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.

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.

Kekulene: On-Surface Synthesis, Orbital Structure, and Aromatic Stabilization.

We revisit the question of kekulene's aromaticity by focusing on the electronic structure of its frontier orbitals as determined by angle-resolved photoemission spectroscopy. To this end, we have developed a specially designed precursor, 1,4,7(2,7)-triphenanthrenacyclononaphane-2,5,8-triene, which allows us to prepare sufficient quantities of kekulene of high purity directly on a Cu(111) surface, as confirmed by scanning tunneling microscopy. Supported by density functional calculations, we determine the orbital structure of kekulene's highest occupied molecular orbital by photoemission tomography. In agreement with a recent aromaticity assessment of kekulene based solely on C-C bond lengths, we conclude that the π-conjugation of kekulene is better described by the Clar model rather than a superaromatic model. Thus, by exploiting the capabilities of photoemission tomography, we shed light on the question which consequences aromaticity holds for the frontier electronic structure of a π-conjugated molecule.

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.

Electronic Excitations of Polythiophene within Many-Body Perturbation Theory with and without the Tamm-Dancoff Approximation.

Excited electronic states of small and large π-conjugated organic molecules can be described within ab initio many-body perturbation theory, notably by the GW approximation for the electron self-energy operator combined with the Bethe-Salpeter equation for correlated electron-hole excitations. In this context, the Tamm-Dancoff approximation is routinely employed to reduce the computational effort. It is known that the use of this approximation introduces errors of several 100 meV for small organic molecules but is negligible for extended systems. In this paper, we investigate how exactly the transition between these two regimes happens, by calculating the optical excitation energies of a series of polythiophene molecules of different sizes. We determine which parts of the electron-hole interaction are responsible for the deviation and show that the quantitative effects of the Tamm-Dancoff approximation depend sensitively on the size of the electronic system, in particular on the electronic conjugation length.

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.

Thickness-Dependent Differential Reflectance Spectra of Monolayer and Few-Layer MoS2, MoSe2, WS2 and WSe2.

The research field of two dimensional (2D) materials strongly relies on optical microscopy characterization tools to identify atomically thin materials and to determine their number of layers. Moreover, optical microscopy-based techniques opened the door to study the optical properties of these nanomaterials. We presented a comprehensive study of the differential reflectance spectra of 2D semiconducting transition metal dichalcogenides (TMDCs), MoS2, MoSe2, WS2, and WSe2, with thickness ranging from one layer up to six layers. We analyzed the thickness-dependent energy of the different excitonic features, indicating the change in the band structure of the different TMDC materials with the number of layers. Our work provided a route to employ differential reflectance spectroscopy for determining the number of layers of MoS2, MoSe2, WS2, and WSe2.

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.

Molecular Model of a Quantum Dot Beyond the Constant Interaction Approximation.

We present a physically intuitive model of molecular quantum dots beyond the constant interaction approximation. It accurately describes their charging behavior and allows the extraction of important molecular properties that are otherwise experimentally inaccessible. The model is applied to data recorded with a noncontact atomic force microscope on three different molecules that act as a quantum dot when attached to the microscope tip. The results are in excellent agreement with first-principles simulations.

Quantitative assessment of intermolecular interactions by atomic force microscopy imaging using copper oxide tips.

Atomic force microscopy is an impressive tool with which to directly resolve the bonding structure of organic compounds1-5. The methodology usually involves chemical passivation of the probe-tip termination by attaching single molecules or atoms such as CO or Xe (refs 1,6-9). However, these probe particles are only weakly connected to the metallic apex, which results in considerable dynamic deflection. This probe particle deflection leads to pronounced image distortions, systematic overestimation of bond lengths, and in some cases even spurious bond-like contrast features, thus inhibiting reliable data interpretation8-12. Recently, an alternative approach to tip passivation has been used in which slightly indenting a tip into oxidized copper substrates and subsequent contrast analysis allows for the verification of an oxygen-terminated Cu tip13-15. Here we show that, due to the covalently bound configuration of the terminal oxygen atom, this copper oxide tip (CuOx tip) has a high structural stability, allowing not only a quantitative determination of individual bond lengths and access to bond order effects, but also reliable intermolecular bond characterization. In particular, by removing the previous limitations of flexible probe particles, we are able to provide conclusive experimental evidence for an unusual intermolecular N-Au-N three-centre bond. Furthermore, we demonstrate that CuOx tips allow the characterization of the strength and configuration of individual hydrogen bonds within a molecular assembly.

Strain Control of Exciton-Phonon Coupling in Atomically Thin Semiconductors.

Semiconducting transition metal dichalcogenide (TMDC) monolayers have exceptional physical properties. They show bright photoluminescence due to their unique band structure and absorb more than 10% of the light at their excitonic resonances despite their atomic thickness. At room temperature, the width of the exciton transitions is governed by the exciton-phonon interaction leading to strongly asymmetric line shapes. TMDC monolayers are also extremely flexible, sustaining mechanical strain of about 10% without breaking. The excitonic properties strongly depend on strain. For example, exciton energies of TMDC monolayers significantly redshift under uniaxial tensile strain. Here, we demonstrate that the width and the asymmetric line shape of excitonic resonances in TMDC monolayers can be controlled with applied strain. We measure photoluminescence and absorption spectra of the A exciton in monolayer MoSe2, WSe2, WS2, and MoS2 under uniaxial tensile strain. We find that the A exciton substantially narrows and becomes more symmetric for the selenium-based monolayer materials, while no change is observed for atomically thin WS2. For MoS2 monolayers, the line width increases. These effects are due to a modified exciton-phonon coupling at increasing strain levels because of changes in the electronic band structure of the respective monolayer materials. This interpretation based on steady-state experiments is corroborated by time-resolved photoluminescence measurements. Our results demonstrate that moderate strain values on the order of only 1% are already sufficient to globally tune the exciton-phonon interaction in TMDC monolayers and hold the promise for controlling the coupling on the nanoscale.

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.

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