We perform coherent nonlinear spectroscopy of excitons in single-layers of MoSe$_2$ and WSe$_2$ encapsulated between thin films of hexagonal boron nitride. Employing four-wave mixing microscopy we identify virtually disorder free areas, generating exciton optical response at the homogeneous limit. Focussing on such areas, we measure exciton homogeneous broadening as a function of environmental factors, namely temperature and exciton density. Exploiting FWM imaging, we find that at such locations, nonlinear absorption of the exciton excited states and their coherent couplings can be observed. Using the WSe$_2$ heterostructure, we infer coherence and density dynamics of the exciton 2S state. Owing to its increased radiative lifetime, at low temperatures, the dephasing of the 2S state is longer than of the 1S transition. While scanning various heterostructures across tens of micrometers, we conclude that the disorder, principally induced by strain variations, remain to be present creating spatially varying inhomogeneous broadening.
Layered two-dimensional materials exhibit rich transport and optical phenomena in twisted or lattice-incommensurate heterostructures with spatial variations of interlayer hybridization arising from moiré interference effects. Here, we report experimental and theoretical studies of excitons in twisted heterobilayers and heterotrilayers of transition metal dichalcogenides. Using MoSe$_2$-WSe$_2$ stacks as representative realizations of twisted van der Waals bilayer and trilayer heterostructures, we observe contrasting optical signatures and interpret them in the theoretical framework of interlay…
The optical spectra of vertically stacked MoSe$_2$/WSe$_2$ heterostructures contain additional 'interlayer' excitonic peaks that are absent in the individual monolayer materials and exhibit a significant spatial charge separation in out-of-plane direction. Extending on a previous study, we used a many-body perturbation theory approach to simulate and analyse the excitonic spectra of MoSe$_2$/WSe$_2$ heterobilayers with three stacking orders, considering both momentum-direct and momentum-indirect excitons. We find that the small oscillator strengths and corresponding optical responses of the in…
Coherent coupling between excitons is at the heart of many-body interactions with transition metal dichalcogenide (TMD) heterostructures as an emergent platform for the investigation of these interactions. We employ multi-dimensional coherent spectroscopy on monolayer MoSe\textsubscript{2}/WSe\textsubscript{2} heterostructures and observe coherent coupling between excitons spatially localized in monolayer MoSe$_2$ and WSe$_2$. Through many-body spectroscopy, we further observe the absorption state arising from free interlayer electron-hole pairs. This observation yields a spectroscopic measure…
We present a detailed investigation of the exciton and trion dynamics in naturally doped MoSe2 and WSe2 single atomic layers as a function of temperature in the range 10-300K under above band-gap laser excitation. By combining time-integrated and time-resolved photoluminescence (PL) spectroscopy we show the importance of exciton and trion localization in both materials at low temperatures. We also reveal the transition to delocalized exciton complexes at higher temperatures where the exciton and trion thermal energy exceeds the typical localization energy. This is accompanied with strong chang…
Strain is a powerful tool to modify the optical properties of semiconducting transition metal dichalcogenides like MoS2, MoSe2, WS2 and WSe2. In this work we provide a thorough description of the technical details to perform uniaxial strain measurements on these two-dimensional semiconductors and we provide a straightforward calibration method to determine the amount of applied strain with high accuracy. We then employ reflectance spectroscopy to analyze the strain tunability of the electronic properties of single-, bi- and tri-layer MoS2, MoSe2, WS2 and WSe2. Finally, we quantify the flake-to…
Identifying quantum numbers to label elementary excitations is essential for the correct description of light-matter interaction in solids. In monolayer semiconducting transition metal dichalcogenides (TMDs) such as MoSe$_2$ or WSe$_2$, most optoelectronic phenomena are described well by labelling electron and hole states with the spin projection along the normal to the layer (S$_z$). In contrast, for WSe$_2$/MoSe$_2$ interfaces recent experiments show that taking S$_z$ as quantum number is not a good approximation, and spin mixing needs to be always considered. Here we argue that the correct …
Interlayer excitons (IXs) possess a much longer lifetime than intralayer excitons due to the spatial separation of the electrons and holes; hence, they have been pursued to create exciton condensates for decades. The recent emergence of two-dimensional (2D) materials, such as transition metal dichalcogenides (TMDs), and of their van der Waals heterostructures (HSs), in which two different 2D materials are layered together, has created new opportunities to study IXs. Here we present the observation of IX gases within two stacked structures consisting of hBN/WSe$_2$/hBN/p: WSe$_2$/hBN. The IX en…
Two-dimensional moiré materials provide a highly tunable platform to investigate strongly correlated electronic states. Such emergent many-body phenomena can be optically probed in moiré systems created by stacking two layers of transition metal dichalcogenide semiconductors: optically injected excitons can interact with itinerant carriers occupying narrow moiré bands to form exciton-polarons sensitive to strong correlations. Here, we investigate the behaviour of excitons dressed by a Fermi sea localised by the moiré superlattice of a molybdenum diselenide (MoSe$_2$) / tungsten diselenide (WSe…
Based on first-principles calculations, the materials properties (structural, electronic, vibrational, and optical properties) of out-of-plane heterostructures formed from the transiti on metal dichalcogenides, specifically MoS$_2$-WSe$_2$ and WS$_2$-MoSe$_2$ were investigated. The heterostructures of MoS$_2$-WSe$_2$ and WS$_2$-MoSe$_2$ are found to be direct and ind irect band gap semiconductors, respectively. However, a direct band gap in the WS$_2$-MoSe$_2$ heterostructure can be achieved by applying compressive strain. Furthermore, the excitoni c peaks in both monolayer and bilayer heteros…
Monolayer WSe$_2$ hosts a series of exciton Rydberg states denoted by the principal quantum number n = 1, 2, 3, etc. While most research focuses on their absorption properties, their optical emission is also important but much less studied. Here we measure the photoluminescence from the 1s - 5s exciton Rydberg states in ultraclean monolayer WSe$_2$ encapsulated by boron nitride under magnetic fields from -31 T to 31 T. The exciton Rydberg states exhibit similar Zeeman shifts but distinct diamagnetic shifts from each other. From their luminescence spectra, Zeeman and diamagnetic shifts, we dedu…
Calculations combining first-principles electron-phonon ($e$-ph) interactions with the Boltzmann equation enable studies of ultrafast carrier and phonon dynamics. However, in materials with weak Coulomb screening, electrons and holes form bound excitons and their scattering processes become correlated, posing additional challenges for modeling nonequilibrium physics. Here we show calculations of ultrafast exciton dynamics and related time-domain spectroscopies using $ab~initio$ exciton-phonon (ex-ph) interactions together with an excitonic Boltzmann equation. Starting from the nonequilibrium e…
The optical properties of monolayer and bilayer transition metal dichalcogenide semiconductors are governed by excitons in different spin and valley configurations, providing versatile aspects for van der Waals heterostructures and devices. We present experimental and theoretical studies of exciton energy splittings in external magnetic field in neutral and charged WSe$_2$ monolayer and bilayer crystals embedded in a field effect device for active doping control. We develop theoretical methods to calculate the exciton $g$-factors from first principles and tight-binding for all possible spin-va…
Controlling the Atomic Reconstruction in Twisted MoSe$_2$/WSe$_2$ with a Monolayer hBN Spacer
Walter Schottky Institute and Physics Department, TU Munich（慕尼黑工业大学瓦尔特·肖特基研究所与物理系）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Department of Materials Science and Engineering, Massachusetts Institute of Technology（麻省理工学院材料科学与工程系）；MIT.nano, Massachusetts Institute of Technology（麻省理工学院MIT.nano）；Research Center for Electronic and Optical Materials, National Institute for Materials Science（国家材料研究所电子与光学材料研究中心）；Research Center for Materials Nanoarchitectonics, National Institute for Materials Science（国家材料研究所材料纳米架构研究中心）
The variety of excitonic states in tungsten-based dichalcogenide monolayers stems from unique interplay between the spin and valley degrees of freedom. One of the exciton species is the indirect exciton (momentum or valley dark), which is responsible to a series of resonances when the monolayer is charge neutral. We investigate the short-range electron-hole exchange interaction of the indirect exciton, as well as its recombination mechanism mediated by impurities. The analysis provides thorough understanding of the energy and polarization of the zero-phonon indirect exciton resonance in the em…
We investigate the twist-angle and gate dependence of the proximity-induced exchange coupling in the monolayer transition-metal dichalcogenides (TMDCs) MoSe$_2$ and WSe$_2$ due to the vdW coupling to the ferromagnetic semiconductor CrI$_3$, from first-principles calculations. A model Hamiltonian, that captures the relevant band edges at the $K/K^{\prime}$ valleys of the proximitized TMDCs, is employed to quantify the proximity-induced exchange. Upon twisting from 0° to 30°, we find a transition of the TMDC valence band (VB) edge exchange splitting from about $-2$ to $2$ meV, while the conducti…
Moiré patterns with angular mismatch in van der Waals heterostructures composed of atomically thin semiconducting materials are a fascinating platform to engineer the optically generated excitonic properties towards novel quantum phenomena. The moiré pattern as a periodic trap potential can give rise to spatially ordered zero-dimensional (0D) exciton ensembles, which offers the possibility for dense coherent quantum emitters and quantum simulation of many-body physics. The intriguing moiré exciton properties are affected by their dynamics and exciton-phonon interaction. However, the moiré exci…
We report on the far-field photoluminescence intensity distribution of interlayer excitons in MoSe$_{2}$-WSe$_{2}$ heterostacks as measured by back focal plane imaging in the temperature range between 1.7 K and 20 K. By comparing the data with an analytical model describing the dipolar emission pattern in a dielectric environment, we are able to obtain the relative contributions of the in- and out-of-plane transition dipole moments associated to the interlayer exciton photon emission. We determine the transition dipole moments for all observed interlayer exciton transitions to be (99 $\pm$ 1)%…
The nanoscale periodic potentials introduced by moiré patterns in semiconducting van der Waals (vdW) heterostructures provide a new platform for designing exciton superlattices. To realize these applications, a thorough understanding of the localization and delocalization of interlayer excitons in the moiré potentials is necessary. Here, we investigated interlayer exciton dynamics and transport modulated by the moiré potentials in WS$_2$-WSe$_2$ heterobilayers in time, space, and momentum domains using transient absorption microscopy combined with first-principles calculations. Experimental re…
Single-layer transition metal dichalcogenides (TMDs) provide a promising material system to explore the electron's valley degree of freedom as a quantum information carrier. The valley degree of freedom in single-layer TMDs can be directly accessed by means of optical excitation. The rapid valley relaxation of optically excited electron-hole pairs (excitons) through the long-range electron-hole exchange interaction, however, has been a major roadblock. Theoretically such a valley relaxation does not occur for the recently discovered dark excitons, suggesting a potential route for long valley l…
The spectral and spatiotemporal dynamics of photoluminescence in monolayers of transition metal dichalcogenide WSe$_2$ obtained by mechanical exfoliation on a Si/SiO$_2$ substrate is studied over a wide range of temperatures and excitation powers. It is shown that the dynamics is nonexponential and, for times $t$ exceeding $\sim$50 ps after the excitation pulse, is described by a dependence of the form $1/(t+t_0)$. Photoluminescence decay is accelerated with a decrease in temperature, as well as with a decrease in the energy of emitting states. It is shown that the observed dynamics cannot be …
Moiré patterns of transition metal dichalcogenide (TMD) heterobilayers have proven to be an ideal platform to host unusual correlated electronic phases, emerging magnetism, and correlated exciton physics. While the existence of novel moiré excitonic states is established through optical measurements, the microscopic nature of these states is still poorly understood, often relying on empirically fit models. Here, combining large-scale first-principles GW-BSE calculations and micro-reflection spectroscopy, we identify the nature of the exciton resonances in WSe$_2$/WS$_2$ moiré superlattices, di…
With the both spin and valley degrees of freedom, the low-lying excitonic spectra of photo-excited transition-metal dichalcogenide monolayers (TMDC-MLs) are featured by rich fine structures, comprising the intra-valley bright exciton states as well as various intra- and inter-valley dark ones. The latter states can be classified as those of the spin- and momentum-forbidden dark excitons according to the violated optical selection rules. Because of the optical invisibility, the two types of the dark states are in general hardly observed and even distinguished in conventional spectroscopies alth…
The dielectric environment of atomically-thin monolayer (ML) of semiconducting transition metal dichalcogenides affects both the electronic band gap and the excitonic binding energy in the ML. We investigate the effect of the environment on the in-plane magnetic field brightening of neutral and charged dark exciton emissions in the WSe$_2$ ML. The monolayers placed in three dielectric environments are studied, in particular, the ML encapsulated in hexagonal BN (hBN) flakes, the ML deposited on a hBN layer, and the ML embedded between the hBN flake and SiO$_2$/Si substrate. We observe that the …
Recent advances in emerging atomically thin transition metal dichalcogenide semiconductors with strong light-matter interactions and tunable optical properties provide novel approaches for realizing new material functionalities. Coupling two-dimensional semiconductors with all-dielectric resonant nanostructures represents an especially attractive opportunity for manipulating optical properties in both the near-field and far-field regimes. Here, by integrating single-layer WSe2 and titanium oxide (TiO2) dielectric metasurfaces with toroidal resonances, we realized robust exciton emission enhanc…
The bilayer heterostructures composed of an ultrathin ferromagnetic metal (FM) and a material hosting strong spin-orbit (SO) coupling are principal resource for SO torque and spin-to-charge conversion nonequilibrium effects in spintronics. We demonstrate how hybridization of wavefunctions of Co layer and a monolayer of transition metal dichalcogenides (TMDs)---such as semiconducting MoSe$_2$ and WSe$_2$ or metallic TaSe$_2$---can lead to dramatic transmutation of electronic and spin structure of Co within some distance away from its interface with TMD, when compared to the bulk of Co or its su…
In monolayer transition-metal dichalcogenide semiconductors, many-body correlations can manifest in optical spectra when photoexcited electron-hole pairs (excitons) are introduced into a 2D Fermi sea of mobile carriers. At low carrier densities, the formation of positively and negatively charged excitons ($X^\pm$) is well documented. However, in WSe$_2$ monolayers, an additional absorption resonance, often called $X^{-\prime}$, emerges at high electron density. Its origin is not understood. Here we investigate the $X^{-\prime}$ state via polarized absorption spectroscopy of electrostatically-g…
Excitons and trions (or exciton-polarons) in transition metal dichalcogenides (TMDs) are known to decay predominantly through intravalley transitions. Electron-hole recombination across different valleys can also play a significant role in the excitonic dynamics, but intervalley transitions are rarely observed in monolayer TMDs, because they violate the conservation of momentum. Here we reveal the intervalley recombination of dark excitons and trions through more than one path in monolayer WSe$_2$. We observe the intervalley dark excitons, which can recombine by the assistance of defect scatte…
Layer-Dependent Interfacial Coupling and Exciton Pinning in WSe2/Graphene Heterostructures
Empa – Swiss Federal Laboratories for Materials Science and Technology（瑞士联邦材料科技研究所）；University of Basel（巴塞尔大学）；Swiss Nanoscience Institute, University of Basel（巴塞尔大学瑞士纳米科学研究所）；The Pennsylvania State University（宾夕法尼亚州立大学）
The electronic and the structural properties of two dimensional van der Waals metal/semiconductor heterostructures have been investigated through first-principles calculations. We have considered the recently synthesized borophene [Science {\bf 350}, 1513 (2015)], and the planar boron sheets (S1 and S2) [Nature Chemistry {\bf 8}, 563 (2016)] as the 2D metal layer, and the transition metal dichalcogenides (TMDCs) \mose, and \wse\ as the semiconductor monolayer. We find that the energetic stability of those 2D metal/semiconductor heterojunctions is mostly ruled by the vdW interactions; however, …
Electronic transmission in monolayer ReS$_{2}$ and ReS$_{2}$ based van der Waals (vdW) heterointerfaces are studied here. Since ReS$_{2}$/WSe$_{2}$ and ReS$_{2}$/MoSe$_{2}$ type-II vdW heterostructures are suitable for near infrared (NIR)/short-wave infrared (SWIR) photodetection, the role of interlayer coupling at the heterointerfaces is examined in this work. Besides, a detailed theoretical study is presented employing density functional theory (DFT) and nonequilibrium Green's function (NEGF) combination to analyse the transmission spectra of the two-port devices with ReS$_{2}$/WSe$_{2}$ and…
We report on large exciton tuning in WSe$_2$ monolayers via substrate induced non-degenerate doping. We observe a redshift of $\sim$62 meV for the $A$ exciton together with a 1-2 orders of magnitude photoluminescence (PL) quenching when the monolayer WSe$_2$ is brought in contact with highly oriented pyrolytic graphite (HOPG) compared to the dielectric substrates such as hBN and SiO$_2$. As the evidence of doping from HOPG to WSe$_2$, a drastic increase of the trion emission intensity was observed. Using a systematic PL and Kelvin probe force microscopy (KPFM) investigation on WSe$_2$/HOPG, WS…
An emerging class of semiconductor heterostructures involves stacking discrete monolayers such as the transition metal dichalcogenides (TMDs) to form van der Waals heterostructures. In these structures, it is possible to create interlayer excitons (ILEs), spatially indirect, bound electron-hole pairs with the electron in one TMD layer and the hole in an adjacent layer. We are able to clearly resolve two distinct emission peaks separated by 24 meV from an ILE in a MoSe2/WSe2 heterostructure fabricated using state-of-the-art preparation techniques. These peaks have nearly equal intensity, indica…
Excitons, Coulomb bound electron-hole pairs, are composite bosons and their interactions in traditional semiconductors lead to condensation and light amplification. The much stronger Coulomb interaction in transition metal dichalcogenides such as WSe$_2$ monolayers combined with the presence of the valley degree of freedom is expected to provide new opportunities for controlling excitonic effects. But so far the bosonic character of exciton scattering processes remains largely unexplored in these two-dimensional (2D) materials. Here we show that scattering between B-excitons and A-excitons pre…
We investigate exciton dynamics in 2H-WSe2 bilayers in time-resolved photoluminescence (PL) spectroscopy. Fast PL emission times are recorded for both the direct exciton with $τ_{D}$ ~ 3 ps and the indirect optical transition with $τ_{i}$ ~ 25 ps. For temperatures between 4 to 150 K $τ_{i}$ remains constant. Following polarized laser excitation, we observe for the direct exciton transition at the K point of the Brillouin zone efficient optical orientation and alignment during the short emission time $τ_{D}$. The evolution of the direct exciton polarization and intensity as a function of excita…
Monolayer MX$_2$ (M = Mo, W; X = S, Se) has drawn much attention recently for its possible application possibilities for optoelectronics, spintronics, and valleytronics. Its exotic optical and electronic properties include a direct band gap, circular polarization dependent optical transitions, and valence band (VB) spin band splitting at the $K$ and $-K$ points. These properties can be described within a minimal model, called the massive Dirac fermion model for which the parameters need to be experimentally determined. We propose that the parameters can be obtained from angle resolved photoemi…
Interlayer excitons in layered materials constitute a novel platform to study many-body phenomena arising from long-range interactions between quantum particles. The ability to localise individual interlayer excitons in potential energy traps is a key step towards simulating Hubbard physics in artificial lattices. Here, we demonstrate spatial localisation of long-lived interlayer excitons in a strongly confining trap array using a WS$_{2}$/WSe$_{2}$ heterostructure on a nanopatterned substrate. We detect long-lived interlayer excitons with lifetime approaching 0.2 ms and show that their confin…
Twisted bilayers of two-dimensional materials, such as twisted bilayer graphene, often feature flat electronic bands that enable the observation of electron correlation effects. In this work, we study the electronic structure of twisted transition metal dichalcogenide (TMD) homo- and heterobilayers that are obtained by combining MoS$_2$, WS$_2$, MoSe$_2$ and WSe$_2$ monolayers, and show how flat band properties depend on the chemical composition of the bilayer as well as its twist angle. We determine the relaxed atomic structure of the twisted bilayers using classical force fields and calculat…
Interlayer excitons are observed coexisting with intralayer excitons in bi-layer, few-layer, and bulk MoSe2 single crystals by confocal reflection contrast spectroscopy. Quantitative analysis using the Dirac-Bloch-Equations provides unambiguous state assignment of all the measured resonances. The interlayer excitons in bilayer MoSe2 have a large binding energy of 153 meV, narrow linewidth of 20 meV, and their spectral weight is comparable to the commonly studied higher-order intralayer excitons. At the same time, the interlayer excitons are characterized by distinct transition energies and per…
We investigate the excitonic transitions in single- and few-layer MoSe2 phototransistors by photocurrent spectroscopy. The measured spectral profiles show a well-defined peak at the optically active (bright) A0 exciton resonance. More interestingly, when a gate voltage is applied to the MoSe2 to bring its Fermi level near the bottom of the conduction band, another prominent peak emerges at an energy 30 meV above the A0 exciton. We attribute this second peak to a gate-induced activation of the spin-forbidden dark exciton transition, AD0. Additionally, we evaluate the thickness-dependent optical…
The optical properties of two-dimensional transition metal dichalcogenide monolayers such as MoS$_2$ or WSe$_2$ are dominated by excitons, Coulomb bound electron-hole pairs. Screening effects due the presence of hexagonal-BN surrounding layers have been investigated by solving the Bethe Salpeter Equation on top of GW wave functions in density functional theory calculations. We have calculated the dependence of both the quasi-particle gap and the binding energy of the neutral exciton ground state E$_b$ as a function of the hBN layer thickness. This study demonstrates that the effects of screeni…
Many of the fundamental optical and electronic properties of atomically thin transition metal dichalcogenides are dominated by strong Coulomb interactions between electrons and holes, forming tightly bound atom-like excitons. Here, we directly trace the ultrafast formation of excitons by monitoring the absolute densities of bound and unbound electron-hole pairs in monolayers of WSe$_2$ following femtosecond non-resonant optical excitation. To this end, phase-locked mid-infrared probe pulses and field-sensitive electro-optic sampling are used to map out the full complex-valued optical conductiv…
Atomically thin two-dimensional crystals have revolutionized materials science. In particular, monolayer transition metal dichalcogenides promise novel optoelectronic applications, due to their direct energy gaps in the optical range. Their electronic and optical properties, however, are complicated by exotic room-temperature excitons, whose fundamental structure and dynamics has been under intense investigation. While interband spectroscopy probes energies of excitons with vanishing centre-of-mass momenta, the majority of excitons has remained elusive, raising questions about their unusual in…
