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Interlayer (IL) excitons, comprising electrons and holes residing in different layers of van der Waals bonded two-dimensional semiconductors, have opened new opportunities for room-temperature excitonic devices. So far, two-dimensional IL excitons have been realized in heterobilayers with type-II band alignment. However, the small oscillator strength of the resulting IL excitons and difficulties with producing heterostructures with definite crystal orientation over large areas have challenged the practical applicability of this design. Here, following the theoretical prediction and recent experimental confirmation of the existence of IL excitons in bilayer MoS2, we demonstrate the electrical control of such excitons up to room temperature. We find that the IL excitonic states preserve their large oscillator strength as their energies are manipulated by the electric field. We attribute this effect to the mixing of the pure IL excitons with intralayer excitons localized in a single layer. By applying an electric field perpendicular to the bilayer MoS2 crystal plane, excitons with IL character split into two peaks with an X-shaped field dependence as a clear fingerprint of the shift of the monolayer bands with respect to each other. Finally, we demonstrate the full control of the energies of IL excitons distributed homogeneously over a large area of our device. The existence of interlayer excitons with strong oscillator strength in bilayer MoS2 enables their electrical manipulation up to room temperature.

We analyze a data set comprising 370 GW band structures composed of 61716 quasiparticle (QP) energies of two-dimensional (2D) materials spanning 14 crystal structures and 52 elements. The data results from PAW plane wave based one-shot G$_0$W$_0$@PBE calculations with full frequency integration. We investigate the distribution of key quantities like the QP self-energy corrections and renormalization factor $Z$ and explore their dependence on chemical composition and magnetic state. The linear QP approximation is identified as a significant error source and propose schemes for controlling and drastically reducing this error at low computational cost. We analyze the reliability of the $1/N_\text{PW}$ basis set extrapolation and find that is well-founded with narrow distributions of $r^2$ peaked very close to 1. Finally, we explore the validity of the scissors operator approximation concluding that it is generally not valid for reasonable error tolerances. Our work represents a step towards the development of automatized workflows for high-throughput G$_0$W$_0$ band structure calculations for solids., Comment: 11 pages, 9 figures, 1 table

Atomically thin layers of transition metal dichalcogenides (TMDC) have exceptional optical properties, exhibiting a characteristic absorption and emission at excitonic resonances. Due to their extreme flexibility, strain can be used to alter the fundamental exciton energies and line widths of TMDCs. Here, we report on the Stokes shift, i.e. the energetic difference of light absorption and emission, of the A exciton in TMDC mono- and bilayers. We demonstrate that mechanical strain can be used to tune the Stokes shift. We perform optical transmission and photoluminescence (PL) experiments on mono- and bilayers and apply uniaxial tensile strain of up to 1.2% in MoSe2 and WS2 bilayers. An A exciton red shift of -38 meV/% and -70 meV/% is found in transmission in MoSe2 and WS2, while smaller values of -27 meV/% and -62 meV/% are measured in PL, respectively. Therefore, a reduction of the Stokes shift is observed under increasing tensile strain. At the same time, the A exciton PL line widths narrow significantly with -14 meV/% (MoSe2) and -21 meV/% (WS2), demonstrating a drastic change in the exciton-phonon interaction. By comparison with ab initio calculations, we can trace back the observed shifts of the excitons to changes in the electronic band structure of the materials. Variations of the relative energetic positions of the different excitons lead to a decrease of the exciton-phonon coupling. Furthermore, we identify the indirect exciton emission in bilayer WS2 as the ΓK transition by comparing the experimental and theoretical gauge factors.

Subsystem Density-Functional Theory and its extension to excited states, namely, subsystem Time-Dependent Density-Functional Theory, have been proven to be efficient and accurate fragmentation approaches for ground and excited states. In the present study we extend this approach to the subsystem-based description of total systems by means of GW and the Bethe-Salpeter equation (BSE). For this, we derive the working equations starting from a subsystem-based partitioning of the screened-Coulomb interaction for an arbitrary number of subsystems. Making use of certain approximations, we develop a parameter-free approach in which environmental screening contributions are effectively included for each subsystem. We demonstrate the applicability of these approximations by comparing quasi-particle energies and excitation energies from subsystem-based GW/BSE calculations to the supermolecular reference. Furthermore, we demonstrate the computational efficiency and the usefulness of this method for the description of photoinduced processes in complex chemical environments.

Photoreflectance (PR) spectrum of bulk $2H\text{\ensuremath{-}}{\mathrm{MoS}}_{2}$ at energies around its direct band gap is shown to have at least three distinct spectral features over a certain temperature range, although only two are seen in absorption and reflectance spectra. These observations are compared with results from many-body perturbation theory band structure calculations that include exciton formation through the Bethe-Salpeter equation. Apart from the ground state $A\phantom{\rule{4pt}{0ex}}(n=1)$ exciton transition around 1.92 eV at 25 K, the next spectral feature around 1.96 eV, whose origin has been much debated, is identified here with a transition $I$ with strong interlayer contributions. Its greater sensitivity to electric fields is established through electroreflectance measurements. The third one around 1.99 eV, which is prominent only in PR, is shown to arise from the first excited state $A\phantom{\rule{4pt}{0ex}}(n=2)$ exciton transition. We discuss the previously unexplained observation as to why the $A\phantom{\rule{4pt}{0ex}}(n=2)$ feature dominates the PR spectrum at high temperatures. The $A$ exciton is shown to have a quasi-two-dimensional (2D) nature with binding energy of $77\ifmmode\pm\else\textpm\fi{}3$ meV under a 2D hydrogenic exciton model.

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 recent discovery of ferromagnetic two-dimensional material has moved the subject of 2D magnetism into the center of interest. Besides materials with intrinsic magnetic properties, nonmagnetic 2D materials in the proximity of bulk magnets or in heterostructures have been proposed as candidates. By breaking the time-reversal symmetry the energy degeneracy is lifted and allows for an independent manipulation of different valleys in the band structure. In contrast to these systems, magnetic adsorbates allow for an easy manipulation and a huge variety of molecular magnets has already been identified. In this work we study the interaction of magnetic molecules adsorbed on the transitions metal dichalcogenide monolayer ${\mathrm{MoS}}_{2}$ by performing first-principles $GW$ and Bethe-Salpeter equation calculations. For the (spin-polarized) triplet ${\mathrm{O}}_{2}$ on ${\mathrm{MoS}}_{2}$ we find that both the electronic band structure close to the band edges as well as the low-energy excitons localized at different valleys obtain a small splitting which should be measurable by circular polarized light. Its size ranges up to about 10 meV and can be controlled by different coverages or by the distance dependent overlap.

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.

Recently, spatially indirect ("interlayer") excitons have been discovered in bulk 2H-MoTe2. They are theoretically predicted to exist in other Mo-based transition metal dichalcogenides (TMDCs) and are expected to be present in W-based TMDCs as well. We investigate interlayer excitons (XIL) in bulk 2H-MoSe2 and 2H-WSe2 using valley-resolved magneto-reflectance spectroscopy under high magnetic fields of up to 29 T combined with ab initio GW-BSE calculations. In the experiments, we observe interlayer excitons in MoSe2, while their signature is surprisingly absent in WSe2. In the calculations, we find that interlayer excitons exist in both Mo- and W-based TMDCs. However, their energetic positions and their oscillator strengths are remarkably different. In Mo-based compounds, the interlayer exciton resonance XIL is clearly separated from the intralayer exciton X1sA and has a high amplitude. In contrast, in W-based compounds, XIL is close in energy to the intralayer A exciton X1sA and possesses a small oscillator strength, which explains its absence in the experimental data of WSe2. Our combined experimental and theoretical observations demonstrate that interlayer excitons can gain substantial oscillator strength by mixing with intralayer states and hence pave the way for exploring interlayer exciton physics in Mo-based bulk transition metal dichalcogenides.

One- and two-dimensional materials are being intensively investigated due to their interesting properties for next-generation optoelectronic devices. Among these, armchair-edged graphene nanoribbons are very promising candidates with optical properties that are dominated by excitons. In the presence of additional charges, trions (i.e., charged excitons) can occur in the optical spectrum. With our recently developed first-principle many-body approach (Phys. Rev. Lett. 116, 196804), we predict strongly bound trions in free-standing nanoribbons with large binding energies of 140-660 meV for widths of 14.6-3.6 Å. Both for the trions and for the excitons, we observe an almost linear dependency of their binding energies on the band gap. We observe several trion states with different character derived from the corresponding excitons. Because of the large bindings energies, this opens a route to applications by which optical properties are easily manipulated, for example, by electrical fields.

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.

Atomically thin materials such as graphene or MoS2 are of high in-plane symmetry. Crystals with reduced symmetry hold the promise for novel optoelectronic devices based on their anisotropy in current flow or light polarization. Here, we present polarization-resolved optical transmission and photoluminescence spectroscopy of excitons in 1T′-ReSe2. On reducing the crystal thickness from bulk to a monolayer, we observe a strong blue shift of the optical band gap from 1.37 to 1.50 eV. The excitons are strongly polarized with dipole vectors along different crystal directions, which persist from bulk down to monolayer thickness. The experimental results are well reproduced by ab initio calculations based on the GW-BSE approach within LDA+GdW approximation. The excitons have high binding energies of 860 meV for the monolayer and 120 meV for bulk. They are strongly confined within a single layer even for the bulk crystal. In addition, we find in our calculations a direct band gap in 1T′-ReSe2 regardless of crysta...

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.

We discover an excited bound three-particle state, the $2s$ trion, appearing energetically below the $2s$ exciton in monolayer ${\mathrm{WS}}_{2}$, using absorption spectroscopy and ab initio GW and Bethe-Salpeter equation calculations. The measured binding energy of the $2s$ trion (22 meV) is smaller compared to the $1s$ intravalley and intervalley trions (37 and 31 meV). With increasing temperature, the $1s$ and $2s$ trions transfer their oscillator strengths to the respective neutral excitons, establishing an optical fingerprint of trion-exciton resonance pairs. Our discovery underlines the importance of trions for the entire excitation spectrum of two-dimensional semiconductors.

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.

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.

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.

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.

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

In this paper we review a recently introduced microscopy technique, scanning quantum dot microscopy (SQDM), which delivers quantitative maps of local electrostatic potential near surfaces in three dimensions. The key to achieving SQDM imaging is the functionalization of a scanning probe microscope tip with a π-conjugated molecule that acts as a gateable QD. Mapping of electrostatic potential with SQDM is performed by gating the QD by the bias voltage applied to the scanning probe microscope junction and registering changes of the QD charge state with frequency-modulated atomic force microscopy.

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.