The creation of multilayer graphene (Gr), while preserving the brilliant properties of monolayer Gr derived from its unique band structure, can expand the application field of Gr to the macroscale. However, the energy-favorable AB stacking structure in the multilayer Gr induces a strong interlayer interaction and alters the band structure. Consequently, the intrinsic properties of each monolayer are degraded. In this work, we insert carbon nanotubes (CNTs) as nanospacers to modulate the microstructure of multilayer stacking Gr. Nanospacers can increase the interlayer distance and reduce the interlayer interaction. The Gr/CNT stacking structure is experimentally fabricated using a dry transfer method in a layer-by-layer manner. Raman spectroscopy verifies the reduction in the interlayer interaction within the stacking structure. Atomic force microscopy shows an increase in the interlayer distance, which can explain the weakening of the interlayer interactions. The microstructure of the stacked Gr and CNTs is studied by molecular dynamics simulation to systematically investigate the effect of CNT insertion. We found that the distribution distance, size, and arrangement of the CNT can modulate the interlayer distance. These results will help us to understand and improve the properties of the composite systems consisting of Gr and CNTs.
Aiming to clarify the mechanisms governing the interlayer magnetic coupling, we have investigated the stacking energy and interlayer magnetism of bilayer CrBr$_3$ systemically. The magnetic ground states of bilayer CrBr$_3$ with different R-type and H-type stacking orders are established, which is found to be in good agreement with recent experiment (Science $\mathbf{366}$,983(2019)).Further analyses indicate that the stacking energy is mainly determined by the Coulomb interaction between the interlayer nearest-neighbor Br-Br atoms. While interlayer magnetism can be understood by a competition…
We address the interplay between stacking and interlayer exchange for ferromagnetically ordered CrI$_3$, both for bilayers and bulk. Whereas bulk CrI$_3$ is ferromagnetic, both magneto-optical and transport experiments show that interlayer exchange for CrI$_3$ bilayers is antiferromagnetic. Bulk CrI$_3$ is known to assume two crystal structures, rhombohedral and monoclinic, that differ mostly in the stacking between monolayers. Below 210-220 Kelvin, bulk CrI$_3$ orders in a rhombohedral phase. Our density functional theory calculations show a very strong dependence of interlayer exchange and s…
Controlling the crystal structure is a powerful approach for manipulating the fundamental properties of solids. Unique to two-dimensional (2D) van der Waals materials, the control can be achieved by modifying the stacking order through rotation and translation between the layers. Here, we report the first observation of stacking dependent interlayer magnetism in the 2D magnetic semiconductor, chromium tribromide (CrBr3), enabled by the successful growth of its monolayer and bilayer through molecular beam epitaxy. Using in situ spin-polarized scanning tunneling microscopy and spectroscopy, we d…
We study the effect of perpendicular electric fields on the band structures of ABA and ABC graphene multilayers, and find that the electronic screening effect is significantly different between them. In ABA multilayers, the field produces a band overlap and gives a linear screening, while in ABC multilayers, in contrast, it opens an energy gap in the surface-state band at low energy, leading to a strong screening effect essentially non-linear to the field amplitude. The energy gap of a large ABC stack sharply rises when the external field exceeds a certain critical value.
Stacking order can significantly influence the physical properties of two-dimensional (2D) van der Waals materials. The recent isolation of atomically thin magnetic materials opens the door for control and design of magnetism via stacking order. Here we apply hydrostatic pressure up to 2 GPa to modify the stacking order in a prototype van der Waals magnetic insulator CrI3. We observe an irreversible interlayer antiferromagnetic (AF) to ferromagnetic (FM) transition in atomically thin CrI3 by magnetic circular dichroism and electron tunneling measurements. The effect is accompanied by a monocli…
With the help of the quantum chemistry methods we have investigated the nature of interlayer interactions between graphene fragments in different stacking arrangements (AA and AB). We found that the AB stacking pattern as the ground state of the system, is characterized by the effective inter-band orbital interactions which are barely present in the AA. Their vanishing induces electronic decoupling between the graphene layers, so that the bonding interaction $ΔE_{oi}$ between the flakes is drastically reduced from -0.482 eV to -0.087 eV as the stacking pattern is changed from AB to AA. The eff…
We study a family of globally smooth spatially varying two dimensional stacking textures in bilayer graphene. We find that the strain-minimizing stacking patterns connecting inequivalent ground states with local $AB$ and $BA$ interlayer registries are two dimensional twisted textures of an interlayer displacement field. We construct and display these topological stacking textures for bilayer graphene, examine their interactions and develop the composition rules that allow us to represent other more complex stacking textures, including globally twisted graphenes and extended one dimensional dom…
Diverse interlayer tunability of physical properties of two-dimensional layers mostly lies in the covalent-like quasi-bonding that is significant in electronic structures but rather weak for energetics. Such characteristics result in various stacking orders that are energetically comparable but may significantly differ in terms of electronic structures, e.g. magnetism. Inspired by several recent experiments showing interlayer anti-ferromagnetically coupled CrI3 bilayers, we carried out first-principles calculations for CrI3 bilayers. We found that the anti-ferromagnetic coupling results from a…
The interlayer interaction in graphene/boron-nitride heterostructures is studied using density functional theory calculations with the correction for van der Waals interactions. It is shown that the use of the experimental interlayer distance allows to describe the potential energy surface at the level of more accurate but expensive computational methods. On the other hand, it is also demonstrated that the dependence of the interlayer interaction energy on the relative in-plane position of the layers can be fitted with high accuracy by a simple expression determined by the system symmetry. The…
Two-dimensional (2D) layered materials have been extensively studied owing to their fascinating and technologically relevant properties. Their functionalities can be often tailored by the interlayer stacking pattern. Low-frequency (LF) Raman spectroscopy provides a quick, non-destructive and inexpensive optical technique for stacking characterization, since the intensities of LF interlayer vibrational modes are sensitive to the details of the stacking. A simple and generalized interlayer bond polarizability model is proposed here to explain and predict how the LF Raman intensities depend on co…
We reveal stacking-induced strong coupling between atomic motion and interlayer excitons through photocurrent measurements of WSe$_2$/MoSe$_2$ heterojunction photodiodes. Strong coupling manifests as pronounced periodic sidebands in the photocurrent spectrum in frequency windows close to the interlayer exciton resonances. The sidebands, which repeat over large swathes of the interlayer exciton photocurrent spectrum, occur in energy increments corresponding directly to a prominent vibrational mode of the heterojunction. Such periodic patterns, together with interlayer photoconductance oscillati…
We have investigated the interlayer shear and breathing phonon modes in MoS$_{2}$ with pure 3R and 2H stacking order by using polarization-dependent ultralow-frequency Raman spectroscopy. We observe up to three shear branches and four breathing branches in MoS$_{2}$ with thickness from 2 to 13 layers. The breathing modes show the same Raman activity behavior for both polytypes, but the 2H breathing frequencies are consistently several wavenumbers higher than the 3R breathing frequencies, signifying that 2H MoS$_{2}$ has slightly stronger interlayer lattice coupling than 3R MoS$_{2}$. In contra…
Peeling, shearing, and sliding are important mechanical phenomena in van der Waals solids. However, theoretically they have been studied mostly using minimal periodic cells and in the context of accurate quantum simulations. Here, we investigate the peeling of large-scale multilayer graphene stacks with varying thicknesses, stackings, and peeling directions by using classical molecular dynamics simulations with a registry-dependent interlayer potential. Simulations show that, while at large scale the peeling proceeds smoothly, at small scale the registry shifts and sliding patterns of the laye…
The infrared absorption spectra of ABC-stacking tri- and tetra-layer graphenes are studied using the density functional theory. It is found that they exhibit very different characteristic peaks compared with those of AB-stacking ones, caused by the different stacking sequence and interlayer coupling. The anisotropy of the spectra with respect to the direction of the light electric field is significant. The spectra are more sensitive to the stacking number when the electric field is perpendicular to the graphene plane due to the interlayer polarization. The high sensitivities make it possible t…
Stacking-dependent interlayer interactions are important for understanding the structural and electronic properties in incommensurable two dimensional material assemblies where long-range moiré patterns arise due to small lattice constant mismatch or twist angles. Here, we study the stacking-dependent interlayer coupling energies between graphene (G) and hexagonal boron nitride (BN) homo- and hetero-structures using high-level random-phase approximation (RPA) ab initio calculations. Our results show that although total binding energies within LDA and RPA differ substantially between a factor o…
We have studied boron nitride monolayer and bilayer band structures. For bilayers, the ground state energies of the different five stackings are computed using DFT in order to determine the most stable configuration. Also, the interlayer distance for the five different types of stacking in which boron-nitride bilayers can be found is determined. Using a minimal tight binding model for the band structures of boron nitride bilayers, the hopping parameters and the onsite energies have been extracted by fitting a tight binding empirical model to the DFT results.
We investigate the ultralow-frequency Raman response of atomically thin ReS2, a special type of two-dimensional (2D) semiconductors with unique distorted 1T structure. Bilayer and few-layer ReS2 exhibit rich Raman spectra at frequencies below 50 cm-1, where a panoply of interlayer shear and breathing modes are observed. The emergence of these interlayer phonon modes indicate that the ReS2 layers are coupled and stacked orderly, in contrast to the general belief that the ReS2 layers are decoupled from one another. While the interlayer breathing modes can be described by a linear chain model as …
We study interlayer transport of multilayer graphenes in magnetic field with various stacking structures (AB, ABC, and AA types) by calculating the Hall and longitudinal conductivities as functions of Fermi energy. Their behavior depends strongly on the stacking structures and selection of the layers. The Hall conductivity between different layers is no longer quantized. Moreover, for AB stacking, the interlayer conductivity vanishes around zero energy with increasing layer separation, and shows negative values in particular cases. The fact that longitudinal interlayer conductivity suppressed …
We perform an optical spectroscopy study to investigate the properties of different artificial MoS$_2$ bi- and trilayer stacks created from individual monolayers by a deterministic transfer process. These twisted bi- and trilayers differ from the common 2H stacking in mineral MoS$_2$ in the relative stacking angle of adjacent layers and the interlayer distance. The combination of Raman spectroscopy, second-harmonic-generation microscopy and photoluminescence measurements allows us to determine the degree of interlayer coupling in our samples. We find that even for electronically decoupled arti…
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…
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…
The electronic excitations of bilayer graphene (BLG) under a magnetic field are investigated with the use of the Peierls tight-binding model in conjunction with random-phase approximation (RPA). The interlayer atomic interactions, interlayer Coulomb interactions, and magnetic field effects are simultaneously included in the dielectric-function matrix. That enables us to derive the magneto-Coulomb-excitation spectrum of different stacking structures. The two typical arrangements of BLGs, AB and AA, are considered in this article. AB-BLG exhibits many discrete energy-loss peaks, which correspond…
A conversion of AA- to AB-stacking bilayer graphene (BLG) due to interlayer interaction is demonstrated. Two types of interlayer interactions, an attractive and a repulsive, between the Boron and Nitrogen dopant atoms in BLG are found. In the presence of the attractive interaction, an AA-stacking of BN-codoped BLG is formed with a less stable structure leading to weak mechanical properties of the system. Low values of the Young modulus, the ultimate strength and stress, and the fracture strength are observed comparing to a pure BLG. In addition, the attractive interaction induces a small bandg…
Stacking order has strong influence on the coupling between the two layers of twisted bilayer graphene (BLG), which in turn determines its physical properties. Here, we report the investigation of the interlayer coupling of the epitaxially grown single-crystal 30° twisted BLG on Cu(111) at the atomic scale. The stacking order and morphology of BLG is controlled by a rationally designed two-step growth process, that is, the thermodynamically controlled nucleation and kinetically controlled growth. The crystal structure of the 30°-twisted bilayer graphene (30°-tBLG) is determined to have the qua…
We study the superlattice minibands produced by the interplay between moiré pattern induced by hexagonal BN substrate on graphene layer and the interlayer coupling in bilayer graphene with Bernal stacking (BLG). We compare moiré miniband features in BLG, where they are affected by the interlayer asymmetry of BLG-hBN heterostructure and trigonal warping characteristic for electrons in Bernal-stacked bilayers with those found in monolayer graphene.
Using molecular dynamics simulations, we investigated an integrated bio-nano interface consisting of a \b{eta}-sheet protein stacked onto graphene. We found that the stacking assembly of the model protein on graphene could be controlled by water molecules. The interlayer water filled within interstices of the bio-nano interface could suppress the molecular vibration of surface groups on protein, and could impair the CH...π interaction driving the attraction of the protein and graphene. The intermolecular coupling of interlayer water would be relaxed by the relative motion of protein upon graph…
Conduction between graphene layers is suppressed by momentum conservation whenever the layer stacking has a rotation. Here we show that phonon scattering plays a crucial role in facilitating interlayer conduction. The resulting dependence on orientation is radically different than previously expected, and far more favorable for device applications. At low temperatures, we predict diode-like current-voltage characteristics due to a phonon bottleneck. Simple scaling relationships give a good description of the conductance as a function of temperature, doping, rotation angle, and bias voltage, re…
We calculate the dynamical conductivity of AA-stacked bilayer graphene as a function of frequency and in the presence of a finite chemical potential due to charging. Unlike the monolayer, we find a Drude absorption at charge neutrality in addition to an interband absorption with onset of twice the interlayer hopping energy. At finite doping, the interband absorption exhibits two edges which depend on both chemical potential and interlayer hopping energy. We study the behaviour as a function of varying chemical potential relative to the interlayer hopping energy scale and compute the partial op…
Optoelectronic properties of van der Waals homostructures can be selectively engineered by the relative twist angle between layers. Here, we study the twist-dependent moire coupling in MoSe2 homobilayers. For small angles, we find a pronounced redshift of the K-K and Γ-K excitons accompanied by a transition from K-K to Γ-K emission. Both effects can be traced back to the underlying moire pattern in the MoSe2 homobilayers, as confirmed by our low-energy continuum model for different moire excitons. We identify two distinct intralayer moire excitons for R-stacking, while H-stacking yields two de…
Motivated by the recent experiment demonstration of stacking dependent interlayer magnetic interaction [T. Song et al., Nat. Mater. 18, 1298 (2019); T. Li et al., Nat. Mater. 18, 1303 (2019); W. Chen et al., Science 366, 983 (2019)], we investigate the magnetization textures and the control possibilities in the moiré pattern formed of twisted bilayer two-dimensional (2D) magnets CrX$_3$ (X=Br, I). We find that the stacking dependent interlayer magnetic interaction results in the formation of periodic magnetization domains in a long-period moiré pattern. Magnetization textures with various topo…
Graphene stacked in a Bernal configuration (60 degrees relative rotations between sheets) differs electronically from isolated graphene due to the broken symmetry introduced by interlayer bonds forming between only one of the two graphene unit cell atoms. A variety of experiments have shown that non-Bernal rotations restore this broken symmetry; consequently, these stacking varieties have been the subject of intensive theoretical interest. Most theories predict substantial changes in the band structure ranging from the development of a Van Hove singularity and an angle dependent electron local…
Following the recent isolation of monolayer CrI3, there has been a surge of new two-dimensional van der Waals magnetic materials, whose incorporation in van der Waals heterostructures offers a new platform for spintronics, proximity magnetism, and quantum spin liquids. A primary question in this burgeoning field is how exfoliating crystals to the few-layer limit influences their magnetism. Studies on CrI3 have shown a different magnetic ground state for ultrathin exfoliated films but the origin is not yet understood. Here, we use electron tunneling through few-layer crystals of the layered ant…
We model bilayer graphene-like materials with Si$_2$C$_{14}$ and BC$_{14}$N stoichiometry, where the interlayer interactions play important roles shaping the physical properties of the systems. We find the interlayer interaction in Si$_2$C$_{14}$ to be repulsive due to the interaction of Si-Si atoms, and in BC$_{14}$N it is attractive due to B and N atoms for both the AA- and the AB-stacking. The repulsive interlayer interaction opens up a bandgap in Si$_2$C$_{14}$ while the attractive interlayer interaction in BC$_{14}$N induces a small indirect bandgap or overlaping of the valence conduction…
Stacking two-dimensional (2D) materials into multi-layers or heterostructures, known as van der Waals (vdW) epitaxy, is an essential degree of freedom for tuning their properties on demand. Few-layer black phosphorus (FLBP), a material with high potential for nano- and optoelectronics applications, appears to have interlayer couplings much stronger than graphene and other 2D systems. Indeed, these couplings call into question whether the stacking of FLBP can be governed only by vdW interactions, which is of crucial importance for epitaxy and property refinement. Here, we perform a theoretical …
We observed distinct interlayer shear mode Raman spectra for trilayer graphene with ABA and ABC stacking order. There are two rigid-plane shear-mode phonon branches in trilayer graphene. We found that ABA trilayers exhibit pronounced Raman response from the high-frequency shear branch, without any noticeable response from the low-frequency branch. In contrast, ABC trilayers exhibit no response from the high-frequency shear branch, but significant Raman response from the low-frequency branch. Such complementary behaviors of Raman shear modes can be explained by the distinct symmetry of the two …
Atomically thin NbSe2 is a metallic layered transition metal dichalcogenide (TMD) with considerably different crystallographic structure and electronic properties from other TMDs, such as MoS2, MoSe2, WS2 and WSe2. Properties of TMD atomic layers are sensitive to interlayer coupling. Here we investigate the interlayer phonons of few-layer NbSe2 by ultralow-frequency Raman spectroscopy. We observe both the interlayer breathing modes and shear modes at frequencies below 40 cm-1 for samples of 2 to 15 layers. Their frequency, Raman activity, and environmental instability depend systematically on …
We report a La2CuO4-like interlayer antiferromagnetic order in Sr2IrO4 films with large orthorhombic distortion (> 1.5%). The biaxial lattice strain in epitaxial heterostructures of Sr2IrO4/Ca3Ru2O7 lowers the crystal symmetry of Sr2IrO4 from tetragonal (C4) to orthorhombic (C2), guiding the Ir 5d Jeff = 1/2 pseudospin moment parallel to the elongated b-axis via magnetic anisotropy. From resonant X-ray scattering experiments, we observed an antiferromagnetic order in the orthorhombic Sr2IrO4 film whose interlayer stacking pattern is inverted from that of the tetragonal Sr2IrO4 crystal. This in…
Twisted layers of atomically thin two-dimensional materials realize a broad range of novel quantum materials with engineered optical and transport phenomena arising from spin and valley degrees of freedom and strong electron correlations in hybridized interlayer bands. Here, we report experimental and theoretical studies of WSe$_2$ homobilayers obtained in two stable configurations of 2H ($60^\circ$ twist) and 3R ($0^\circ$ twist) stackings by controlled chemical vapor synthesis of high-quality large-area crystals. Using optical absorption and photoluminescence spectroscopy at cryogenic temper…
We investigate the electronic structure of alternating-twist triple Bernal-stacked bilayer graphene (t3BG) as a function of interlayer coupling $ω$, twist angle $θ$, interlayer potential difference $Δ$, and top-bottom bilayers sliding vector $\boldsymbolτ$ for three possible configurations AB/AB/AB, AB/BA/AB, and AB/AB/BA. The parabolic low-energy band dispersions in a Bernal-stacked bilayer and gap-opening through a finite interlayer potential difference $Δ$ allows the flattening of bands in t3BG down to $\sim 20$~meV for twist angles $θ\lesssim 2^{\circ}$ regardless of the stacking types. Th…
Using resonant 2-photon excitation of interlayer electrons in twisted bilayer graphene (tBLG), we resolve photoluminescence (PL) that tunes spectrally with stacking angle, θ. This weak signal is 4- 5$\times$ larger than the non-resonant background and is emitted from the interlayer band anti-crossing regions traditionally associated with van Hove singularity resonances. However, our observation of resonant PL emission with delayed ~1 ps electronic thermalization suggests interlayer carriers may instead form bound-excitons. Using both the 2-photon PL and intraband transient absorption spectra, …
We demonstrate that the electronic, thermal, and optical properties of a graphene bilayer with boron and nitrogen dopant atoms can be controlled by the interlayer distance between the layers in which the interaction energy and the van der Waals interaction between the dopant atoms play an essential role. We find a conversion of an AA- to an AB-stacked bilayer graphene caused by the repulsive interaction between dopant atoms. At a short interlayer distance, a strong repulsive interaction inducing a strong electric dipole moment of the dopant atoms is found. This gives rise to a breaking of the …
This article reviews progress in the theoretical modelling of the electronic structure of rotationally faulted multilayer graphenes. In these systems the crystallographic axes of neighboring layers are misaligned so that the layer stacking does not occur in the Bernal structure observed in three dimensional graphite and frequently found in exfoliated bilayer graphene. Notably, rotationally faulted graphenes are commonly found in other forms of multilayer graphene including epitaxial graphenes thermally grown on ${\rm SiC \, (000 \bar 1)}$, graphenes grown by chemical vapor deposition, folded m…
We report experimental signatures of plasmonic effects due to electron tunneling between adjacent graphene layers. At sub-nanometer separation, such layers can form either a strongly coupled bilayer graphene with a Bernal stacking or a weakly coupled double-layer graphene with a random stacking order. Effects due to interlayer tunneling dominate in the former case but are negligible in the latter. We found through infrared nano-imaging that bilayer graphene supports plasmons with a higher degree of confinement compared to single- and double-layer graphene, a direct consequence of interlayer tu…
Rhombohedral multilayer graphene is a physical realization of the chiral two-dimensional electron gas that can host zero-line modes (ZLMs), also known as kink states, when the local ap opened by inversion symmetry breaking potential changes sign in real space. Here we study how the variations in the local stacking coordination of multilayer graphene affects the formation of the ZLMs. Our analysis indicates that the valley Hall effect develops whenever an interlayer potential difference is able to open up a band gap in stacking faulted multilayer graphene, and that ZLMs can appear at the domain…
The interlayer magnetic interaction in bilayer CrI$_3$ plays a crucial role for its device applications. In this work, we studied the interlayer magnetic interaction in $π/3$-twisted bilayer CrI$_3$ using first-principles calculations. Our calculations show that the interlayer coupling can be ferromagnetic or antiferromagnetic depending crucially on lateral shift. The strongest antiferromagnetic interlayer interaction appears in the $\bar{A}A$-stacking. The magnetic force theory calculations demonstrate that such an antiferromagnetic interaction is dominanted by the $e_g$-$e_g$ channel. Partic…
A detailed account of a recently developed method [Marom et al., Phys. Rev. Lett. 105, 046801 (2010)] to quantify the registry mismatch in layered materials is presented. The registry index, which was originally defined for planar hexagonal boron-nitride, is extended to treat graphitic systems and generalized to describe multi-layered nanotubes. It is shown that using simple geometric considerations it is possible to capture the complex physical features of interlayer sliding in layered materials. The intuitive nature of the presented model and the efficiency of the related computations sugges…
Van der Waals (vdW) coupling is emerging as a powerful method to engineer and tailor physical properties of atomically thin two-dimensional (2D) materials. In graphene/graphene and graphene/boron-nitride structures it leads to interesting physical phenomena ranging from new van Hove singularities1-4 and Fermi velocity renormalization5, 6 to unconventional quantum Hall effects7 and Hofstadter's butterfly pattern8-12. 2D transition metal dichalcogenides (TMDCs), another system of predominantly vdW-coupled atomically thin layers13, 14, can also exhibit interesting but different coupling phenomena…
