Search

Correlated quantum phenomena in one-dimensional (1D) systems that exhibit competing electronic and magnetic order are of strong interest for studying fundamental interactions and excitations, such as Tomonaga-Luttinger liquids and topological orders and defects with properties completely different from the quasiparticles expected in their higher-dimensional counterparts. However, clean 1D electronic systems are difficult to realize experimentally, particularly magnetically ordered systems. Here, we show that the van der Waals layered magnetic semiconductor CrSBr behaves like a quasi-1D material embedded in a magnetically ordered environment. The strong 1D electronic character originates from the Cr-S chains and the combination of weak interlayer hybridization and anisotropy in effective mass and dielectric screening with an effective electron mass ratio of $m^e_X/m^e_Y \sim 50$. This extreme anisotropy experimentally manifests in strong electron-phonon and exciton-phonon interactions, a Peierls-like structural instability and a Fano resonance from a van Hove singularity of similar strength of metallic carbon nanotubes. Moreover, due to the reduced dimensionality and interlayer coupling, CrSBr hosts spectrally narrow (1 meV) excitons of high binding energy and oscillator strength that inherit the 1D character. Overall, CrSBr is best understood as a stack of weakly hybridized monolayers and appears to be an experimentally attractive candidate for the study of exotic exciton and 1D correlated many-body physics in the presence of magnetic order., main: 16 pages, 5 figures; SI: 15 pages, 9 figures

In contrast to the intensively investigated transition metal dichalcogenides like MoS2, ReS2 crystals possess a reduced in-plane symmetry, leading to anisotropic optical properties. Here, we report on the impact of strain on the Raman response of a ReS2 monolayer. Since mechanical strain can be used to shift the Raman-active phonon frequencies, we apply uniaxial tensile strain of up to 0.74% along the Re-chain direction (x axis) of the atomically thin crystal and measure the Raman response with the scattered light polarized parallel and perpendicular to the strain direction along the x axis. Complementarily, we carry out ab initio calculations to determine the phonon energies and Raman intensities under strain. We find a shift to lower energies for all phonon modes when tensile strain is applied to the monolayer. The determined gauge factors/Grüneisen parameters are in good agreement between experiment and theory. Our study demonstrates that the optomechanical properties of ReS2 can be tuned by external straining, which is of importance for potential future strain-sensor applications, e.g., in the biomedical sector.

The C2DB is a highly curated open database organizing a wealth of computed properties for more than 4000 atomically thin two-dimensional (2D) materials. Here we report on new materials and properties that were added to the database since its first release in 2018. The set of new materials comprise several hundred monolayers exfoliated from experimentally known layered bulk materials, (homo)bilayers in various stacking configurations, native point defects in semiconducting monolayers, and chalcogen/halogen Janus monolayers. The new properties include exfoliation energies, Bader charges, spontaneous polarisations, Born charges, infrared polarisabilities, piezoelectric tensors, band topology invariants, exchange couplings, Raman- and second harmonic generation spectra. We also describe refinements of the employed material classification schemes, upgrades of the computational methodologies used for property evaluations, as well as significant enhancements of the data documentation and provenance. Finally, we explore the performance of Gaussian process-based regression for efficient prediction of mechanical and electronic materials properties. The combination of open access, detailed documentation, and extremely rich materials property data sets make the C2DB a unique resource that will advance the science of atomically thin materials., Comment: 30 pages, 26 figures

We perform absorption and photoluminescence spectroscopy of trions in hBN-encapsulated WSe$_2$, WS$_2$, MoSe$_2$, and MoS$_2$ monolayers, depending on temperature. The different trends for W- and Mo-based materials are excellently reproduced considering a Fermi-Dirac distribution of bright and dark trions. We find a dark trion, $\rm{X_D^-}$ 19 meV $\textit{below}$ the lowest bright trion, $\rm{X}_1^-$ in WSe$_2$ and WS$_2$. In MoSe$_2$, $\rm{X_D^-}$ lies 6 meV $\textit{above}$ $\rm{X}_1^-$, while $\rm{X_D^-}$ and $\rm{X}_1^-$ almost coincide in MoS$_2$. Our results agree with GW-BSE $\textit{ab-initio}$ calculations and quantitatively explain the optical response of doped monolayers with temperature., Comment: 16 pages including supporting information, 4 figures in the main text, 10 figures in the supporting information

The effect of a magnetic field on the optical absorption in semiconductors has been measured experimentally and modeled theoretically for various systems in previous decades. We present a new first-principles approach to systematically determine the response of excitons to magnetic fields, i.e., exciton $g$ factors. By utilizing the $GW$-Bethe-Salpeter equation methodology we show that $g$ factors extracted from the Zeeman shift of electronic bands are strongly renormalized by many-body effects which we trace back to the extent of the excitons in reciprocal space. We apply our approach to monolayers of transition metal dichalcogenides (${\mathrm{MoS}}_{2}$, ${\mathrm{MoSe}}_{2}$, ${\mathrm{MoTe}}_{2}$, ${\mathrm{WS}}_{2}$, and ${\mathrm{WSe}}_{2}$) with strongly bound excitons for which $g$ factors are weakened by about 30%.

Vertically stacked two-dimensional materials form an ideal platform for controlling and exploiting light-matter interactions at the nanoscale. As a unique feature, these materials host electronic excitations of both intra- and interlayer type with distinctly different properties. In this Letter, using first-principles many-body calculations, we provide a detailed picture of the most prominent excitons in bilayer MoS2, a prototypical van der Waals material. By applying an electric field perpendicular to the bilayer, we explore the evolution of the excitonic states as the band alignment is varied from perfect line-up to staggered (Type II) alignment. For moderate field strengths, the lowest exciton has intralayer character and is almost independent of the electric field. However, we find higher lying excitons that have interlayer character. They can be described as linear combinations of the intralayer B exciton and optically dark charge transfer excitons, and interestingly, these mixed interlayer excitons have strong optical amplitude and can be easily tuned by the electric field. The first-principles results can be accurately reproduced by a simple excitonic model Hamiltonian that can be straightforwardly generalized to more complex van der Waals materials.

Electronic excitations in van der Waals heterostructures can have interlayer or intralayer character depending on the spatial localization of the involved charges (electrons and holes). In the case of neutral electron-hole pairs (excitons), both types of excitations have been explored theoretically and experimentally. In contrast, studies of charged trions have so far been limited to the intralayer type. Here we investigate the complete set of interlayer excitations in a MoS2/WS2 heterostructure using a novel ab initio method, which allows for a consistent treatment of both excitons and trions at the same theoretical footing. Our calculations predict the existence of bound interlayer trions below the neutral interlayer excitons. We obtain binding energies of 18/28 meV for the positive/negative interlayer trions with both electrons/holes located on the same layer. In contrast, a negligible binding energy is found for trions which have the two equally charged particles on different layers. Our results advance the understanding of electronic excitations in doped van der Waals heterostructures and their effect on the optical properties.

We present an extension of the tunneling theory for scanning tunneling microcopy (STM) to include different types of vibrational-electronic couplings responsible for inelastic contributions to the tunnel current in the strong-coupling limit. It allows for a better understanding of more complex scanning tunneling spectra of molecules on a metallic substrate in separating elastic and inelastic contributions. The starting point is the exact solution of the spectral functions for the electronic active local orbitals in the absence of the STM tip. This includes electron-phonon coupling in the coupled system comprising the molecule and the substrate to arbitrary order including the anti-adiabatic strong coupling regime as well as the Kondo effect on a free electron spin of the molecule. The tunneling current is derived in second order of the tunneling matrix element which is expanded in powers of the relevant vibrational displacements. We use the results of an ab-initio calculation for the single-particle electronic properties as an adapted material-specific input for a numerical renormalization group approach for accurately determining the electronic properties of a NTCDA molecule on Ag(111) as a challenging sample system for our theory. Our analysis shows that the mismatch between the ab-initio many-body calculation of the tunnel current in the absence of any electron-phonon coupling to the experiment scanning tunneling spectra can be resolved by including two mechanisms: (i) a strong unconventional Holstein term on the local substrate orbital leads to reduction of the Kondo temperature and (ii) a different electron-vibrational coupling to the tunneling matrix element is responsible for inelastic steps in the $dI/dV$ curve at finite frequencies., 34 pages, 26 figure

Inspired by the recent synthesis of monolayer MoSSe, we conduct a first-principles high-throughput investigation of 216 MXY Janus monolayers consisting of a middle layer of metal atoms (M) sandwiched between different types of chalcogen, halogen, or pnictogen atoms (X,Y). Using density functional theory and many-body perturbation theory, we perform an exhaustive computational characterization of the 70 most stable semiconducting monolayers. These are found to exhibit diverse and fascinating properties including finite out-of-plane dipoles, giant Rashba-splittings, direct and indirect band gaps ranging from 0.7 to 3.0 eV, large exciton binding energies, and very strong light-matter interactions. The data have been generated using the workflow behind the Computational 2D Materials Database and are freely available online. Our work expands the class of known Janus monolayers and points to several potentially synthesizable structures, which could be interesting candidates for valley- or optoelectronic applications or for generating out-of-plane electric fields to control charge transfer, charge separation, or band alignments in van der Waals heterostructures.

Optical experiments on nanostructures such as molecules, one- or two-dimensional materials, are often performed with the nanostructures in close proximity of a substrate or some other polarizable media. In this case, the Bethe-Salpeter equation (BSE) can be used to calculate the optical excitations of the nanostructure by including the effect of the substrate via the screened electron-hole interaction. Here we show, that in such an approach, where the states of the substrate are not explicitly included in the BSE Hamiltonian but only enter through the screened Coulomb interaction, it is important also to screen the electron-hole exchange interaction. For the case of molecules like benzene physisorbed on the metallic Au(111) surface, the screening of the exchange interaction by the substrate redshifts the lowest optical transition by up to 300 meV. Furthermore, the screening of the exchange is essential in order to obtain the correct ordering of the size of quasiparticle and optical energy gap.

Weakly bound systems, like noble-gas dimers or two-dimensional layered materials (graphite, hexagonal boron nitride, or transition-metal dichalcogenides), exhibit excited electronic states of a particular nature. These so-called exciplex states combine on-site (or intralayer) and charge-transfer (or interlayer) configurations in a well-balanced way. We show by ab initio many-body perturbation theory that the energy and composition of the exciplex states depend sensitively on the bond length or interlayer distance of the material. When the constituents approach each other, the charge-transfer contribution increases and the excitation is redshifted to lower energy. If the system is excited into the exciplex state, then a covalent-like bond results. In consequence, noble-gas dimers form excimer complexes, while layered materials exhibit interlayer contraction.

We have performed a computational screening of topological two-dimensional (2D) materials from the Computational 2D Materials Database (C2DB) employing density functional theory. A full ab initio scheme for calculating hybrid Wannier functions directly from the Kohn-Sham orbitals has been implemented and the method was used to extract Z2 indices, Chern numbers, and mirror Chern numbers of 3331 2D systems including both experimentally known and hypothetical 2D materials. We have found a total of 48 quantum spin Hall insulators, seven quantum anomalous Hall insulators, and 21 crystalline topological insulators. Roughly 75% are predicted to be dynamically stable and one-third was known prior to the screening. The most interesting of the topological insulators are investigated in more detail. We show that the calculated topological indices of the quantum anomalous Hall insulators are highly sensitive to the approximation used for the exchange-correlation functional and reliable predictions of the topological properties of these materials thus require methods beyond density functional theory. We also performed GW calculations, which yield a gap of 0.65 eV for the quantum spin Hall insulator PdSe2 in the MoS2 crystal structure. This is significantly higher than any known 2D topological insulator and three times larger than the Kohn-Sham gap.

In his comment Maździarz 2019 (2D Mater. 6 048001) raises doubts concerning the reliability of our test for dynamical (in particular elastic) stability of monolayer materials, which neglects the shear components of the stiffness tensor and only considers the sign of the planar stiffness coefficients. We agree that our analysis has not been complete, but find that it suffices in practice except for very few cases (less than 1% of the materials). Nevertheless, for completeness we are currently calculating the shear components of the elastic tensor for all the materials in the C2DB.

Even if individual two-dimensional materials own various interesting and unexpected properties, the stacking of such layers leads to van der Waals solids which unite the characteristics of two dimensions with novel features originating from the interlayer interactions. In this topical review, we cover fabrication and characterization of van der Waals heterosructures with a focus on heterobilayers made of monolayers of semiconducting transition metal dichalcogenides. Experimental and theoretical techniques to investigate those heterobilayers are introduced. Most recent findings focusing on different transition metal dichalcogenides heterostructures are presented and possible optical transitions between different valleys, appearance of moire patterns and signatures of moire excitons are discussed. The fascinating and fast growing research on van der Waals hetero-bilayers provide promising insights required for their application as emerging quantum-nano materials., 14 pages, 6 figures

Results of optical spectroscopy studies on bulk $2H\ensuremath{-}{\mathrm{WS}}_{2}$ at energies close to its direct band gap are presented. Reflectance and absorption measurements at low temperature show only one dominant feature due to the $A$ exciton of bulk ${\mathrm{WS}}_{2}$ at $\ensuremath{\sim}2.02$ eV. However, a laser-modulated photoreflectance spectrum looks quite different, revealing a second even stronger feature ${A}^{*}\ensuremath{\sim}62$ meV above $A$. The relative intensity of these two features is shown to change significantly in a lateral electroreflectance measurement with electric field applied perpendicular to the c axis of ${\mathrm{WS}}_{2}$. The experimental results are analyzed by comparison with many-body perturbation theory calculations, including the solutions of the Bethe-Salpeter equation. ${A}^{*}$ is identified as the first excited state of the $A$ exciton, that is, $A(n=2)$. The anomalous behavior of ${A}^{*}$ is explained by its distinct wave function spread along the c axis, the direction of weak van der Waals bonding, which makes it more susceptible to perturbations. Our ab initio calculations suggest that the $A$ exciton in the ground state has a two-dimensional (2D) nature with a large binding energy ${E}_{\text{b}}$, in fair agreement with ${E}_{\text{b}}\phantom{\rule{4pt}{0ex}}\ensuremath{\sim}90\ifmmode\pm\else\textpm\fi{}20$ meV estimated from a temperature-dependent reflectance study. The applicability of the 2D hydrogenic Wannier-Mott model for the exciton spectrum of a layered semiconductor like bulk ${\mathrm{WS}}_{2}$ is discussed.

We study the neutral and charged optical excitations (excitons and trion) in the prototypical wide-gap insulator LiF using the first-principles $GW/\mathrm{BSE}$ approach and its extension for trions. In addition to neutral excitons we find bound trion states with a trion binding energy of 20--30 meV. At the same time the lowest bright exciton and trion are well separated by about 400 meV in the absorption spectrum both for the bulk and the (001) surface crystal. Even though the charged trions are slightly more extended compared to their neutral counterparts, they remain localized on a few atoms only and keep the Frenkel-like character of the neutral excitons. With such strongly localized trions, LiF stands out from currently investigated trionic materials and highlights itself for further studies.

Monolayers of transition metal dichalcogenides (TMDCs) have unique optoelectronic properties. Density functional theory allows only for a limited description of the electronic excitation energies in these systems, while a more advanced treatment within many-body perturbation theory employing the $\mathit{GW}/\mathrm{BSE}$ approximation is often rather time consuming. Here, we show that the recently developed $\mathrm{LDA}+\mathit{GdW}$ approach provides an efficient and at the same time reliable description of one-particle energies, as well as optical properties including bound excitons in TMDCs. For five exemplary materials (${\mathrm{MoSe}}_{2}, {\mathrm{MoS}}_{2}, {\mathrm{WSe}}_{2}, {\mathrm{WS}}_{2}$, and ${\mathrm{ReSe}}_{2}$), we discuss the numerical convergence, in particular with respect to k-point sampling, and show that the $\mathit{GdW}/\mathrm{BSE}$ approximation gives results similar to common $\mathit{GW}/\mathrm{BSE}$ calculations. Such efficient approaches are essential to treat larger multilayer systems or defects.

Black phosphorus (bP) is a promising two-dimensional (2D) material for opto-electronic applications. Strongly bound excitons with binding energies up to 0.3 eV and remarkably large trion binding energies up to 100 meV have been observed for supported monolayer bP. Surprisingly, this trion binding energy is significantly larger than those found in other 2D materials (e.g. about 30 meV in transition metal dichalcogenides). This has previously been ascribed to the quasi-1D nature of bP. In this work we show, using first principles calculations, that the trion binding energy of bP is indeed large (80 meV) when referenced to the lowest bright exciton but only 30 meV when its energy is measured relative to the lowest dark exciton. Our analysis thus shows that the trion binding energy in bP is not larger than in other 2D materials, and the previous conclusions have to be understood incorporating the large splitting between the dark and bright excitons in bP. We also explore the effect of substrate and in-plane strain of the exciton and trion binding energies and show that these effects do not change the main conclusions. Our results correct the misconception that trion binding energies in monolayer bP are particularly large due to its quasi-1D structure and contribute to the establishment of more a detailed understanding of optical properties of atomically thin semiconductors.

Monolayers of transition metal dichalcogenides (TMDCs) possess unique optoelectronic properties, including strongly bound excitons and trions. To date, most studies have focused on optically active excitations, but recent experiments have highlighted the existence of dark states, which are equally important in many respects. Here, we use ab initio many-body calculations to unravel the nature of the dark excitations in monolayer MoSe2, MoS2, WSe2, andWS(2). Our results show that all these monolayer TMDCs host dark states as their lowest neutral and charged excitations. We further show that dark excitons possess larger binding energies than their bright counterparts while the opposite holds for trions.

Bound electron–hole pairs called excitons govern the electronic and optical response of many organic and inorganic semiconductors. Excitons with spatially displaced wave functions of electrons and holes (interlayer excitons) are important for Bose–Einstein condensation, superfluidity, dissipationless current flow, and the light-induced exciton spin Hall effect. Here we report on the discovery of interlayer excitons in a bulk van der Waals semiconductor. They form due to strong localization and spin-valley coupling of charge carriers. By combining high-field magneto-reflectance experiments and ab initio calculations for 2H-MoTe2, we explain their salient features: the positive sign of the g-factor and the large diamagnetic shift. Our investigations solve the long-standing puzzle of positive g-factors in transition metal dichalcogenides, and pave the way for studying collective phenomena in these materials at elevated temperatures., Excitons, quasi-particles of bound electron-hole pairs, are at the core of the optoelectronic properties of layered transition metal dichalcogenides. Here, the authors unveil the presence of interlayer excitons in bulk van der Waals semiconductors, arising from strong localization and spin-valley coupling of charge carriers.

Almost all experiments and future applications of transition metal dichalcogenide monolayers rely on a substrate for mechanical stability, which can significantly modify the optical spectra of the monolayer. Doping from the substrate might lead to the domination of the spectra by trions. Here we show by ab initio many-body theory that the negative trion (A−) splits into three excitations, with both inter- and intra-valley character, while the positive counterpart (A+) consists of only one inter-valley excitation. Furthermore, the substrate enhances the screening, which renormalizes both band gap and exciton as well as the trion-binding energies. We verify that these two effects do not perfectly cancel each other, but lead to red-shifts of the excitation energies for three different substrates ranging from a wide-bandgap semiconductor up to a metal. Our results explain recently found experimental splittings of the lowest trion line as well as excitation red-shifts on substrates., The optical and electrical properties of atomically thin transition metal dichalcogenides critically depend on the underlying substrate. Here, the authors develop an abinitio many-body formalism to investigate the full spectrum of negative and positive trions in these layered semicondutors.

Due to their unique band structure, single layers of transition metal dichalcogenides are promising for new atomic-scale physics and devices. It has been shown that the band structure and the excitonic transitions can be tuned by straining the material. Recently, the discovery of single-photon emission from localized excitons has put monolayer WSe2 in the spotlight. The localized light emitters might be related to local strain potentials in the monolayer. Here, we measure strain-dependent energy shifts for the A, B, C, and D excitons for uniaxial tensile strain up to 1.4% in monolayer WSe2 by performing absorption measurements. A gauge factor of and is derived for the A, B, C, and D exciton, respectively. These values are in good agreement with ab initio GW-BSE calculations. Furthermore, we examine the spatial strain distribution in the WSe2 monolayer at different applied strain levels. We find that the size of the monolayer is crucial for an efficient transfer of strain from the substrate to the monolayer.

We investigate the adsorption of a single tetracyanoethylene (TCNE) molecule on the silver (001) surface. Adsorption structures, electronic properties, and scanning tunneling microscopy (STM) images are calculated within density-functional theory. Adsorption occurs most favorably in on-top configuration, with the C=C double bond directly above a silver atom and the four N atoms bound to four neighboring Ag atoms. The lowest unoccupied molecular orbital of TCNE becomes occupied due to electron transfer from the substrate. This state dominates the electronic spectrum and the STM image at moderately negative bias. We discuss and employ a spatial extrapolation technique for the calculation of STM and scanning tunneling spectroscopy (STS) images. Our calculated images are in good agreement with experimental data.

Trion states of three correlated particles (e.g., two electrons and one hole) are essential to understand the optical spectra of doped or gated nanostructures, like carbon nanotubes or transition-metal dichalcogenides. We develop a theoretical many-body description for such correlated states using an ab-initio approach. It can be regarded as an extension of the widely used $GW$ method and Bethe-Salpeter equation, thus allowing for a direct comparison with excitons. We apply this method to a semiconducting (8,0) carbon nanotube, and find that the lowest optically active trions are red-shifted by $\sim 130$ meV compared to the excitons, confirming experimental findings for similar tubes. Moreover, our method provides detailed insights in the physical nature of trion states. In the prototypical carbon nanotube we find a variety of different excitations, discuss the spectra, energy compositions, and correlated wave functions., main text, supplement

By means of low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS), we have investigated the adsorption of single Au atoms on a PTCDA monolayer physisorbed on the Au(111) surface. A chemical reaction between the Au atom and the PTCDA molecule leads to the formation of a radical that has an unpaired electron in its highest occupied orbital. This orbital is a $\ensuremath{\pi}$ orbital that extends over the whole Au-PTCDA complex. Because of the large Coulomb repulsion in this orbital, the unpaired electron generates a local moment when the molecule is adsorbed on the Au(111) surface. We demonstrate the formation of the radical and the existence of the local moment after adsorption by observing a zero-bias differential conductance peak that originates from the Kondo effect. By temperature dependent measurements of the zero-bias differential conductance, we determine the Kondo temperature to be ${T}_{\mathrm{K}}=(38\ifmmode\pm\else\textpm\fi{}8)\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. For the theoretical description of the properties of the Au-PTCDA complex we use a hierarchy of methods, ranging from density functional theory (DFT) including a van der Waals correction to many-body perturbation theory (MBPT) and the numerical renormalization group (NRG) approach. Regarding the high-energy orbital spectrum, we obtain an excellent agreement with experiments by both spin-polarized DFT/MBPT and NRG. Moreover, the NRG provides an accurate description of the low-energy excitation spectrum of the spin degree of freedom, predicting a Kondo temperature very close to the experimental value. This is achieved by a detailed analysis of the universality of various definitions of ${T}_{\mathrm{K}}$ and by taking into account the full energy dependence of the coupling function between the molecule-metal complex and the metallic substrate.

Interactions between atomic and molecular objects are to a large extent defined by the nanoscale electrostatic potentials which these objects produce. We introduce a scanning probe technique that enables three-dimensional imaging of local electrostatic potential fields with sub-nanometer resolution. Registering single electron charging events of a molecular quantum dot attached to the tip of a (qPlus tuning fork) atomic force microscope operated at 5 K, we quantitatively measure the quadrupole field of a single molecule and the dipole field of a single metal adatom, both adsorbed on a clean metal surface. Because of its high sensitivity, the technique can record electrostatic potentials at large distances from their sources, which above all will help to image complex samples with increased surface roughness., Comment: main text: 5 pages, 4 figures, supplementary information file: 4 pages, 2 figures

We introduce the Computational 2D Materials Database (C2DB), which organises a variety of structural, thermodynamic, elastic, electronic, magnetic, and optical properties of around 1500 two-dimensional materials distributed over more than 30 different crystal structures. Material properties are systematically calculated by state-of-the art density functional theory and many-body perturbation theory (G$_0\!$W$\!_0$ and the Bethe-Salpeter Equation for $\sim$200 materials) following a semi-automated workflow for maximal consistency and transparency. The C2DB is fully open and can be browsed online or downloaded in its entirety. In this paper, we describe the workflow behind the database, present an overview of the properties and materials currently available, and explore trends and correlations in the data. Moreover, we identify a large number of new potentially synthesisable 2D materials with interesting properties targeting applications within spintronics, (opto-)electronics, and plasmonics. The C2DB offers a comprehensive and easily accessible overview of the rapidly expanding family of 2D materials and forms an ideal platform for computational modeling and design of new 2D materials and van der Waals heterostructures., Comment: Add journal reference and DOI; Minor updates to figures and wording

Monolayers and bilayers of transition metal dichalcogenides (TMDCs) are currently being intensively scrutinized not least due to their rich opto-electronic properties which are governed by strongly bound excitons. Until now the main focus has been on excitons with zero momentum. In this study we employ ab initio many-body perturbation theory within the GW/BSE approximation to describe the entire Q-resolved exciton band structure for mono- and bilayers of the MX2 (M = Mo, W and X = Se, S) TMDCs. We find that the strong excitonic effects, i.e. strong electron-hole interactions, are present throughout the entire Q-space. While the exciton binding energies of the lowest excitons do not vary significantly with Q, we find a strong variation in their coupling strength. In particular, the latter are strongly peaked for excitons at Q = 0 and Q = Λ. For MoX2 monolayers the K → K' excitons constitutes the exciton ground state, while in WX2 monolayers direct transitions at K are lowest in energy. Our calculations further show that the exciton landscape is highly sensitive to strain and interlayer hybridization. For all four bilayers the exciton ground state is shifted to Γ → Λ or K → Λ transitions closely following the trends of the single-particle band structures.