In layered magnetic materials, the magnetic coupling between neighboring van der Waals layers is challenging to understand and anticipate, although the exchange interaction inside a layer can be well rationalized for example by the superexchange mechanism. In this work, we elucidate the interlayer exchange mechanism and propose an electron-counting rule to determine the interlayer magnetic order between van der Waals layers, based on counting the $d$-orbital occupation ($d^n$, where $n$ is the number of $d$-electrons at the magnetic cation). With this rule, we classify magnetic monolayers into two groups, type-I ($n<5$) and type-II ($n\geq5$), and derive three types of interlayer magnetic coupling for both insulators and metals. The coupling between two type-II layers prefers the antiferromagnetic (AFM) order, while type-I and type-II interfaces favor the ferromagnetic (FM) way. However, for two type-I layers, they display competition between FM and AFM orders and even lead to the stacking dependent magnetism. Additionally, metallic layers can also be incorporated into this rule with a minor correction from the free carrier hopping. Therefore, this rule provides simple guidance to understand the interlayer exchange and further design van der Waals junctions with desired magnetic orders.
Van der Waals (vdW) heterobilayers formed by two-dimensional (2D) transition metal dichalcogenides (TMDCs) created a promising platform for various electronic and optical properties. ab initio band results indicate that the band offset of type-II band alignment in TMDCs vdW heterobilayer could be tuned by introducing Janus WSSe monolayer, instead of an external electric field. On the basis of symmetry analysis, the allowed interlayer hopping channels of TMDCs vdW heterobilayer were determined, and a four-level kp model was developed to obtain the interlayer hopping. Results indicate that the i…
We propose a tubal van der Waals heterostructure by rolling up the graphene and MoS2 atomic layers into a tubal form. We illustrate that the interlayer space for the tubal van der Waals heterostructure can be varied in a specific range, which is determined by the competition between the interlayer van der Waals force and the mechanical properties of the atomic layers. The variability of the interlayer space can be utilized to efficiently tune mechanical properties of the tubal van der Waals heterostructure. More specifically, we demonstrate that the Poisson's ratio of the tubal van der Waals h…
Manipulating the interlayer magnetic coupling in van der Waals magnetic materials and heterostructures is the key to tailoring their magnetic and electronic properties for various electronic applications and fundamental studies in condensed matter physics. By utilizing the MnBi2Te4-family compounds and their heterostructures as a model system, we systematically studied the dependence of the sign and strength of interlayer magnetic coupling on constituent elements by using first-principles calculations. It was found that the coupling is a long-range superexchange interaction mediated by the cha…
A methodology to test the interlayer bonding strength of two-dimensional (2D) surfaces and associated one (1D)- and two (2D)- dimensional surface defects using scanning tunneling microscope tip-induced deformation, is demonstrated. Surface elastic deformation characteristics of soft 2D monatomic sheets of graphene and graphite in contrast to NbSe2 indicates related association with the underlying local bonding configurations. Surface deformation of 2D graphitic moire patterns reveal the inter-layer van der Waals strength varying across its domains. These results help in the understanding of th…
Van der Waals heterostructures assembled from two-dimensional materials offer a promising platform to engineer structures with desired optoelectronic characteristics. Here we use waveguide-coupled disk resonators made of hexagonal boron nitride (h-BN) to demonstrate cavity-coupled emission from interlayer excitons of a heterobilayer of two monolayer transition metal dichalcogonides. We sandwich a MoSe$_{\rm 2}$ - WSe$_{\rm 2}$ heterobilayer between two slabs of h-BN and directly pattern the resulting stack into waveguide-coupled disk resonators. This enables us to position the active materials…
We examined what interactions control the sign and strength of the interlayer coupling in van der Waals ferromagnets such as Fe3-xGeTe2, Cr2Ge2Te6, CrI3 and VI3, to find that high-spin orbital interaction across the van der Waals gaps are a key to understanding their ferromagnetism. Interlayer ferromagnetic coupling in Fe3-xGeTe2 Cr2Ge2Te6, and CrI3 is governed by the high-spin two-orbital two-electron destabilization, but that in VI3 by the high-spin four-orbital two-electron stabilization. These interactions explain a number of seemingly puzzling observations in van der Waals fer-romagnets.
Using density functional theory and Monte Carlo calculations, we study the thickness dependence of the magnetic and electronic properties of a van der Waals interlayer antiferromagnet in the two-dimensional limit. Considering $\mathrm{MnBi_2Te_4}$ as a model material, we find it to demonstrate a remarkable set of thickness-dependent magnetic and topological transitions. While a single septuple layer block of $\mathrm{MnBi_2Te_4}$ is a topologically trivial ferromagnet, the thicker films made of an odd (even) number of blocks are uncompensated (compensated) interlayer antiferromagnets, which sh…
Van der Waals heterostructures (vdWH) provide an ideal playground for exploring light-matter interactions at the atomic scale. In particular, structures with a type-II band alignment can yield detailed insight into free carrier-to-photon conversion processes, which are central to e.g. solar cells and light emitting diodes. An important first step in describing such processes is to obtain the energies of the interlayer exciton states existing at the interface. Here we present a general first-principles method to compute the electronic quasi-particle (QP) band structure and excitonic binding ene…
Van der Waals (vdW) heterostructures have attracted great interest because of their rich material combinations.The discovery of two-dimensional magnets has provided a new platform for magnetic vdW heterointerfaces; however, research on magnetic vdW heterointerfaces has been limited to those with ferromagnetic surfaces. Here we report a magnetic vdW heterointerface using layered intralayer-antiferromagnetic MPSe3 (M=Mn, Fe) and monolayer transition metal dichalcogenides (TMDs). We found an anomalous upshift of the excitonic peak in monolayer TMDs below the antiferromagnetic transition temperatu…
Defect-free epitaxial growth of 2D materials is one of the holy grails for a successful integration of van der Waals (vdW) materials in the semiconductor industry. The large-area (quasi-)vdW epitaxy of layered 2D chalcogenides is consequently carefully being researched since these materials hold very promising properties for future nanoelectronic applications. The formation of defects such as stacking faults like 60o twins and consequently 60o grain boundaries is still of major concern for the defect-free epitaxial growth of 2D chalcogenides. Although growth strategies to overcome the occurren…
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…
The interlayer coupling in van der Waals heterostructures governs a variety of optical and electronic properties. The intrinsic dipole moment of Janus transition metal dichalcogenides (TMDs) offers a simple and versatile approach to tune the interlayer interactions. In this work, we demonstrate how the van der Waals interlayer coupling and charge transfer of Janus MoSSe/MoS2 heterobilayers can be tuned by the twist angle and interface composition. Specifically, the Janus heterostructures with a sulfur/sulfur (S/S) interface display stronger interlayer coupling than the heterostructures with a …
Van der Waals assembly of two-dimensional (2D) crystals continue attract intense interest due to the prospect of designing novel materials with on-demand properties. One of the unique features of this technology is the possibility of trapping molecules or compounds between 2D crystals. The trapped molecules are predicted to experience pressures as high as 1 GPa. Here we report measurements of this interfacial pressure by capturing pressure-sensitive molecules and studying their structural and conformational changes. Pressures of 1.2 +/- 0.3 GPa are found using Raman spectrometry for molecular …
An emerging class of semiconductor heterostructures involves stacking discrete monolayers such as the transition metal dichalcogenides (TMDs) to form van der Waals heterostructures. In these structures, it is possible to create interlayer excitons (ILEs), spatially indirect, bound electron-hole pairs with the electron in one TMD layer and the hole in an adjacent layer. We are able to clearly resolve two distinct emission peaks separated by 24 meV from an ILE in a MoSe2/WSe2 heterostructure fabricated using state-of-the-art preparation techniques. These peaks have nearly equal intensity, indica…
The weak interlayer coupling in van der Waals (vdW) magnets has confined their application to two dimensional (2D) spintronic devices. Here, we demonstrate that the interlayer coupling in a vdW magnet Fe$_3$GeTe$_2$ (FGT) can be largely modulated by a protonic gate.With the increase of the protons intercalated among vdW layers,interlayer magnetic coupling increases.Because of the existence of antiferromagnetic layers in FGT nanoflakes, the increasing interlayer magnetic coupling induces exchange bias in protonated FGT nanoflakes. Most strikingly, a rarely seen zero-field cooled (ZFC) exchange …
Transition metal dichalcogenide heterostructures can host interlayer excitons (IXs), which consist of electrons and holes spatially separated in different layers. IXs possess permanent dipoles and have proven to offer a wealth of novel physics. We develop a discrete, random-walk model which includes annihilation and repulsion interactions among IXs. Using this model, we simulate the trapping of IXs in traps of different depths, densities, and shapes. Our results show that dipole-dipole interactions play an important role in regulating IX trapping. The effects of dipole interactions can be miti…
Control of the interlayer twist angle in two-dimensional (2D) van der Waals (vdW) heterostructures enables one to engineer a quasiperiodic moiré superlattice of tunable length scale. In twisted bilayer graphene (TBG), the simple moiré superlattice band description suggests that the electronic band width can be tuned to be comparable to the vdW interlayer interaction at a 'magic angle', exhibiting strongly correlated behavior. However, the vdW interlayer interaction can also cause significant structural reconstruction at the interface by favoring interlayer commensurability, which competes with…
Interest in layered two dimensional materials, particularly stacked heterostructures of transition metal dichalcogenides, has led to the need for a better understanding of the structural and electronic changes induced by stacking. Here, we investigate the effects of idealized heterostructuring, with periodic commensurate stacking, on the structural, electronic, and vibrational properties, when compared to the counterpart bulk transition metal dichalcogenide. We find that in heterostructures with dissimilar chalcogen species there is a strong compression of the inter-layer spacing, compared to …
Interlayer electronic coupling in two-dimensional (2D) materials enables tunable and emergent properties by stacking engineering. However, it also brings significant evolution of electronic structures and attenuation of excitonic effects in 2D semiconductors as exemplified by quickly degrading excitonic photoluminescence and optical nonlinearities in transition metal dichalcogenides when monolayers are stacked into van der Waals structures. Here we report a novel van der Waals crystal, niobium oxide dichloride, featuring a vanishing interlayer electronic coupling and scalable second harmonic g…
In van der Waals heterostructures of two-dimensional transition-metal dichalcogenides (2D TMDCs) electron and hole states are spatially localized in different layers forming long-lived interlayer excitons. Here, we have investigated, from first principles, the influence of additional electron or hole layers on the electronic properties of a MoS2/WSe2 heterobilayer (HBL), which is a direct band gap material. Additional layers modify the interlayer hybridization, mostly affecting the quasiparticle energy and real-space extend of hole states at the G and electron states at the Q valleys. For a su…
Photoexcited intralayer excitons in van der Waals heterostructures (vdWHs) with type-II band alignment have been observed to tunnel into interlayer excitons on ultrafast timescales. Such interlayer excitons have sufficiently long lifetimes that inducing dissociation with external in-plane electric fields becomes an attractive option of improving efficiency of photocurrent devices. In the present paper, we calculate interlayer exciton binding energies, Stark shifts, and dissociation rates for six different transition metal dichalcogenide (TMD) vdWHs using a numerical procedure based on exterior…
Determining the material properties of layered systems like graphite and bigraphene from \emph{ab initio} calculations is very difficult. This is mostly due to the complex van der Waals forces which help bind the layers. Recently, Chen~\emph{et al.} [Chen et al., Sci. Rep. 3, 3046 (2013)] reported a novel approach for extracting geometry dependent energetic properties of general, layered graphitic systems from periodic graphite calculations on AA, AB and ABC graphite. Unfortunately, their analysis suffered from a number of technical and theoretical flaws which make their results unreliable for…
Antiferromagnetic (AFM) van der Waals (vdW) materials provide a novel platform for synthetic AFM spintronics, in which the spin-related functionalities are derived from manipulating spin configurations between the layers. Metallic vdW antiferromagnets are expected to have several advantages over the widely-studied insulating counterparts in switching and detecting the spin states through electrical currents but have been much less explored due to the lack of suitable materials. Here, utilizing the extreme sensitivity of the vdW interlayer magnetism to material composition, we report the itiner…
The ability to assemble layers of two-dimensional (2D) materials to form permutations of van der Waals heterostructures provides significant opportunities in materials design and synthesis. Interlayer interactions provide a path to new properties and functionality, and understanding such interactions is essential to that end. Here we report formation of interlayer exciton-phonon bound states in Bi2Se3/WS2 heterostructures, where the Bi2Se3 A1(3) surface phonon, a mode particularly susceptible to electron-phonon coupling, is imprinted onto the excitonic emission of the WS2. The exciton-phonon b…
Recent studies have revealed that the interlayer interaction in two-dimensional (2D) layered materials is not simply of van der Waals character but could coexist with quasi-bonding character. Here we classify the interlayer quasi-bonding interactions into two main categories (I: homo-occupancy interaction, II: hetero-occupancy interaction) according to the occupancy of the involved energy bands near the Fermi level. Then we investigate the quasi-bonding-interaction-induced band structure evolution of several representative 2D materials based on density functional theory calculations. Further c…
Activating metamagnetic transitions between ordered states in van der Waals magnets and devices bring great opportunities in spintronics. We show that external pressure, which enhances the interlayer hopping without introducing chemical disorders, triggers multiple metamagnetic transitions upon cooling in the topological van der Waals magnets Mn(Bi$_{1-x}$Sb$_x$)$_4$Te$_7$, where the antiferromagnetic interlayer superexchange coupling competes with the ferromagnetic interlayer coupling mediated by the antisite Mn spins. The temperature-pressure phase diagrams reveal that while the ordering tem…
The electronic and optical properties of monolayer transition-metal dichalcogenides (TMDs) and van der Waals heterostructures are strongly subject to their dielectric environment. In each layer the field lines of the Coulomb interaction are screened by the adjacent material, which reduces the single-particle band gap as well as exciton and trion binding energies. By combining an electrostatic model for a dielectric hetero-multi-layered environment with semiconductor many-particle methods, we demonstrate that the electronic and optical properties are sensitive to the interlayer distances on the…
In van der Waals (vdW) heterostructures formed by stacking two monolayers of transition metal dichalcogenides, multiple exciton resonances with highly tunable properties are formed and subject to both vertical and lateral confinement. We investigate how a unique control knob, the twist angle between the two monolayers, can be used to control the exciton dynamics. We observe that the interlayer exciton lifetimes in $\text{MoSe}_{\text{2}}$/$\text{WSe}_{\text{2}}$ twisted bilayers (TBLs) change by one order of magnitude when the twist angle is varied from 1$^\circ$ to 3.5$^\circ$. Using a low-en…
We propose the nano-scale displacement sensor with high resolution for weak-force systems could be realized based on vertical stacked two-dimensional (2D) atomic corrugated layer materials bound through Van der Waals (VdW) interaction. Using first-principles calculations, we found the electronic structure of bi-layer blue phosphorus (BLBP) varies appreciably to both the lateral and vertical interlayer displacement. The variation of electronic structure due to the lateral displacement is attributed to the changing of the interlayer distance dz led by atomic layer corrugation, which is in a unif…
$α$-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…
The properties of van der Waals (vdW) heterostructures are drastically altered by a tunable moiré superlattice arising from periodic variations of atomic alignment between the layers. Exciton diffusion represents an important channel of energy transport in semiconducting transition metal dichalcogenides (TMDs). While early studies performed on TMD heterobilayers have suggested that carriers and excitons exhibit long diffusion lengths, a rich variety of scenarios can exist. In a moiré crystal with a large supercell size and deep potential, interlayer excitons may be completely localized. As the…
Vertically stacked van der Waals heterostructures constitute a promising platform for providing tailored band alignment with enhanced excitonic systems. Here we report observations of neutral and charged interlayer excitons in trilayer WSe2-MoSe2-WSe2 van der Waals heterostructures and their dynamics. The addition of a WSe2 layer in the trilayer leads to significantly higher photoluminescence quantum yields and tunable spectral resonance compared to its bilayer heterostructures at cryogenic temperatures. The observed enhancement in the photoluminescence quantum yield is due to significantly la…
We investigate the optical properties of spin-triplet interlayer excitons in heterobilayer transition metal dichalcogenides in comparison with the spin-singlet ones. Surprisingly, the optical transition dipole of the spin-triplet exciton is found to be in the same order of magnitude to that of the spin-singlet exciton, in sharp contrast to the monolayer excitons where the spin triplet species is considered as dark compared to the singlet. Unlike the monolayer excitons whose spin-conserved (spin-flip) transition dipole can only couple to light of in-plane (out-of-plane) polarization, such restr…
Graphene/MoS$_2$ van der Waals (vdW) heterostructures have promising technological applications due to their unique properties and functionalities. Many experimental and theoretical research groups across the globe have made outstanding contributions to benchmark the properties of graphene/MoS$_2$ heterostructures. Even though some research groups have already made an attempt to model the graphene/MoS$_2$ heterostructures using {\it first-principles} calculations, there exists several discrepancies in the results from different theoretical research groups and the experimental findings. In the …
Atomistic van der Waals heterostacks are ideal systems for high-temperature exciton condensation because of large exciton binding energies and long lifetimes. Charge transport and electron energy-loss spectroscopy showed first evidence of excitonic many-body states in such two-dimensional materials. Pure optical studies, the most obvious way to access the phase diagram of photogenerated excitons have been elusive. We observe several criticalities in photogenerated exciton ensembles hosted in MoSe2-WSe2 heterostacks with respect to photoluminescence intensity, linewidth, and temporal coherence …
Interlayer interactions in 2D materials, also known as van der Waals (vdWs) interactions, play a critical role in the physical properties of layered materials. It is fascinating to manipulate the vdWs interaction, and hence to "redefine" the material properties. Here, we demonstrate that in-plane biaxial strain can effectively tune the vdWs interaction of few-layer black phosphorus with thickness of 2-10 layers, using infrared spectroscopy. Surprisingly, our results reveal that in-plane tensile strain efficiently weakens the interlayer coupling, even though the sample shrinks in the vertical d…
Vertically stacked atomic layers from different layered crystals can be held together by van der Waals forces, which can be used for building novel heterostructures, offering a platform for developing a new generation of atomically thin, transparent and flexible devices. The performance of these devices is critically dependent on the layer thickness and the interlayer electronic coupling, influencing the hybridisation of the electronic states as well as charge and energy transfer between the layers. The electronic coupling is affected by the relative orientation of the layers as well as by the…
The atomic-level vdW heterostructures have been one of the most interesting quantum material systems, due to their exotic physical properties. The interlayer coupling in these systems plays a critical role to realize novel physical observation and enrich interface functionality. However, there is still lack of investigation on the tuning of interlayer coupling in a quantitative way. A prospective strategy to tune the interlayer coupling is to change the electronic structure and interlayer distance by high pressure, which is a well-established method to tune the physical properties. Here, we co…
Magnetic topological insulators (TI) provide an important material platform to explore quantum phenomena such as quantized anomalous Hall (QAH) effect and Majorana modes, etc. Their successful material realization is thus essential for our fundamental understanding and potential technical revolutions. By realizing a bulk van der Waals material MnBi4Te7 with alternating septuple [MnBi2Te4] and quintuple [Bi2Te3] layers, we show that it is ferromagnetic in plane but antiferromagnetic along the c axis with an out-of-plane saturation field of ~ 0.22 T at 2 K. Our angle-resolved photoemission spect…
Topological magnetism in low-dimensional systems is of fundamental and practical importance in condensed-matter physics and material science. Here, using first-principles and Monte-Carlo simulations, we present that multiple topological magnetism (i.e., skyrmion and bimeron) can survive in van der Waals Heterostructure of MnTe2ZrS2. Arising from interlayer coupling, MnTe2ZrS2 can harbor a large Dzyaloshinskii-Moriya interaction. This, combined with ferromagnetic exchange interaction, yields an intriguing skyrmion phase consisting of sub-10 nm magnetic skyrmions under a tiny magnetic field of 7…
A novel type of exciton-phonon bound state -- interlayer polaron -- in a double-layer two-dimensional semiconductor with transition metal dichalcogenides as an example, is predicted. In these systems the interaction of the interlayer exciton with the soft modes of out-of-plane lattice vibrations caused by van der Waals forces and flexural rigidity gives rise to a bound quasiparticle. The energy and effective mass of the formed polaron for weak and strong exciton-phonon coupling regimes are calculated and analyzed. Possible manifestations of these effects in transport- and spectroscopy-related …
Electron-beam-induced Contactless Manipulation of Interlayer Twist in van der Waals Heterostructures
Polytechnic University of Turin（都灵理工大学）；Empa, Swiss Federal Laboratories for Materials Science and Technology（瑞士联邦材料科学与技术研究所）；Italian Institute of Technology（意大利理工学院）；University of Cagliari（卡利亚里大学）
We report measurements of antiferromagnetic resonances in the van der Waals easy-axis antiferromagnet CrSBr. The interlayer exchange field and magnetocrystalline anisotropy fields are comparable to laboratory magnetic fields, allowing a rich variety of gigahertz-frequency dynamical modes to be accessed. By mapping the resonance frequencies as a function of the magnitude and angle of applied magnetic field we identify the different regimes of antiferromagnetic dynamics. The spectra show good agreement with a Landau-Lifshitz model for two antiferromagnetically-coupled sublattices, accounting for…
The recent non-local correlation functional of Vydrov and van Voorhis[J. Chem. Phys. 133, 244103 (2010)] is investigated and two new versions of the functional are suggested as being appropriate for describing van der Waals interactions in solids. A refitting of the original functional is demonstrated to result in very accurate interlayer binding energies for weakly bonded layered solids. A VV10 functional based on the generalized gradient approximation by Armiento and Mattsson[Phys. Rev. B 72, 085108 (2005)], while performing slightly worse for interlayer binding is highly successful in descr…
