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.

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.

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.

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%.

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.

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.

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.

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.

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.

Highly Anisotropic in-Plane Excitons in Atomically Thin and Bulklike 1T'-ReSe2.

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 crystal thickness, indicating weak interlayer coupling effects on the band gap characteristics. Our results pave the way for polarization-sensitive applications, such as optical logic circuits operating in the infrared spectral region.

Three-particle correlation from a Many-Body Perspective: Trions in a Carbon Nanotube.

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 redshifted by ∼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.

Scanning Quantum Dot Microscopy.

We introduce a scanning probe technique that enables three-dimensional imaging of local electrostatic potential fields with subnanometer resolution. Registering single electron charging events of a molecular quantum dot attached to the tip of an atomic force microscope operated at 5 K, equipped with a qPlus tuning fork, we image the quadrupole field of a single molecule. To demonstrate quantitative measurements, we investigate the dipole field of a single metal adatom adsorbed on a metal surface. We show that because of its high sensitivity the technique can probe electrostatic potentials at large distances from their sources, which should allow for the imaging of samples with increased surface roughness.

Charge-transfer excited states in aqueous DNA: Insights from many-body Green's function theory.

Charge-transfer (CT) excited states play an important role in the excited-state dynamics of DNA in aqueous solution. However, there is still much controversy on their energies. By ab initio many-body Green's function theory, together with classical molecular dynamics simulations, we confirm the existence of CT states at the lower energy side of the optical absorption maximum in aqueous DNA as observed in experiments. We find that the hydration shell can exert strong effects (∼1 eV) on both the electronic structure and CT states of DNA molecules through dipole electric fields. In this case, the solvent cannot be simply regarded as a macroscopic screening medium as usual. The influence of base stacking and base pairing on the CT states is also discussed.

Photoluminescence of single-walled carbon nanotubes: the role of Stokes shift and impurity levels.

Recent experiments have indicated that dopants and defects can trigger new redshifted photoluminescence (PL) peaks below the E11 peak in single-walled carbon nanotubes (SWCNTs). To understand the origin of the new PL peaks, we study theoretically the excited-state properties of SWCNTs with some typical dopants and defects by ab initio many-body perturbation theory. Our calculations demonstrate that the Stokes shift in doped centers can be as large as 170 meV, which is much larger than that of intact SWCNTs and must be taken into account. We find dipole-allowed transitions from localized midgap and shallow impurity levels, which can give rise to pronounced PL peaks. Dark excitons, on the other hand, seem to have oscillator strengths that are too small to account for the new PL peaks.

Electronic excitations of bulk LiCl from many-body perturbation theory.

We present the quasiparticle band structure and the optical excitation spectrum of bulk LiCl, using many-body perturbation theory. Density-functional theory is used to calculate the ground-state geometry of the system. The quasiparticle band structure is calculated within the GW approximation. Taking the electron-hole interaction into consideration, electron-hole pair states and optical excitations are obtained by solving the Bethe-Salpeter equation for the electron-hole two-particle Green function. The calculated band gap is 9.5 eV, which is in good agreement with the experimental result of 9.4 eV. And the calculated optical absorption spectrum, which contains an exciton peak at 8.8 eV and a resonant-exciton peak at 9.8 eV, is also in good agreement with experimental data.

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.

Redshift of excitons in carbon nanotubes caused by the environment polarizability.

Optical excitations of molecular systems can be modified by their physical environment. We analyze the underlying mechanisms within many-body perturbation theory, which is particularly suited to study nonlocal polarizability effects on the electronic structure. Here we focus on the example of a semiconducting carbon nanotube, which observes redshifts of its excitons when the tube is touched by another nanotube or other physisorbates. We show that the redshifts mostly result from the polarizability of the attached ad system. Electronic coupling may enhance the redshifts, but depends very sensitively on the structural details of the contact.

Single-molecule switching with non-contact atomic force microscopy.

We report upon controlled switching of a single 3,4,9,10-perylene tetracarboxylic diimide derivative molecule on a rutile TiO(2)(110) surface using a non-contact atomic force microscope at room temperature. After submonolayer deposition, the molecules adsorb tilted on the bridging oxygen row. Individual molecules can be manipulated by the atomic force microscope tip in a well-controlled manner. The molecules are switched from one side of the row to the other using a simple approach, taking benefit of the sample tilt and the topography of the titania substrate. From density functional theory investigations we obtain the adsorption energies of different positions of the molecule. These adsorption energies are in very good agreement with our experimental observations.

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.