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The equilibrium and non-equilibrium optical properties of single-layer transition metal dichalcogenides (TMDs) are determined by strongly bound excitons. Exciton relaxation dynamics in TMDs have been extensively studied by time-domain optical spectroscopies. However, the formation dynamics of excitons following non-resonant photoexcitation of free electron-hole pairs have been challenging to directly probe because of their inherently fast timescales. Here, we use extremely short optical pulses to non-resonantly excite an electron-hole plasma and show the formation of two-dimensional excitons in single-layer MoS2 on the timescale of 30 fs via the induced changes to photo-absorption. These formation dynamics are significantly faster than in conventional 2D quantum wells and are attributed to the intense Coulombic interactions present in 2D TMDs. A theoretical model of a coherent polarization that dephases and relaxes to an incoherent exciton population reproduces the experimental dynamics on the sub-100-fs timescale and sheds light into the underlying mechanism of how the lowest-energy excitons, which are the most important for optoelectronic applications, form from higher-energy excitations. Importantly, a phonon-mediated exciton cascade from higher energy states to the ground excitonic state is found to be the rate-limiting process. These results set an ultimate timescale of the exciton formation in TMDs and elucidate the exceptionally fast physical mechanism behind this process., The formation dynamics of excitons in 2D transition metal dichalcogenides are challenging to probe directly because of their inherently fast timescales. Here, the authors use extremely short optical pulses to excite an electron-hole plasma, and show the formation of 2D excitons in MoS2 on the timescale of 30 fs.

We present a rigorous quasinormal mode approach to describe the strong coupling behavior between a monolayer of ${\mathrm{MoSe}}_{2}$ and a single gold nanoparticle. The onset of strong coupling, described through a classical spectral mode splitting (analog of vacuum Rabi splitting) is quantified by computing the full three-dimensional hybrid quasinormal modes of the combined structure, allowing one to accurately model light-matter interactions without invoking the usual phenomenological theories of strong coupling. We explore the hybrid quasinormal modes as a function of gap size and temperature, and find spectral splittings in the range of around 80--110 meV, with no fitting parameters for the material models. We also show how the hybrid modes exhibit Fano-like resonances and quantify the complex poles of the hybrid modes as well as the Purcell factor resonances from embedded dipole emitters. The Rabi splitting is found to be larger at elevated temperatures for very small gap separations between the metal nanoparticle and the monolayer, but smaller at elevated temperatures for larger gaps. We also show how these spectral splittings can differ qualitatively from the actual complex poles of the hybrid quasinormal modes.

van der Waals heterostructures composed of transition metal dichalcogenide monolayers (TMDCs) are characterized by their truly rich excitonic properties which are determined by their structural, geometric, and electronic properties: In contrast to pure monolayers, electrons and holes can be hosted in different materials, resulting in highly tunable dipolar many-particle complexes. However, for genuine spatially indirect excitons, the dipolar nature is usually accompanied by a notable quenching of the exciton oscillator strength. Via electric and magnetic field dependent measurements, we demonstrate that a slightly biased pristine bilayer ${\mathrm{MoS}}_{2}$ hosts strongly dipolar excitons, which preserve a strong oscillator strength. We scrutinize their giant dipole moment, and shed further light on their orbital and valley physics via bias-dependent magnetic field measurements.

While valleys (energy extrema) are present in all band structures of solids, their preeminent role in determining exciton resonances and dynamics in atomically thin transition metal dichalcogenides (TMDC) is unique. Using two-dimensional coherent electronic spectroscopy, we find that exciton decoherence occurs on a much faster time scale in MoSe$_2$ bilayers than that in the monolayers. We further identify two population relaxation channels in the bilayer, a coherent and an incoherent one. Our microscopic model reveals that phonon-emission processes facilitate scattering events from the $K$ valley to other lower energy $\Gamma$ and $\Lambda$ valleys in the bilayer. Our combined experimental and theoretical studies unequivocally establish different microscopic mechanisms that determine exciton quantum dynamics in TMDC monolayers and bilayers. Understanding exciton quantum dynamics provides critical guidance to manipulation of spin/valley degrees of freedom in TMDC bilayers., Comment: 6 pages, 4 figures

Enhanced Coulomb interactions in monolayer transition metal dichalcogenides cause tightly bound electron-hole pairs (excitons) that dominate their linear and nonlinear optical response. The latter includes bleaching, energy renormalizations, and higher-order Coulomb correlation effects like biexcitons and excitation-induced dephasing. While the first three are extensively studied, no theoretical footing for excitation-induced dephasing in exciton-dominated semiconductors is available so far. In this Letter, we present microscopic calculations based on excitonic Heisenberg equations of motion and identify the coupling of optically pumped excitons to exciton-exciton scattering continua as the leading mechanism responsible for an optical-power-dependent linewidth broadening (excitation-induced dephasing) and sideband formation. Performing time-, momentum-, and energy-resolved simulations, we quantitatively evaluate the exciton-induced dephasing for the most common monolayer transition metal dichalcogenides and find an excellent agreement with recent experiments.

Excitons, Coulomb-bound electron-hole pairs, are the fundamental excitations governing the optoelectronic properties of semiconductors. While optical signatures of excitons have been studied extensively, experimental access to the excitonic wave function itself has been elusive. Using multidimensional photoemission spectroscopy, we present a momentum-, energy- and time-resolved perspective on excitons in the layered semiconductor WSe2. By tuning the excitation wavelength, we determine the energy-momentum signature of bright exciton formation and its difference from conventional single-particle excited states. The multidimensional data allows to retrieve fundamental exciton properties like the binding energy and the exciton-lattice coupling and to reconstruct the real-space excitonic distribution function via Fourier transform. All quantities are in excellent agreement with microscopic calculations. Our approach provides a full characterization of the exciton properties and is applicable to bright and dark excitons in semiconducting materials, heterostructures and devices. The data we uploaded here is the four-dimensional trARPES data used in this paper., This work was funded by the Max Planck Society, the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation and the H2020-EU.1.2.1. FET Open programs (Grant Nos. ERC-2015-CoG-682843, ERC-2015-AdG-694097, and OPTOlogic 899794), the Max Planck Society's Research Network BiGmax on Big-Data-Driven Materials-Science, and the German Research Foundation (DFG) within the Emmy Noether program (Grant No. RE 3977/1), through SFB 951 "Hybrid Inorganic/Organic Systems for Opto-Electronics (HIOS)" (Project No. 182087777, projects B12 and B17), the SFB/TRR 227 "Ultrafast Spin Dynamics" (projects A09 and B07), the Research Unit FOR 1700 "Atomic Wires" (project E5), and the Priority Program SPP 2244 (project 443366970). D.C.thanks the graduate school Advanced Materials (SFB 951) for support. S.B. acknowledges financial support from the NSERC-Banting Postdoctoral Fellowships Program. T.P. acknowledges financial support from the Alexander von Humboldt Foundation.

Low-temperature photoluminescence (PL) of hBN-encapsulated monolayer tungsten diselenide (WSe2) shows a multitude of sharp emission peaks below the bright exciton. Some of them have been recently i...

Layered transition metal dichalcogenides exhibit the emergence of a direct bandgap at the monolayer limit along with pronounced excitonic effects. In these materials, interaction with phonons is the dominant mechanism that limits the exciton coherence lifetime. Exciton-phonon interaction also facilitates energy and momentum relaxation, and influences exciton diffusion under most experimental conditions. However, the fundamental changes in the exciton-phonon interaction are not well understood as the material undergoes the transition from a direct to an indirect bandgap semiconductor. Here, we address this question through optical spectroscopy and microscopic theory. In the experiment, we study room-temperature statistics of the exciton line width for a large number of mono- and bilayer WS2 samples. We observe a systematic increase in the room-temperature line width of the bilayer compared to the monolayer of 50 meV, corresponding to an additional scattering rate of ∼0.1 fs-1. We further address both phonon emission and absorption processes by examining the temperature dependence of the width of the exciton resonances. Using a theoretical approach based on many-body formalism, we are able to explain the experimental results and establish a microscopic framework for exciton-phonon interactions that can be applied to naturally occurring and artificially prepared multilayer structures.

Heterostructures of van der Waals bonded layered materials offer unique means to tailor dielectric screening with atomic-layer precision, opening a fertile field of fundamental research. The optical analyses used so far have relied on interband spectroscopy. Here we demonstrate how a capping layer of hexagonal boron nitride (hBN) renormalizes the internal structure of excitons in a WSe$_2$ monolayer using intraband transitions. Ultrabroadband terahertz probes sensitively map out the full complex-valued mid-infrared conductivity of the heterostructure after optical injection of $1s$ A excitons. This approach allows us to trace the energies and linewidths of the atom-like $1s$-$2p$ transition of optically bright and dark excitons as well as the densities of these quasiparticles. The fundamental excitonic resonance red shifts and narrows in the WSe$_2$/hBN heterostructure compared to the bare monolayer. Furthermore, the ultrafast temporal evolution of the mid-infrared response function evidences the formation of optically dark excitons from an initial bright population. Our results provide key insight into the effect of non local screening on electron-hole correlations and open new possibilities of dielectric engineering of van der Waals heterostructures.

Single layers of transition metal dichalcogenides exhibit tightly bound excitons with large oscillator strength making them to promising materials for future optoelectronic applications. Despite that the linear response of these ultrathin materials is extensively studied, a profound understanding of the excitonic second-order nonlinear optical response, including trigonal warping and Berry curvature effects, is lacking so far. To bridge this gap, in this paper we report a microscopic model for the second-order nonlinear susceptibility tensor of these materials. Based on a $kp$ description of the underlying many-particle Hamiltonian we are able to address excitonic features as well as trigonal warping effects, spin-valley coupling, and also Berry curvature to the susceptibility tensor. We present explicit calculation of the latter for the exemplary materials ${\mathrm{MoS}}_{2}$ and ${\mathrm{WS}}_{2}$ on silicon substrate and encapsulated in hBN. For instance we predict resonant susceptibility for second-harmonic generation $0.5--1.3\phantom{\rule{4pt}{0ex}}\mathrm{nm}/\mathrm{V}$ and double-resonant susceptibility $10--30\phantom{\rule{4pt}{0ex}}\mathrm{n}\mathrm{m}/\mathrm{V}$ for the difference and sum-frequency generation processes. Our results are in good agreement with available experimental findings in the literature.

Atomically thin transition metal dichalcogenides can be stacked to van der Waals heterostructures enabling the design of new materials with tailored properties. The strong Coulomb interaction gives rise to interlayer excitons, where electrons and holes are spatially separated in different layers. In this work, we reveal the time- and momentum-dependent elementary processes behind the formation, thermalization and photoemission of interlayer excitons for the exemplary MoSe2–WSe2 heterostructure. We identify tunneling of holes from MoSe2 to WSe2 on a ps timescale as the crucial process for interlayer exciton formation. We also predict a drastic reduction of the formation time as a function of the interlayer energy offset suggesting that interlayer excitons can be externally tuned. Finally, we explain the experimental observation of a dominant photoluminescence from interlayer excitons despite the vanishingly small oscillator strength as a consequence of huge interlayer exciton occupations at low temperatures. Single layers of transition metal dichalcogenides are expected to be suitable for a number of applications and by stacking layers of different materials on top of each other (heterostructures) an even richer variety of properties can be explored. To this end the authors theoretically investigate cross material exciton states in a heterostructures of MoSe2 and WSe2 layers.

Time- and angle-resolved photoemission spectroscopy (trARPES) is a powerful spectroscopic method to measure the ultrafast electron dynamics directly in momentum space. However, band gap materials with exceptionally strong Coulomb interaction such as monolayer transition-metal dichalcogenides exhibit tightly bound excitons, which dominate their optical properties. This raises the question of whether excitons, in particular their formation and relaxation dynamics, can be detected in photoemissions. Here, we develop a fully microscopic theory of the temporal dynamics of excitonic time- and angle-resolved photoemission with a particular focus on the phonon-mediated thermalization of optically excited excitons to momentum-forbidden dark exciton states. We find that trARPES is able to probe the ultrafast exciton formation and relaxation throughout the Brillouin zone.

We investigate the impact of optically induced F\"orster coupling in van der Waals heterostructures consisting of graphene and a monolayer transition metal dichalcogenide (TMD). In particular, we predict the corresponding dephasing rates and a fast energy transfer between the TMD layer and graphene being in the picosecond range. Exemplary we find a transition rate of thermalized excitons of about 4 ps$^{-1}$ in a MoSe$_2$-graphene stack at room temperature. This timescale is in good agreement with the recently measured exciton lifetime in this heterostructure.

Monolayer transition metal dichalcogenides (TMDs) are known to be highly sensitive to externally applied tensile or compressive strain. In particular, strain can be exploited as a tool to control the optical response of TMDs. However, the role of excitonic effects under strain has not been fully understood yet. Utilizing the strain-induced modification of electron and phonon dispersion obtained by first principle calculations, we present in this work microscopic insights into the strain-dependent optical response of various TMD materials. In particular, we explain recent experiments on the change of excitonic linewidths in strained TMDs and predict their behavior for tensile and compressive strain at low temperatures., 7 pages, 7 figures

Niehues, Iris et al., 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., A.K., M.S., and D.C. acknowledge support by the Deutsche Forschungsgemeinschaft (DFG) through SFB 951 (to A.K.) and SFB 910 (to D.C.) and the School of Nanophotonics SFB 787 (to M.S.). E.M. and G.B. were supported by funding from the European Unions Horizon 2020 research and innovation program under grant agreement No. 696656 (Graphene Flagship) and the Swedish Research Council (VR).

Monolayer transition metal dichalcogenides (TMDs) exhibit a remarkably strong Coulomb interaction that manifests in tightly bound excitons. Due to the complex electronic band structure exhibiting several spin-split valleys in the conduction and valence band, dark excitonic states can be formed. They are inaccessibly by light due to the required spin-flip and/or momentum transfer. The relative position of these dark states with respect to the optically accessible bright excitons has a crucial impact on the emission efficiency of these materials and thus on their technological potential. Based on the solution of the Wannier equation, we present the excitonic landscape of the most studied TMD materials including the spectral position of momentum- and spin-forbidden excitonic states. We show that the knowledge of the electronic dispersion does not allow to conclude about the nature of the material's band gap, since excitonic effects can give rise to significant changes. Furthermore, we reveal that an exponentially reduced photoluminescence yield does not necessarily reflect a transition from a direct to a non-direct gap material, but can be ascribed in most cases to a change of the relative spectral distance between bright and dark excitonic states.

Monolayer transition metal dichalcogenides (TMDs) undergo substantial changes in the single-particle band structure and excitonic optical response upon the addition of just one layer. As opposed to the single-layer limit, the bandgap of bilayer (BL) TMD semiconductors is indirect which results in reduced photoluminescence with richly structured spectra that have eluded a detailed understanding to date. Here, we provide a closed interpretation of cryogenic emission from BL WSe2 as a representative material for the wider class of TMD semiconductors. By combining theoretical calculations with comprehensive spectroscopy experiments, we identify the crucial role of momentum-indirect excitons for the understanding of BL TMD emission. Our results shed light on the origin of quantum dot formation in BL crystals and will facilitate further advances directed at opto-electronic applications of layered TMD semiconductors in van der Waals heterostructures and devices., The electronic band structure of atomically thin transition metal dichalcogenides is strongly sensitive to the number of layers, resulting in modified light emission. Here, the authors investigate the cryogenic emission from bilayer WSe2 to identify the role of momentum-indirect excitons for its optical response.

Atomically thin transition metal dichalcogenides are direct-gap semiconductors with strong light–matter and Coulomb interactions. The latter accounts for tightly bound excitons, which dominate their optical properties. Besides the optically accessible bright excitons, these systems exhibit a variety of dark excitonic states. They are not visible in the optical spectra, but can strongly influence the coherence lifetime and the linewidth of the emission from bright exciton states. Here, we investigate the microscopic origin of the excitonic coherence lifetime in two representative materials (WS2 and MoSe2) through a study combining microscopic theory with spectroscopic measurements. We show that the excitonic coherence lifetime is determined by phonon-induced intravalley scattering and intervalley scattering into dark excitonic states. In particular, in WS2, we identify exciton relaxation processes involving phonon emission into lower-lying dark states that are operative at all temperatures., The interplay between dark and bright excitons has a significant impact on the optical properties of semiconducting transition metal dichalcogenides. Here, the authors perform computational and experimental studies which unveil the microscopic origin of the excitonic coherence lifetime in WS2 and MoSe2.

Monolayer transition metal dichalcogenides (TMDs) show an optimal surface-to-volume ratio and are thus promising candidates for novel molecule sensor devices. It was recently predicted that a certain class of molecules exhibiting a large dipole moment can be detected through the activation of optically inaccessible (dark) excitonic states in absorption spectra of tungsten-based TMDs. In this paper, we investigate the molecule signatures in photoluminescence spectra in dependence of a number of different experimentally accessible quantities, such as excitation density, temperature, as well as molecular characteristics including the dipole moment and its orientation, molecule-TMD distance, molecular coverage, and distribution. We show that under certain optimal conditions even room-temperature detection of molecules can be achieved.

Excitons dominate the optical properties of monolayer transition metal dichalcogenides (TMDs). Besides optically accessible bright exciton states, TMDs exhibit also a multitude of optically forbidden dark excitons. Here, we show that efficient exciton-phonon scattering couples bright and dark states and gives rise to an asymmetric excitonic line shape. The observed asymmetry can be traced back to phonon-induced sidebands that are accompanied by a polaron redshift. We present a joint theory-experiment study investigating the microscopic origin of these sidebands in different TMD materials taking into account intra- and intervalley scattering channels opened by optical and acoustic phonons. The gained insights contribute to a better understanding of the optical fingerprint of these technologically promising nanomaterials.

The remarkably strong Coulomb interaction in atomically thin transition metal dichalcogenides (TMDs) results in an extraordinarily rich many-particle physics including the formation of tightly bound excitons. Besides optically accessible bright excitonic states, these materials also exhibit a variety of dark excitons. Since they can even lie below the bright states, they have a strong influence on the exciton dynamics, lifetimes, and photoluminescence. While very recently, the presence of dark excitonic states has been experimentally demonstrated, the origin of these states, their formation, and dynamics have not been revealed yet. Here, we present a microscopic study shedding light on time- and energy-resolved formation and thermalization of bright and dark intra- and intervalley excitons as well as their impact on the photoluminescence in different TMD materials. We demonstrate that intervalley dark excitons, so far widely overlooked in current literature, play a crucial role in tungsten-based TMDs giving rise to an enhanced photoluminescence and reduced exciton lifetimes at elevated temperatures.

A valley-selective circular dichroism and a pronounced spin-valley locking in monolayer transition metal dichalcogenides (TMDCs) enable the investigation of new many-body physics revealed in the ultrafast nonlinear optical response of these atomically thin materials. While this topic is experimentally well studied in pump-probe spectroscopy, only a fragmented theoretical understanding is available due to the complexity and multitude of occurring effects. Here, a microscopic approach is presented to describe the ultrafast pump-probe response of monolayer TMDCs in the coherent limit. We focus on close to band edge excitations dominated by strongly correlated, bound electron-hole pairs, namely excitonic excitations. The approach includes Hartree–Fock and correlation effects up to two excitonic excitations known from conventional semiconductors as well as TMDC typical Coulomb mechanisms such as intra- and intervalley excitation and charge transfer. The investigated coherent limit is able to explain different signatures observed in ultrafast pump-probe spectroscopy for temporal pump-probe overlap within one consistent formalism dominated by excitons, biexcitons, and exciton-exciton scattering states.

Monolayers of semiconducting transition metal dichalcogenides hold the promise for a new paradigm in electronics by exploiting the valley degree of freedom in addition to charge and spin. For MoS2, WS2, and WSe2, valley polarization can be conveniently initialized and read out by circularly polarized light. However, the underlying microscopic processes governing valley polarization in these atomically thin equivalents of graphene are still not fully understood. Here, we present a joint experiment-theory study on the ultrafast time-resolved intervalley dynamics in monolayer WS2. Based on a microscopic theory, we reveal the many-particle mechanisms behind the observed spectral features. We show that Coulomb-induced intervalley coupling explains the immediate and prominent pump-probe signal in the unpumped valley and the seemingly low valley polarization degrees typically observed in pump-probe measurements compared to photoluminescence studies. The gained insights are also applicable to other light-emitting monolayer transition metal dichalcogenides, such as MoS2 and WSe2, where the Coulomb-induced intervalley coupling also determines the initial carrier dynamics.

A remarkable property of atomically thin transition metal dichalcogenides (TMDs) is the possibility to selectively address single valleys by circularly polarized light. In the context of technological applications, it is very important to understand possible intervalley coupling mechanisms. Here, we show how the Dexter-like intervalley coupling mixes A and B states from opposite valleys leading to a significant broadening γB 1s of the B 1s exciton. The effect is much more pronounced in tungsten-based TMDs, where the coupling excitonic states are quasi-resonant. We calculate a ratio γB B 1s /γA B 1s ≈ 4.0, which is in good agreement with the experimentally measured value of 3.9 ± 0.7. In addition to the broadening effect, the Dexter-like intervalley coupling also leads to a considerable energy renormalization resulting in an increased energetic distance between A 1s and B 1s states.

The authors present a microscopic explanation for the bleaching at the excitonic $B$ transition in monolayers of transition metal dichalcogenides, based on the joint action of exchange coupling and phonon-mediated thermalization into dark exciton states. The paper shows how intra- and intervalley coupling on a femtosecond timescale governs the optical valley response of 2D semiconductors.

Monolayers of transition metal dichalcogenides (TMDCs) are promising materials for valleytronic applications, since they possess two individually addressable excitonic transitions at the nonequivalent K and K' points with different spins, selectively excitable with light of opposite circular polarization. Here, it is of crucial importance to understand the elementary processes determining the lifetime of optically injected valley excitons. In this study, we perform microscopic calculations based on a Heisenberg equation of motion formalism to investigate the efficiency of the intervalley coupling in the presence (W-based TMDCs) and absence (Mo-based TMDCs) of energetically low-lying momentum-dark exciton states after pulsed excitation. While we predict a spin polarization lifetime on the order of some hundreds of femtoseconds in the absence of low-lying momentum-dark states, we demonstrate a strong elongation of the spin-polarization lifetime in the presence of such states due to a suppression of the intervalley exchange coupling.