Pressure Dependence of Intra- and Interlayer Excitons in 2H-MoS2 Bilayers.

The optical and electronic properties of multilayer transition metal dichalcogenides differ significantly from their monolayer counterparts due to interlayer interactions. The separation of individual layers can be tuned in a controlled way by applying pressure. Here, we use a diamond anvil cell to compress bilayers of 2H-MoS2 in the gigapascal range. By measuring optical transmission spectra, we find that increasing pressure leads to a decrease in the energy splitting between the A and the interlayer exciton. Comparing our experimental findings with ab initio calculations, we conclude that the observed changes are not due to the commonly assumed hydrostatic compression. This effect is attributed to the MoS2 bilayer adhering to the diamond, which reduces the in-plane compression. Moreover, we demonstrate that the distinct real-space distributions and resulting contributions from the valence band account for the different pressure dependencies of the inter- and intralayer excitons in compressed MoS2 bilayers.

The Bulk van der Waals Layered Magnet CrSBr is a Quasi-1D Material.

Correlated quantum phenomena in one-dimensional (1D) systems that exhibit competing electronic and magnetic order are of strong interest for the study of 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 for 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 mXe/mYe ∼ 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 to that of metallic carbon nanotubes. Moreover, because of 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.

Covalent photofunctionalization and electronic repair of 2H-MoS2via nitrogen incorporation.

A route towards covalent functionalization of chemically inert 2H-MoS2 exploiting sulfur vacancies is explored by means of (TD)DFT and GW/BSE calculations. Functionalization via nitrogen incorporation at sulfur vacancies is shown to result in more stable covalent binding than via thiol incorporation. In this way, defective monolayer MoS2 is repaired and the quasiparticle band structure as well as the remarkable optical properties of pristine MoS2 are restored. Hence, defect-free functionalization with various molecules is possible. Our results for covalently attached azobenzene, as a prominent photo-switch, pave the way to create photoresponsive two-dimensional (2D) materials.

Electrical tuning of optically active interlayer excitons in bilayer MoS2.

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.

Valley-Dependent Interlayer Excitons in Magnetic WSe2/CrI3.

Heterostructures of two-dimensional transition-metal dichalcogenides and ferromagnetic substrates are important candidates for the development of viable new spin- or valleytronic devices. For the prototypical bilayer of WSe2 on top of a ferromagnetic layer of CrI3, we find substantially different coupling of both WSe2 K-valleys to the sublayer. Besides an energy splitting of a few meV, the corresponding excitons have significantly different interlayer character with charge transfer allowed at the K̅- point but forbidden at K̅+. The different exciton wave functions result in a distinctly different response to magnetic fields with g factors of about -4.4 and -4.0, respectively. By means of ab initio GW/Bethe-Salpeter equation calculations, these findings establish g factors as tool for investigating the exciton character and shedding light on the detailed quantum-mechanical interplay of magnetic and optical properties which are essential for the targeted development of optoelectronic devices.

Subsystem-Based GW/Bethe-Salpeter Equation.

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.

Strain tuning of the Stokes shift in atomically thin semiconductors.

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.

Ab Initio Studies of Exciton g Factors: Monolayer Transition Metal Dichalcogenides in Magnetic Fields.

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 (MoS_{2}, MoSe_{2}, MoTe_{2}, WS_{2}, and WSe_{2}) with strongly bound excitons for which g factors are weakened by about 30%.

Light-matter interaction in van der Waals hetero-structures.

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 hetero-structures with a focus on hetero-bilayers made of monolayers of semiconducting transition metal dichalcogenides. Experimental and theoretical techniques to investigate those hetero-bilayers are introduced. Most recent findings focusing on different transition metal dichalcogenides hetero-structures are presented and possible optical transitions between different valleys, appearance of moiré patterns and signatures of moiré 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.

Excited-State Trions in Monolayer WS_{2}.

We discover an excited bound three-particle state, the 2s trion, appearing energetically below the 2s exciton in monolayer 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.

Classifying the Electronic and Optical Properties of Janus Monolayers.

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.

Erratum: Three-Particle Correlation from a Many-Body Perspective: Trions in a Carbon Nanotube [Phys. Rev. Lett. 116, 196804 (2016)].

This corrects the article DOI: 10.1103/PhysRevLett.116.196804.

Valley-contrasting optics of interlayer excitons in Mo- and W-based bulk transition metal dichalcogenides.

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.

Interlayer Excitons with Large Optical Amplitudes in Layered van der Waals Materials.

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.

Interlayer Trions in the MoS2/WS2 van der Waals Heterostructure.

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.

Diversity of trion states and substrate effects in the optical properties of an MoS2 monolayer.

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.

Publisher Correction: Interlayer excitons in a bulk van der Waals semiconductor.

A correction to this article has been published and is linked from the HTML version of this article.

Huge Trionic Effects in Graphene Nanoribbons.

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.