electronic structure of the general twisted trilayer graphene (TTG) with the top and bottom layers rotated with respect to the middle layer respectively by $θ$ and $θ'$. Approximate supercells of the moiré-of-moiré superlattices with $θ$ and $θ^{\prime}$ within $1^{\circ}\sim 2^{\circ}$ are established to describe the structural and electronic properties of relaxed TTG with the periodic boundary condition. Full relaxation demonstrates that the commensurate TTG with $θ=θ^{\prime}$ has the local minimum total energy ($E_{tol}$) at a fixed $θ$, while…
The stacking order degree of freedom in trilayer graphene plays a critical role in determining the existence of an electric field tunable band gap. We present spatially-resolved tunneling spectroscopy measurements of dual gated Bernal (ABA) and rhombohedral (ABC) stacked trilayer graphene devices. We demonstrate that while ABA trilayer graphene remains metallic, ABC trilayer graphene exhibits a widely tunable band gap as a function of electric field. However, we find that charged impurities in the underlying substrate cause substantial spatial fluctuation of the gap size. Our work elucidates t…
One popular approach to prepare graphene is to grow them on transition metal substrates via chemical vapor deposition. By using the density functional theory with dispersion correction, we systematically investigate for the first time the interfacial properties of bilayer (BLG) and trilayer graphene (TLG) on metal substrates. Three categories of interfacial structures are revealed. The adsorption of B(T)LG on Al, Ag, Cu, Au, and Pt substrates is a weak physisorption, but a band gap can be opened. The adsorption of B(T)LG on Ti, Ni, and Co substrates is a strong chemisorption, and a stacking-in…
Van der Waals materials composed of stacks of individual atomic layers have attracted considerable attention due to their exotic electronic properties that can be altered by, for example, manipulating the twist angle of bilayer materials or the stacking sequence of trilayer materials. To fully understand and control the unique properties of these few-layer materials, a technique that can provide information about their local in-plane structural deformations, twist direction, and out-of-plane structure is needed. In principle, interference in overlap regions of Bragg disks originating from sepa…
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…
We study the Landau level spectrum of ABA- and ABC-stacked trilayer graphene. We derive analytic low energy expressions for the spectrum, the validity of which is confirmed by comparison to a π-band tight-binding calculation of the density of states on the honeycomb lattice. We further study the effect of a perpendicular electric field on the spectrum, where a zero-energy plateau appears for ABC stacking order, due to the opening of a gap at the Dirac point, while the ABA-stacked trilayer graphene remains metallic. We discuss our results in the context of recent electronic transport experiment…
We perform the first-principles many-body GW and Bethe-Salpeter equation (BSE) calculations on the two-dimensional hexagonal boron nitride (2D-hBN) to explore the effects of opposite atoms on the electronic structure and linear one-photon absorption (OPA). Five AA- and AB-stacked bilayer and eight AAB-stacked trilayer structures are considered. The AAB-stacked trilayer hBN (TL-BN) structures are constructed by mixing the AA- and AB-stacked bilayer hBN (BL-BN). We show that the GW approximation gives rise to different types (i.e., indirect or direct) of fundamental band gaps from the independen…
Here we show that twisted graphene trilayer made by misoriented stacking a graphene monolayer on top of a Bernal graphene bilayer can exhibit rich and tailored electronic properties. For the case that the graphene monolayer and bilayer are strongly coupled, both the massless Dirac fermions and massive chiral fermions coexist in the twisted trilayer, leading to unique in-plane chiral tunneling. For a weak coupling between the two graphene systems, the distinct chiralities and pseudospin textures of quasiparticles in monolayer and bilayer enable vertical valley-polarized quantum tunneling betwee…
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…
In recent times, trilayer graphene has attracted wide attention owing to its stacking and electric field dependent electronic properties. However, a direct and well-resolved experimental visualization of its band structure has not yet been reported. In this work, we present angle resolved photoemission spectroscopy (ARPES) data which show with high resolution the electronic band structure of trilayer graphene obtained on α-SiC(0001) and β-SiC(111) via hydrogen intercalation. Electronic bands obtained from tight-binding calculations are fitted to the experimental data to extract the interatomic…
Stability and electronic properties of atomic layers of GaN are investigated in the framework of the van der Waals-density functional theory. We find that the ground state of the layered GaN is a planar graphene-like configuration rather than a buckled bulk-like configuration. Application of an external perpendicular electric field to the layered GaN induces distinct stacking-dependent features of the tunability of the band gap; the band gap of the monolayer does not change whereas that of the trilayer GaN is significantly reduced for the applied field of 0.4 V/ Å. It is suggested that such a …
The generalized tight-binding model is developed to investigate the feature-rich magneto-optical properties of AAB-stacked trilayer graphene. Three intragroup and six intergroup inter-Landau-level (inter-LL) optical excitations largely enrich the magneto-absorption peaks. In general, the former are much higher than the latter, depending on the phases and amplitudes of LL wavefunctions. The absorption spectra exhibit the single- or twin-peak structures which are determined by the quantum modes, LL energy spectra and Fermion distribution. The splitting LLs, with different localization centers (2…
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…
ABA-stacked trilayer graphene (TLG), the simplest system consisting of both massless and massive Dirac fermions, is expected to exhibit many interesting broken-symmetry quantum Hall states and interaction-induced phenomena. However, difficulties in microscopically identifying the stacking order of the TLG and limited spectroscopic resolution have stymied experimental probes of these interesting states and phenomena in scanning tunneling microscopy (STM) studies. Here we studied the detailed features of the electronic structure in the ABA TLG by using high-resolution STM measurements. Landau-le…
Bloch states of electrons in honeycomb two-dimensional crystals with multi-valley band structure and broken inversion symmetry have orbital magnetic moments of a topological nature. In crystals with two degenerate valleys, a perpendicular magnetic field lifts the valley degeneracy via a Zeeman effect due to these magnetic moments, leading to magnetoelectric effects which can be leveraged for creating valleytronic devices. In this work, we demonstrate that trilayer graphene with Bernal stacking, (ABA TLG) hosts topological magnetic moments with a large and widely tunable valley g-factor, reachi…
Using first-principle calculations, we demonstrate several approaches to manipulate Dzyaloshinskii-Moriya Interaction (DMI) in ultrathin magnetic films. First, we find that DMI is significantly enhanced when the ferromagnetic (FM) layer is sandwiched between nonmagnetic (NM) layers inducing additive DMI in NM/FM/NM structures. For instance, as Pt and Ir below Co induce DMI of opposite chirality, inserting Co between Pt (below) and Ir (above) in Ir/Co/Pt trilayers enhances the DMI of Co/Pt bilayers by 15\%. Furthermore, in case of Pb/Co/Pt trilayers (Ir/Fe/Co/Pt multilayers), DMI can be enhance…
Correlated interlayer quantum Hall state in large-angle twisted trilayer graphene
Daegu Gyeongbuk Institute of Science and Technology (DGIST)（大邱庆北科学技术院）；Ulsan National Institute of Science and Technology（蔚山科学技术院）；University of Seoul（首尔大学）；Pohang University of Science and Technology（浦项科技大学）；National Institute for Materials Science（物质材料研究机构）；Korea Advanced Institute of Science and Technology（韩国科学技术院）；Institute for Basic Science（基础科学研究所）
Using density functional theory calculations, we investigated the properties of few-layer silicene nanosheets, namely bilayers and trilayers, functionalized with group-III or group-V atoms of the periodic table. We considered the Si$_2$X$_2$ bilayers and the Si$_2$X$_4$ trilayers, X = B, N, Al, P. We computed the structural, energetic, dynamic, elastic, and electronic properties of those systems in several stacking configurations, labeled as AA$'$, AB, AA$'$A$''$, and ABC. The results revealed that AA$'$-Si$_2$N$_2$, AB-Si$_2$N$_2$, AA$'$-Si$_2$P$_2$, AB-Si$_2$P$_2$, ABC-Si$_4$B$_2$, ABC-Si$_4…
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…
Twisted trilayer graphene is a particularly promising moiré superlattice system, due to its tunability, strong superconductivity, and complex electronic symmetry breaking. Motivated by these properties, we study lattice relaxation and the long-wavelength phonon modes of this system. We show that mirror-symmetric trilayer graphene hosts, aside from the conventional acoustic phonon modes, two classes of shear modes, which are even and odd under mirror reflection. The mirror-even modes are found to be gapless and equivalent to the "phason" modes of twisted bilayer graphene, with appropriately res…
Large-area bilayer graphene (BG) is grown epitaxially on Ru(0001) surface and characterized by low temperature scanning tunneling microscopy. The lattice of the bottom layer of BG is stretched by 1.2%, while strain is absent from the top layer. The lattice mismatch between the two layers leads to the formation of a moire pattern with a periodicity of ~21.5 nm and a mixture of AA- and AB-stacking. The root3 x root3 superstructure around atomic defects is attributed to the inter-valley scattering of the delocalized pi-electrons, demonstrating that the as-grown BG behaves like intrinsic free-stan…
The physical properties of two-dimensional van der Waals (2D vdW) crystals depend sensitively on the interlayer coupling, which is intimately connected to the stacking arrangement and the interlayer spacing. For example, simply changing the twist angle between graphene layers can induce a variety of correlated electronic phases, which can be controlled further in a continuous manner by applying hydrostatic pressure to decrease the interlayer spacing. In the recently discovered 2D magnets, theory suggests that the interlayer exchange coupling strongly depends on layer separation, while the stac…
Gallium selenide (GaSe) is one of layered group-III metal monochalcogenides, which has an indirect bandgap in monolayer and direct bandgap in bulk unlike other conventional transition metal dichalcogenides (TMDs) such as MoX2 and WX2 (X=S and Se). Four polytypes of bulk GaSe, designated as beta-, epsilon-, gamma-, and delta-GaSe, have been reported. Since different polytypes result in different optical and electrical properties even for the same thickness, identifying the polytype is essential in utilizing this material for various optoelectronic applications. We performed polarized Raman meas…
Magic-angle twisted trilayer graphene (MATTG) has emerged as a novel moiré material that exhibits both strong electronic correlations and unconventional superconductivity. However, spectroscopic studies of its electronic properties are lacking, and the nature of superconductivity and the corresponding order parameter in this system remain elusive. Here we perform high-resolution scanning tunneling microscopy and spectroscopy of MATTG and reveal extensive regions of atomic reconstruction that favor mirror-symmetric stacking. In these regions, we observe a cascade of symmetry-breaking electronic…
Layered perovskite La2CuO4+delta(LCO) thin films were epitaxially grown on SrTiO3 (STO) and LaSrAlO4 (LSAO) substrates by atomic-layer-by-layer molecular beam epitaxy. The lattice de-fects and residual strain in these films were investigated by means of transmission electron mi-croscopy and electron energy loss spectroscopy. The LCO films showed a high epitaxial quality with flat interfaces and top surfaces. Misfit dislocations with Burgers vector a<010> and shear defects were frequently observed at or near the film/substrate interfaces and in the films, respec-tively, for all the LCO films. I…
The van der Waals heterostructures are a fertile frontier for discovering emergent phenomena in condensed matter systems. They are constructed by stacking elements of a large library of two-dimensional materials, which couple together through van der Waals interactions. However, the number of possible combinations within this library is staggering, and fully exploring their potential is a daunting task. Here we introduce van der Waals metamaterials to rapidly prototype and screen their quantum counterparts. These layered metamaterials are designed to reshape the flow of ultrasound to mimic ele…
A double moiré superlattice can be realized by stacking three layers of atomically thin two-dimensional materials with designer interlayer twisting or lattice mismatches. In this novel structure, atomic reconstruction of constituent layers could introduce significant modifications to the lattice symmetry and electronic structure at small twist angles. Here, we employ conductive atomic force microscopy (cAFM) to investigate symmetry breaking and local electrical properties in twisted trilayer graphene. We observe clear double moiré superlattices with two distinct moire periods all over the samp…
Two-dimensional (2D) semiconductor of MoS2 has great potential for advanced electronics technologies beyond silicon1-9. So far, high-quality monolayer MoS2 wafers10-12 are already available and various demonstrations from individual transistors to integrated circuits have also been shown13-15. In addition to the monolayer, multilayers have narrower band gaps but improved carrier mobilities and current capacities over the monolayer5,16-18. However, achieving high-quality multilayer MoS2 wafers remains a challenge. Here we report the growth of high quality multilayer MoS2 4-inch wafers via the l…
The electronic band structure of ABC-stacked multilayer graphene is studied within an effective mass approximation. The electron and hole bands touching at zero energy support chiral quasiparticles characterized by Berry's phase N pi for N-layers, generalizing the low-energy band structure of monolayer and bilayer graphene. We investigate the trigonal-warping deformation of the energy bands and show that the Lifshitz transition, in which the Fermi circle breaks up into separate parts at low energy, reflects Berry's phase N pi. It is particularly prominent in trilayers, N=3, with the Fermi circ…
