Coulomb-bound four- and five-particle intervalley states in an atomically-thin semiconductor

Enhanced Photo-excitation and Angular-Momentum Imprint of Gray Excitons in WSe2 Monolayers by Spin-Orbit-Coupled Vector Vortex Beams

A light beam can be spatially structured in the complex amplitude to possess orbital angular momentum (OAM), which introduces an extra degree of freedom alongside the intrinsic spin angular momentum (SAM) associated with circular polarization. Furthermore, superimposing two such twisted light (TL) beams with distinct SAM and OAM produces a vector vortex beam (VVB) in nonseparable states where not only complex amplitude but also polarization is spatially structured and entangled with each other. In addition to the nonseparability, the SAM and OAM in a VVB are intrinsically coupled by the optical spin-orbit interaction and constitute the profound spin-orbit physics in photonics. In this work, we present a comprehensive theoretical investigation, implemented on the first-principles base, of the intriguing light-matter interaction between VVBs and WSe2 monolayers (WSe2-MLs), one of the best-known and promising two-dimensional (2D) materials in optoelectronics dictated by excitons, encompassing bright exciton (BX) as well as various dark excitons (DXs). One of the key findings of our study is that a substantial enhancement of the photoexcitation of gray excitons (GXs), a type of spin-forbidden DX, in a WSe2-ML can be achieved through the utilization of a 3D-structured TL with the optical spin-orbit interaction. Moreover, we show that a spin-orbit-coupled VVB surprisingly allows for the imprinting of the carried optical information onto GXs in 2D materials, which is robust against the decoherence mechanisms in the materials. This suggests a promising method for deciphering the transferred angular momentum from structured light to excitons.

Atomic-scale visualization of the interlayer Rydberg exciton complex in moiré heterostructures

Excitonic systems, facilitated by optical pumping, electrostatic gating or magnetic field, sustain composite particles with fascinating physics. Although various intriguing excitonic phases have been revealed via global measurements, the atomic-scale accessibility towards excitons has yet to be established. Here, we realize the ground-state interlayer exciton complexes through the intrinsic charge transfer in monolayer YbCl3/graphite heterostructure. Combining scanning tunneling microscope and theoretical calculations, the excitonic in-gap states are directly profiled. The out-of-plane excitonic charge clouds exhibit oscillating Rydberg nodal structure, while their in-plane arrangements are determined by moiré periodicity. Exploiting the tunneling probe to reflect the shape of charge clouds, we reveal the principal quantum number hierarchy of Rydberg series, which points to an excitonic energy-level configuration with unusually large binding energy. Our results demonstrate the feasibility of mapping out the charge clouds of excitons microscopically and pave a brand-new way to directly investigate the nanoscale order of exotic correlated phases.

High-order exciton complexes induced by an interlayer carrier transfer in 2D van der Waals heterostructures

High-order correlated excitonic states, such as biexciton, charged biexciton, and polaron, hold a promising platform in contemporary quantum and nonlinear optics due to their large Bohr radii and thus strong nonlinear interactions. The recently found 2D TMDs further give such excitonic states additional valley properties, with bound state of excitons in opposite valleys in momentum spaces. Despite great efforts that have been made on emission properties of excitonic states, their absorption features, especially the ultrafast absorption dynamics, are rarely reported. Here, we reported the enhanced optical absorption of the high-order charged-excitonic states in monolayer WS2, including singlet, triplet, and semidark trions (3-particle state), and charged biexcitons (5-particle state), by utilizing the interlayer charge transfer-induced photo-doping effect in the graphene-WS2 heterostructure. Depending on recombination rates of doping electrons, absorption intensities of charged complexes exhibit ultrafast decay dynamics, with lifetimes of several picoseconds. Due to many-body interaction, both increasing pump intensity and lattice temperature can broaden these fine excitonic absorption peaks and even reverse the shape of the transient absorption spectrum.

Tuning Interlayer Exciton Emission with TMD Alloys in van der Waals Heterobilayers of Mo0.5W0.5Se2 and Its Binary Counterparts

Semiconductor heterostructures have been the backbone of developments in electronic and optoelectronic devices. One class of structures of interest is the so-called type II band alignment, in which optically excited electrons and holes relax into different material layers. The unique properties observed in two-dimensional transition metal dichalcogenides and the possibility to engineer van der Waals heterostructures make them candidates for future high-tech devices. In these structures, electronic, optical, and magnetic properties can be tuned through the interlayer coupling, thereby opening avenues for developing new functional materials. We report the possibility of explicitly tuning the emission of interlayer exciton energies in the binary-ternary heterobilayer of Mo0.5W0.5Se2 with MoSe2 and WSe2. The respective interlayer energies of 1.516 eV and 1.490 eV were observed from low-temperature photoluminescence measurements for the MoSe2- and WSe2- based heterostructures, respectively. These interlayer emission energies are above those reported for MoSe2/WSe2 (≃1.30-1.45 eV). Consequently, binary-ternary heterostructure systems offer an extended energy range and tailored emission energies not accessible with the binary counterparts. Moreover, even though Mo0.5W0.5Se2 and MoSe2 have almost similar optical gaps, their band offsets are different, resulting in charge transfer between the monolayers following the optical excitation. Thus, confirming TMDs alloys can be used to tune the band-offsets, which adds another design parameter for application-specific optoelectronic devices.

Biexciton and Singlet Trion Upconvert Exciton Photoluminescence in a MoSe2 Monolayer Supported by Acoustic and Optical K-Valley Phonons

Transition metal dichalcogenide monolayers represent unique platforms for studying both electronic and phononic interactions as well as intra- and intervalley exciton complexes. Here, we investigate the upconversion of exciton photoluminescence in MoSe2 monolayers. Within the nominal transparency window of MoSe2 the exciton emission is enhanced for resonantly addressing the spin-singlet negative trion and neutral biexciton at a few tens of meV below the neutral exciton transition. We identify that the A'1 optical phonon at the K valley provides the energy gain in the upconversion process at the trion resonance, while ZA(K) phonons with their spin- and valley-switching properties support the biexciton driven upconversion of the exciton emission. Interestingly, the latter upconversion process yields unpolarized exciton photoluminescence, while the former also leads to circularly polarized emission. Our study highlights high-order exciton complexes interacting with optical and acoustic K-valley phonons and upconverting light into the bright exciton.

Valley Polarized Holes Induced Exciton Polaron Valley Splitting

Monolayer transition metal dichalcogenide semiconductors are promising valleytronic materials. Among various quasi-particle excitations hosted by the system, the valley polarized holes are particularly interesting due to their long valley lifetime preserved by the large spin-orbit splitting and spin-valley locking in the valence band. Here we report that in the absence of any magnetic field a surprising valley splitting of exciton polarons can be induced by such valley polarized holes in monolayer WSe2. The size of the splitting is comparable to that of the Zeeman effect in a magnetic field as high as 7 T and offers a quantitative approach to extract the hole density imbalance between the two valleys. We find that the density difference can easily achieve more than 1011 per cm2, and it is tunable by gate voltage as well as optical excitation power. Our study highlights the response of exciton polarons to optical pumping and advances understanding of valley dependent phenomena in monolayer transition metal dichalcogenide.

The Key Role of Non-Local Screening in the Environment-Insensitive Exciton Fine Structures of Transition-Metal Dichalcogenide Monolayers

In this work, we present a comprehensive theoretical and computational investigation of exciton fine structures of WSe2-monolayers, one of the best-known two-dimensional (2D) transition-metal dichalcogenides (TMDs), in various dielectric-layered environments by solving the first-principles-based Bethe-Salpeter equation. While the physical and electronic properties of atomically thin nanomaterials are normally sensitive to the variation of the surrounding environment, our studies reveal that the influence of the dielectric environment on the exciton fine structures of TMD-MLs is surprisingly limited. We point out that the non-locality of Coulomb screening plays a key role in suppressing the dielectric environment factor and drastically shrinking the fine structure splittings between bright exciton (BX) states and various dark-exciton (DX) states of TMD-MLs. The intriguing non-locality of screening in 2D materials can be manifested by the measurable non-linear correlation between the BX-DX splittings and exciton-binding energies by varying the surrounding dielectric environments. The revealed environment-insensitive exciton fine structures of TMD-ML suggest the robustness of prospective dark-exciton-based optoelectronics against the inevitable variation of the inhomogeneous dielectric environment.

Diffusion of Excitons in a Two-Dimensional Fermi Sea of Free Charges

Propagation of light-emitting quasiparticles is of central importance across the fields of condensed matter physics and nanomaterials science. We experimentally demonstrate diffusion of excitons in the presence of a continuously tunable Fermi sea of free charge carriers in a monolayer semiconductor. Light emission from tightly bound exciton states in electrically gated WSe₂ monolayer is detected using spatially and temporally resolved microscopy. The measurements reveal a nonmonotonic dependence of the exciton diffusion coefficient on the charge carrier density in both electron and hole doped regimes. Supported by analytical theory describing exciton-carrier interactions in a dissipative system, we identify distinct regimes of elastic scattering and quasiparticle formation determining exciton diffusion. The crossover region exhibits a highly unusual behavior of an increasing diffusion coefficient with increasing carrier densities. Temperature-dependent diffusion measurements further reveal characteristic signatures of freely propagating excitonic complexes dressed by free charges with effective mobilities up to 3 × 10³ cm²/(V s).

Mobile Trions in Electrically Tunable 2D Hybrid Perovskites

2D hybrid perovskites are currently in the spotlight of material research for light-harvesting and -emitting applications. It remains extremely challenging, however, to externally control their optical response due to the difficulties of introducing electrical doping. Here, an approach of interfacing ultrathin sheets of perovskites with few-layer graphene and hexagonal boron nitride into gate-tunable, hybrid heterostructures, is demonstrated. It allows for bipolar, continuous tuning of light emission and absorption in 2D perovskites by electrically injecting carriers to densities as high as 10¹²  cm^-2 . This reveals the emergence of both negatively and positively charged excitons, or trions, with binding energies up to 46 meV, among the highest measured for 2D systems. Trions are shown to dominate light emission and propagate with mobilities reaching 200 cm² V^-1 s^-1 at elevated temperatures. The findings introduce the physics of interacting mixtures of optical and electrical excitations to the broad family of 2D inorganic-organic nanostructures. The presented strategy to electrically control the optical response of 2D perovskites highlights it as a promising material platform toward electrically modulated light-emitters, externally guided charged exciton currents, and exciton transistors based on layered, hybrid semiconductors.

Interactions between Fermi polarons in monolayer WS2

Interactions between quasiparticles are of fundamental importance and ultimately determine the macroscopic properties of quantum matter. A famous example is the phenomenon of superconductivity, which arises from attractive electron-electron interactions that are mediated by phonons or even other more exotic fluctuations in the material. Here we introduce mobile exciton impurities into a two-dimensional electron gas and investigate the interactions between the resulting Fermi polaron quasiparticles. We employ multi-dimensional coherent spectroscopy on monolayer WS₂, which provides an ideal platform for determining the nature of polaron-polaron interactions due to the underlying trion fine structure and the valley specific optical selection rules. At low electron doping densities, we find that the dominant interactions are between polaron states that are dressed by the same Fermi sea. In the absence of bound polaron pairs (bipolarons), we show using a minimal microscopic model that these interactions originate from a phase-space filling effect, where excitons compete for the same electrons. We furthermore reveal the existence of a bipolaron bound state with remarkably large binding energy, involving excitons in different valleys cooperatively bound to the same electron. Our work lays the foundation for probing and understanding strong electron correlation effects in two-dimensional layered structures such as moiré superlattices.

Here, the authors investigate the interactions between Fermi polarons in monolayer WS₂ by multi-dimensional coherent spectroscopy, and find that, at low electron doping densities, the dominant interactions are between polaron states that are dressed by the same Fermi sea. They also observe a bipolaron bound state with large binding energy, involving excitons in different valleys cooperatively bound to the same electron.

Optically controllable magnetism in atomically thin semiconductors

We report evidence that ferromagnetic order in electrostatically doped, monolayer transition metal dichalcogenide (TMD) semiconductors can be stabilized and controlled at zero magnetic field by local optical pumping. We use circular dichroism (CD) in reflectivity from excitonic states as a spatially resolved probe of charge-carrier spin polarization. At electron densities n_e ~ 10¹² cm^-2, a diffraction-limited, circularly polarized optical pump breaks symmetry between oppositely polarized magnetic states and stabilizes long-range magnetic order, with carrier polarization exceeding 80% over an 8 μm by 5 μm extent. In time-resolved measurements with pulsed optical excitation, we observe that magnetic interactions amplify the initial pump-induced spin polarization by more than an order of magnitude. The optical control of magnetism with local optical pumps will unlock advancements in spin and optical technologies and provides a versatile tool in the study of correlated phases in two-dimensional electron gases.

Six-Body and Eight-Body Exciton States in Monolayer WSe_{2}

In the archetypal monolayer semiconductor WSe_{2}, the distinct ordering of spin-polarized valleys (low-energy pockets) in the conduction band allows for studies of not only simple neutral excitons and charged excitons (i.e., trions), but also more complex many-body states that are predicted at higher electron densities. We discuss magneto-optical measurements of electron-rich WSe_{2} monolayers and interpret the spectral lines that emerge at high electron doping as optical transitions of six-body exciton states ("hexcitons") and eight-body exciton states ("oxcitons"). These many-body states emerge when a photoexcited electron-hole pair interacts simultaneously with multiple Fermi seas, each having distinguishable spin and valley quantum numbers. In addition, we explain the relations between dark trions and satellite optical transitions of hexcitons in the photoluminescence spectrum.

Upconversion photoluminescence excitation reveals exciton-trion and exciton-biexciton coupling in hBN/WS[Formula: see text]/hBN van der Waals heterostructures

Monolayers of transition-metal dichalcogenides with direct band gap located at the binary [Formula: see text] points of the Brillouin zone are promising materials for applications in opto- and spin-electronics due to strongly enhanced Coulomb interactions and specific spin-valley properties. They furthermore represent a unique platform to study electron-electron and electron-phonon interactions in diverse exciton complexes. Here, we demonstrate processes in which the neutral biexciton and two negative trions, namely the spin-triplet and spin-singlet trions, upconvert light into a bright intravalley exciton in an hBN-encapsulated WS[Formula: see text] monolayer. We propose that the energy gains required in the polarized upconversion photoluminescence originate from different interactions including resonant optical phonons, a cooling of resident electrons and a non-local and an anisotropic electron-hole exchange, respectively. The temperature dependence (7-120 K) of the excitonic upconversion intensity obtained at excitation energies corresponding to the biexciton and trions provides insight into an increasing phonon population as well as a thermally enhanced electron scattering. Our study sheds new light on the understanding of excitonic spin and valley properties of van der Waals heterostructures and improves the understanding of photonic upconversion mechanisms in two-dimensional quantum materials.

Highly Nonlinear Biexcitonic Photocurrent from Ultrafast Interlayer Charge Transfer

Strong Coulomb interactions in monolayer semiconductors allow them to host optically active large many-body states, such as the five-particle state, charged biexciton. Strong nonlinear light absorption by the charged biexciton under spectral resonance, coupled with its charged nature, makes it intriguing for nonlinear photodetection─an area that is hitherto unexplored. Using the high built-in vertical electric field in an asymmetrically designed few-layer graphene encapsulated 1L-WS₂ heterostructure, here we report a large, highly nonlinear photocurrent arising from the strong absorption by two charged biexciton species under zero external bias (self-powered mode). Time-resolved measurement reveals that the generated charged biexcitons transfer to the few-layer graphene in a time scale of sub-5 ps, indicating an ultrafast intrinsic limit of the photoresponse. By using single- and two-color photoluminescence excitation spectroscopy, we show that the two biexcitonic peaks originate from bright-dark and bright-bright exciton-trion combinations. Such innate nonlinearity in the photocurrent due to its biexcitonic origin, coupled with the ultrafast response due to swift interlayer charge transfer, exemplifies the promise of manipulating many-body effects in monolayers toward viable optoelectronic applications.

Theory of Excitons in Atomically Thin Semiconductors: Tight-Binding Approach

Atomically thin semiconductors from the transition metal dichalcogenide family are materials in which the optical response is dominated by strongly bound excitonic complexes. Here, we present a theory of excitons in two-dimensional semiconductors using a tight-binding model of the electronic structure. In the first part, we review extensive literature on 2D van der Waals materials, with particular focus on their optical response from both experimental and theoretical points of view. In the second part, we discuss our ab initio calculations of the electronic structure of MoS2, representative of a wide class of materials, and review our minimal tight-binding model, which reproduces low-energy physics around the Fermi level and, at the same time, allows for the understanding of their electronic structure. Next, we describe how electron-hole pair excitations from the mean-field-level ground state are constructed. The electron-electron interactions mix the electron-hole pair excitations, resulting in excitonic wave functions and energies obtained by solving the Bethe-Salpeter equation. This is enabled by the efficient computation of the Coulomb matrix elements optimized for two-dimensional crystals. Next, we discuss non-local screening in various geometries usually used in experiments. We conclude with a discussion of the fine structure and excited excitonic spectra. In particular, we discuss the effect of band nesting on the exciton fine structure; Coulomb interactions; and the topology of the wave functions, screening and dielectric environment. Finally, we follow by adding another layer and discuss excitons in heterostructures built from two-dimensional semiconductors.

Tuning the Optical Properties of a MoSe2 Monolayer Using Nanoscale Plasmonic Antennas

Nanoplasmonic systems combined with optically active two-dimensional materials provide intriguing opportunities to explore and control light-matter interactions at extreme subwavelength length scales approaching the exciton Bohr radius. Here, we present room- and cryogenic-temperature investigations of a MoSe₂ monolayer on individual gold dipole nanoantennas. By controlling nanoantenna size, the dipolar resonance is tuned relative to the exciton achieving a total tuning of ∼130 meV. Differential reflectance measurements performed on >100 structures reveal an apparent avoided crossing between exciton and dipolar mode and an exciton-plasmon coupling constant of g = 55 meV, representing g/(ℏω_X) ≥ 3% of the transition energy. This places our hybrid system in the intermediate-coupling regime where spectra exhibit a characteristic Fano-like shape. We demonstrate active control by varying the polarization of the excitation light to programmably suppress coupling to the dipole mode. We further study the emerging optical signatures of the monolayer localized at dipole nanoantennas at 10 K.

Free Trions with Near-Unity Quantum Yield in Monolayer MoSe2

Trions, quasiparticles composed of an electron-hole pair bound to a second electron and/or hole, are many-body states with potential applications in optoelectronics. Trions in monolayer transition metal dichalcogenide (TMD) semiconductors have attracted recent interest due to their valley/spin polarization, strong binding energy, and tunability through external gate control. However, low materials quality (i.e., high defect density) has hindered efforts to understand the intrinsic properties of trions. The low photoluminescence (PL) quantum yield (QY) and short lifetime of trions have prevented harnessing them in device applications. Here, we study the behavior of trions in a series of MoSe₂ monolayers, with atomic defect density varying by over 2 orders of magnitude. The QY increases with decreasing defect density and approaches unity in the cleanest material. Simultaneous measurement of the PL lifetime yields both the intrinsic radiative lifetime and the defect-dependent nonradiative lifetime. The long lifetime of ∼230 ps of trions allows direct observation of their diffusion.

Upconversion of Light into Bright Intravalley Excitons via Dark Intervalley Excitons in hBN-Encapsulated WSe2 Monolayers

Semiconducting monolayers of transition-metal dichalcogenides are outstanding platforms to study both electronic and phononic interactions as well as intra- and intervalley excitons and trions. These excitonic complexes are optically either active (bright) or inactive (dark) due to selection rules from spin or momentum conservation. Exploring ways of brightening dark excitons and trions has strongly been pursued in semiconductor physics. Here, we report on a mechanism in which a dark intervalley exciton upconverts light into a bright intravalley exciton in hBN-encapsulated WSe₂ monolayers. Excitation spectra of upconverted photoluminescence reveals resonances at energies 34.5 and 46.0 meV below the neutral exciton in the nominal WSe₂ transparency range. The required energy gains are theoretically explained by cooling of resident electrons or by exciton scattering with Λ- or K-valley phonons. Accordingly, an elevated temperature and a moderate concentration of resident electrons are necessary for observing the upconversion resonances. The interaction process observed between the inter- and intravalley excitons elucidates the importance of dark excitons for the optics of two-dimensional materials.

Negative valley polarization in doped monolayer MoSe2

Monolayer molybdenum di-selenide (1L-MoSe₂) stands out in the transition metal dichalcogenide family of materials as an outlier where optical generation of valley polarization is inefficient. Here we show that using charge doping in conjunction with an external magnetic field, the valley polarization of 1L-MoSe₂ can be controlled effectively. Most remarkably, the valley polarization can be tuned to negative values, where the higher energy Zeeman mode emission is more intense than the lower energy one. Our experimental observations are interpreted with valley-selective exciton-charge dressing that manifests when gate induced doping populates predominantly one valley in the presence of Zeeman splitting.

Dielectric Engineering for Manipulating Exciton Transport in Semiconductor Monolayers

The dielectric screening from the disordered media surrounding atomically thin transition metal dichalcogenides (TMDs) monolayers modifies the effective defect energy levels and thereby the transport and energy dynamics of excitons. In this work, we study this effect in WSe₂ monolayers for different combinations of surrounding dielectric media. Specifically, we study the source of the anomalous diffusion of excitons in the WSe₂ monolayer and attribute the anomaly to the modification of the energy distribution of defect states in different disordered dielectric environments. We use this insight to manipulate exciton transport by engineering the dielectric environment using a graphene/hexagonal boron nitride (h-BN) moiré superlattice. Finally, we observe that the effect of dielectric disorder is even more significant at high excitation fluences, contributing to the nonequilibrium phonon drag effect. These results provide an important step toward achieving control over the exciton energy transport for next-generation opto-excitonic devices.

Observation of Diffusion and Drift of the Negative Trions in Monolayer WS2

Monolayer transition metal dichalcogenides (ML-TMDCs) are a versatile platform to explore the transport dynamics of the tightly bound excitonic states. The diffusion of neutral excitons in various ML-TMDCs has been observed. However, the transport of charged excitons (trions), which can be driven by an in-plane electric field and facilitate the formation of an excitonic current, has yet been well investigated. Here, we report the direct observation of diffusion and drift of the trions in ML-WS₂ through spatially and time-resolved photoluminescence. An effective diffusion coefficient of 0.47 cm²/s was extracted from the broadening of spatial profiles of the trion emission. When an in-plane electric field is applied, the spatial shift of the trion emission profiles indicated a drift velocity of 7400 cm/s. Both the diffusion caused broadening and the drift caused shift of the emission profiles saturate because of the Coulomb interactions between trions and the background charges.

Theory and Ab Initio Calculation of Optically Excited States-Recent Advances in 2D Materials

Recent studies of the optical properties of 2D materials have reported unique phenomena and features that are absent in conventional bulk semiconductors. Many of these interesting properties, such as enhanced light-matter coupling, gate-tunable photoluminescence, and unusual excitonic optical selection rules arise from the nature of the two- and multi-particle excited states such as strongly bound Wannier excitons and charged excitons. The theory, modeling, and ab initio calculations of these optically excited states in 2D materials are reviewed. Several analytical and ab initio approaches are introduced. These methods are compared with each other, revealing their relative strength and limitations. Recent works that apply these methods to a variety of 2D materials and material-defect systems are then highlighted. Understanding of the optically excited states in these systems is relevant not only for fundamental scientific research of electronic excitations and correlations, but also plays an important role in the future development of quantum information science and nano-photonics.

Excitonic Complexes in n-Doped WS2 Monolayer

We investigate the origin of emission lines apparent in the low-temperature photoluminescence spectra of n-doped WS₂ monolayer embedded in hexagonal BN layers using external magnetic fields and first-principles calculations. Apart from the neutral A exciton line, all observed emission lines are related to the negatively charged excitons. Consequently, we identify emissions due to both the bright (singlet and triplet) and dark (spin- and momentum-forbidden) negative trions as well as the phonon replicas of the latter optically inactive complexes. The semidark trions and negative biexcitons are distinguished. On the basis of their experimentally extracted and theoretically calculated g-factors, we identify three distinct families of emissions due to exciton complexes in WS₂: bright, intravalley, and intervalley dark. The g-factors of the spin-split subbands in both the conduction and valence bands are also determined.

Highly Enhanced Light-Matter Interaction in MXene Quantum Dots-Monolayer WS2 Heterostructure

Since the Ti₃ C₂ was discovered in 2011, the family of MXenes has attracted much attention. MXenes offer great potential in the tuning of many fundamental properties by the synthesis of new structures. The synthesis methods of MXene mainly require steps including immersing a MAX phase in hydrofluoric acid (HF) and processing at high temperatures. However, the HF may be hard to acquire in many countries and processing at high temperatures may cause risk issues. In this article, a simple and cost-effective synthesis of Ti₃ C₂ T_x quantum dots (QDs) via chemical solution method that follows the long-time magnetic stirring process-initiated etching of Al atoms from commercial Ti₃ AlC₂ powder at room temperature is introduced. With WS₂ monolayer sitting over the MXenes QD arrays, a higher level of photoluminescence (PL) enhancement is found in the heterostructure with increasing laser power at room temperature and a few novel quasi-particles species in the heterostructure at -190 °C. The observations show that the possible plasmonic behavior initiated by QD arrays and the suspension state of WS₂ may coplay the roles to trigger multiple quasi-particles species. This study can be an important benchmark for the extensive understanding of quasi-particles species, and their dynamics.

Intrinsic donor-bound excitons in ultraclean monolayer semiconductors

The monolayer transition metal dichalcogenides are an emergent semiconductor platform exhibiting rich excitonic physics with coupled spin-valley degree of freedom and optical addressability. Here, we report a new series of low energy excitonic emission lines in the photoluminescence spectrum of ultraclean monolayer WSe2. These excitonic satellites are composed of three major peaks with energy separations matching known phonons, and appear only with electron doping. They possess homogenous spatial and spectral distribution, strong power saturation, and anomalously long population (>6 µs) and polarization lifetimes (>100 ns). Resonant excitation of the free inter- and intravalley bright trions leads to opposite optical orientation of the satellites, while excitation of the free dark trion resonance suppresses the satellites' photoluminescence. Defect-controlled crystal synthesis and scanning tunneling microscopy measurements provide corroboration that these features are dark excitons bound to dilute donors, along with associated phonon replicas. Our work opens opportunities to engineer homogenous single emitters and explore collective quantum optical phenomena using intrinsic donor-bound excitons in ultraclean 2D semiconductors.

Investigations of Electron-Electron and Interlayer Electron-Phonon Coupling in van der Waals hBN/WSe2/hBN Heterostructures by Photoluminescence Excitation Experiments

Monolayers of transition metal dichalcogenides (TMDs) with their unique physical properties are very promising for future applications in novel electronic devices. In TMDs monolayers, strong and opposite spin splittings of the energy gaps at the K points allow for exciting carriers with various combinations of valley and spin indices using circularly polarized light, which can further be used in spintronics and valleytronics. The physical properties of van der Waals heterostructures composed of TMDs monolayers and hexagonal boron nitride (hBN) layers significantly depend on different kinds of interactions. Here, we report on observing both a strong increase in the emission intensity as well as a preservation of the helicity of the excitation light in the emission from hBN/WSe₂/hBN heterostructures related to interlayer electron-phonon coupling. In combined low-temperature (T = 7 K) reflectivity contrast and photoluminescence excitation experiments, we find that the increase in the emission intensity is attributed to a double resonance, where the laser excitation and the combined Raman mode A'₁ (WSe₂) + ZO (hBN) are in resonance with the excited (2s) and ground (1s) states of the A exciton in a WSe₂ monolayer. In reference to the 2s state, our interpretation is in contrast with previous reports, in which this state has been attributed to the hybrid exciton state existing only in the hBN-encapsulated WSe₂ monolayer. Moreover, we observe that the electron-phonon coupling also enhances the helicity preservation of the exciting light in the emission of all observed excitonic complexes. The highest helicity preservation of more than 60% is obtained in the emission of the neutral biexciton and negatively charged exciton (trion) in its triplet state. Additionally, to the best of our knowledge, the strongly intensified emission of the neutral biexciton XX⁰ at double resonance condition is observed for the first time.

Ultrathin Ga2 O3 Glass: A Large-Scale Passivation and Protection Material for Monolayer WS2

Atomically thin transition metal dichalcogenide crystals (TMDCs) have extraordinary optical properties that make them attractive for future optoelectronic applications. Integration of TMDCs into practical all-dielectric heterostructures hinges on the ability to passivate and protect them against necessary fabrication steps on large scales. Despite its limited scalability, encapsulation of TMDCs in hexagonal boron nitride (hBN) currently has no viable alternative for achieving high performance of the final device. Here, it is shown that the novel, ultrathin Ga₂ O₃ glass is an ideal centimeter-scale coating material that enhances optical performance of the monolayers and protects them against further material deposition. In particular, Ga₂ O₃ capping of monolayer WS₂ outperforms commercial-grade hBN in both scalability and optical performance at room temperature. These properties make Ga₂ O₃ highly suitable for large-scale passivation and protection of monolayer TMDCs in functional heterostructures.

Autoionization and Dressing of Excited Excitons by Free Carriers in Monolayer WSe_{2}

We experimentally demonstrate dressing of the excited exciton states by a continuously tunable Fermi sea of free charge carriers in a monolayer semiconductor. It represents an unusual scenario of two-particle excitations of charged excitons previously inaccessible in conventional material systems. We identify excited state trions, accurately determine their binding energies in the zero-density limit for both electron- and hole-doped regimes, and observe emerging many-body phenomena at elevated doping. Combining experiment and theory we gain access to the intra-exciton coupling facilitated by the interaction with free charge carriers. We provide evidence for a process of autoionization for quasiparticles, a unique scattering pathway available for excited states in atomic systems. Finally, we demonstrate a complete transfer of the optical transition strength from the excited excitons to dressed Fermi-polaron states as well as the associated light emission from their nonequilibrium populations.

The highly-efficient light-emitting diodes based on transition metal dichalcogenides: from architecture to performance

Transition metal dichalcogenides (TMDCs) with layered architecture and excellent optoelectronic properties have been a hot spot for light-emitting diodes (LED). However, the light-emitting efficiency of TMDC LEDs is still low due to the large size limit of TMDC flakes and the inefficient device architecture. First and foremost, to develop the highly-efficient and reliable few-layer TMDC LEDs, the modulation of the electronic properties of TMDCs and TMDC heterostructures is necessary. In order to create efficient TMDC LEDs with prominent performance, an in-depth understanding of the working mechanism is needed. Besides conventional structures, the electric (or ionic liquid)-induced p-n junction of TMDCs is a useful configuration for multifunctional LED applications. The significant performances are contrasted in the four aspects of color, polarity, and external quantum efficiency. The color of light ranging from infrared to visible light can be acquired from TMDC LEDs by purposeful and selective architecture construction. To date, the maximum of the external quantum efficiency achieved by TMDC LEDs is 12%. In the demand for performance, the material and configuration of the nano device can be chosen according to this review. Moreover, novel electroluminescence devices involving single-photon emitters and alternative pulsed light emitters can expand their application scope. In this review, we provide an overview of the significant investigations that have provided a wealth of detailed information on TMDC electroluminescence devices at the molecular level.

Neutral and charged dark excitons in monolayer WS2

Low temperature and polarization resolved magneto-photoluminescence experiments are used to investigate the properties of dark excitons and dark trions in a monolayer of WS2 encapsulated in hexagonal BN (hBN). We find that this system is an n-type doped semiconductor and that dark trions dominate the emission spectrum. In line with previous studies on WSe2, we identify the Coulomb exchange interaction coupled neutral dark and grey excitons through their polarization properties, while an analogous effect is not observed for dark trions. Applying the magnetic field in both perpendicular and parallel configurations with respect to the monolayer plane, we determine the g-factor of dark trions to be g ∼ -8.6. Their decay rate is close to 0.5 ns, more than 2 orders of magnitude longer than that of bright excitons.

Up- and Down-Conversion between Intra- and Intervalley Excitons in Waveguide Coupled Monolayer WSe2

The presence of two spin-split valleys in monolayer (1L) transition metal dichalcogenide (TMD) semiconductors supports versatile exciton species classified by their spin and valley quantum numbers. While the spin-0 intravalley exciton, known as the "bright" exciton, is readily observable, other types of excitons, such as the spin-1 intravalley (spin-dark) and spin-0 intervalley (momentum-dark) excitons, are more difficult to access. Here we develop a waveguide coupled 1L tungsten diselenide (WSe₂) device to probe these exciton species. In particular, TM coupling to the atomic layer's out-of-plane dipole moments enabled us to not only efficiently collect but also resonantly populate the spin-1 dark excitons, promising for developing devices with long valley lifetimes. Our work reveals several upconversion processes that bring out an intricate coupling network linking spin-0 and spin-1 intra- and intervalley excitons, demonstrating that intervalley scattering and spin-flip are very common processes in the atomic layer. These experimental results deepen our understanding of tungsten diselenide exciton physics and illustrate that planar photonic devices are capable of harnessing versatile exciton species in TMD semiconductors.

Ground and excited state exciton polarons in monolayer MoSe2

Monolayer transition metal dichalcogenide semiconductors, with versatile experimentally accessible exciton species, offer an interesting platform for investigating the interaction between excitons and a Fermi sea of charges. Using hexagonal boron nitride encapsulated monolayer MoSe₂, we study the impact of charge density tuning on the A and B series of exciton Rydberg states, including A:1s, A:2s, B:1s, and B:2s. The doping dependence of the A:2s state provides an opportunity to examine such interactions with greatly reduced exciton binding energy and more spatially diffuse structures, and we found that the impact of the Fermi sea becomes much more dramatic compared to the A:1s state. Using photoluminescence upconversion, we verify that the B:2s exciton state displays similar behavior when interacting with the Fermi sea despite being well above the bare bandgap in energy. Photoluminescence and reflection spectra of the A:1s state show clear evidence that the interaction of the exciton with a Fermi sea is best described by the exciton-polaron model, rather than a trion model. Our experimental results demonstrate that overall features of charge interaction are quite generic and highly robust, offering key insights into the dressed many body states in a Fermi sea.

Localized Excitons in NbSe2-MoSe2 Heterostructures

Neutral and charged excitons (trions) in atomically thin materials offer important capabilities for photonics, from ultrafast photodetectors to highly efficient light-emitting diodes and lasers. Recent studies of van der Waals (vdW) heterostructures comprised of dissimilar monolayer materials have uncovered a wealth of optical phenomena that are predominantly governed by interlayer interactions. Here, we examine the optical properties in NbSe₂-MoSe₂ vdW heterostructures, which provide an important model system to study metal-semiconductor interfaces, a common element in optoelectronics. Through low-temperature photoluminescence (PL) microscopy, we discover a sharp emission feature, L1, that is localized at the NbSe₂-capped regions of MoSe₂. L1 is observed at energies below the commonly studied MoSe₂ excitons and trions and exhibits temperature- and power-dependent PL consistent with exciton localization in a confining potential. This PL feature is robust, observed in a variety of samples fabricated with different stacking geometries and cleaning procedures. Using first-principles calculations, we reveal that the confinement potential required for exciton localization naturally arises from the in-plane band bending due to the changes in the electron affinity between pristine MoSe₂ and NbSe₂-MoSe₂ heterostructure. We discuss the implications of our studies for atomically thin optoelectronics devices with atomically sharp interfaces and tunable electronic structures.

Optical properties of charged excitons in two-dimensional semiconductors

Strong Coulomb interaction in atomically thin transition metal dichalcogenides makes these systems particularly promising for studies of excitonic physics. Of special interest are the manifestations of the charged excitons, also known as trions, in the optical properties of two-dimensional semiconductors. In order to describe the optical response of such a system, the exciton interaction with resident electrons should be explicitly taken into account. In this paper, we demonstrate that this can be done in both the trion (essentially, few-particle) and Fermi-polaron (many-body) approaches, which produce equivalent results, provided that the electron density is sufficiently low and the trion binding energy is much smaller than the exciton one. Here, we consider the oscillator strengths of the optical transitions related to the charged excitons, fine structure of trions, and Zeeman effect, as well as photoluminescence of trions illustrating the applicability of both few-particle and many-body models.

Phonon-exciton Interactions in WSe2 under a quantizing magnetic field

Strong many-body interaction in two-dimensional transitional metal dichalcogenides provides a unique platform to study the interplay between different quasiparticles, such as prominent phonon replica emission and modified valley-selection rules. A large out-of-plane magnetic field is expected to modify the exciton-phonon interactions by quantizing excitons into discrete Landau levels, which is largely unexplored. Here, we observe the Landau levels originating from phonon-exciton complexes and directly probe exciton-phonon interaction under a quantizing magnetic field. Phonon-exciton interaction lifts the inter-Landau-level transition selection rules for dark trions, manifested by a distinctively different Landau fan pattern compared to bright trions. This allows us to experimentally extract the effective mass of both holes and electrons. The onset of Landau quantization coincides with a significant increase of the valley-Zeeman shift, suggesting strong many-body effects on the phonon-exciton interaction. Our work demonstrates monolayer WSe2 as an intriguing playground to study phonon-exciton interactions and their interplay with charge, spin, and valley.

Multipath Optical Recombination of Intervalley Dark Excitons and Trions in Monolayer WSe_{2}

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 scattering or chiral-phonon emission. We also reveal that a trion can decay in two distinct paths-through intravalley or intervalley electron-hole recombination-into two different final valley states. Although these two paths are energy degenerate, we can distinguish them by lifting the valley degeneracy under a magnetic field. In addition, the intra- and inter-valley trion transitions are coupled to zone-center and zone-corner chiral phonons, respectively, to produce distinct phonon replicas. The observed multipath optical decays of dark excitons and trions provide insight into the internal quantum structure of trions and the complex excitonic interactions with defects and chiral phonons in monolayer valley semiconductors.

Valley phonons and exciton complexes in a monolayer semiconductor

The coupling between spin, charge, and lattice degrees of freedom plays an important role in a wide range of fundamental phenomena. Monolayer semiconducting transitional metal dichalcogenides have emerged as an outstanding platform for studying these coupling effects. Here, we report the observation of multiple valley phonons - phonons with momentum vectors pointing to the corners of the hexagonal Brillouin zone - and the resulting exciton complexes in the monolayer semiconductor WSe₂. We find that these valley phonons lead to efficient intervalley scattering of quasi particles in both exciton formation and relaxation. This leads to a series of photoluminescence peaks as valley phonon replicas of dark trions. Using identified valley phonons, we also uncover an intervalley exciton near charge neutrality. Our work not only identifies a number of previously unknown 2D excitonic species, but also shows that monolayer WSe₂ is a prime candidate for studying interactions between spin, pseudospin, and zone-edge phonons.

Momentum-Dark Intervalley Exciton in Monolayer Tungsten Diselenide Brightened via Chiral Phonon

Inversion symmetry breaking and 3-fold rotation symmetry grant the valley degree of freedom to the robust exciton in monolayer transition-metal dichalcogenides, which can be exploited for valleytronics applications. However, the short lifetime of the exciton significantly constrains the possible applications. In contrast, the dark exciton could be long-lived but does not necessarily possess the valley degree of freedom. In this work, we report the identification of the momentum-dark, intervalley exciton in monolayer WSe₂ through low-temperature magneto-photoluminescence spectra. Interestingly, the intervalley exciton is brightened through the emission of a chiral phonon at the corners of the Brillouin zone (K point), and the pseudoangular momentum of the phonon is transferred to the emitted photon to preserve the valley information. The chiral phonon energy is determined to be ∼23 meV, based on the experimentally extracted exchange interaction (∼7 meV), in excellent agreement with the theoretical expectation of 24.6 meV. The long-lived intervalley exciton with valley degree of freedom adds an exciting quasiparticle for valleytronics, and the coupling between the chiral phonon and intervalley exciton furnishes a venue for valley spin manipulation.

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.

Polarity Tunable Trionic Electroluminescence in Monolayer WSe2

Monolayer WSe₂ exhibits luminescence arising from various types of exciton complexes due to strong many-body effects. Here, we demonstrate selective electrical excitation of positive and negative trions in van der Waals metal-insulator-semiconductor (MIS) heterostructure consisting of few-layer graphene (FLG), hexagonal boron nitride (hBN), and monolayer WSe₂. Intentional unbalanced injection of electrons and holes is achieved via field-emission tunneling and electrostatic accumulation. The device exhibits planar electroluminescence from either positive trion X⁺ or negative trion X^- depending on the bias conditions. We show that hBN serves as a tunneling barrier material allowing selective injection of electron or holes into WSe₂ from FLG layer. Our observation offers prospects for hot carrier injection, trion manipulation, and on-chip excitonic devices based on two-dimensional semiconductors.

Direct Observation of Gate-Tunable Dark Trions in Monolayer WSe2

Spin-forbidden intravalley dark excitons in tungsten-based transition-metal dichalcogenides (TMDCs), because of their unique spin texture and long lifetime, have attracted intense research interest. Here, we show that we can control the dark exciton electrostatically by dressing it with one free electron or free hole, forming the dark trions. The existence of the dark trions is suggested by the unique magneto-photoluminescence spectroscopy pattern of the boron nitride (BN)-encapsulated monolayer WSe₂ device at low temperature. The unambiguous evidence of the dark trions is further obtained by directly resolving the radiation pattern of the dark trions through back focal plane imaging. The dark trions possess a binding energy of ∼15 meV, and they inherit the long lifetime and large g-factor from the dark exciton. Interestingly, under the out-of-plane magnetic field, dressing the dark exciton with one free electron or hole results in distinctively different valley polarization of the emitted photon, as a result of the different intervalley scattering mechanism for the electron and hole. Finally, the lifetime of the positive dark trion can be further tuned from ∼50 ps to ∼215 ps by controlling the gate voltage. The gate-tunable dark trions usher in new opportunities for excitonic optoelectronics and valleytronics.

Energy Spectrum of Two-Dimensional Excitons in a Nonuniform Dielectric Medium

We demonstrate that, in monolayers (MLs) of semiconducting transition metal dichalcogenides, the s-type Rydberg series of excitonic states follows a simple energy ladder: ε_{n}=-Ry^{*}/(n+δ)^{2}, n=1,2,…, in which Ry^{*} is very close to the Rydberg energy scaled by the dielectric constant of the medium surrounding the ML and by the reduced effective electron-hole mass, whereas the ML polarizability is accounted for only by δ. This is justified by the analysis of experimental data on excitonic resonances, as extracted from magneto-optical measurements of a high-quality WSe_{2} ML encapsulated in hexagonal boron nitride (hBN), and well reproduced with an analytically solvable Schrödinger equation when approximating the electron-hole potential in the form of a modified Kratzer potential. Applying our convention to other MoSe_{2}, WS_{2}, MoS_{2} MLs encapsulated in hBN, we estimate an apparent magnitude of δ for each of the studied structures. Intriguingly, δ is found to be close to zero for WSe_{2} as well as for MoS_{2} monolayers, what implies that the energy ladder of excitonic states in these two-dimensional structures resembles that of Rydberg states of a three-dimensional hydrogen atom.

Optical generation of high carrier densities in 2D semiconductor heterobilayers

Controlling charge density in two-dimensional (2D) materials is a powerful approach for engineering new electronic phases and properties. This control is traditionally realized by electrostatic gating. Here, we report an optical approach for generation of high carrier densities using transition metal dichalcogenide heterobilayers, WSe₂/MoSe₂, with type II band alignment. By tuning the optical excitation density above the Mott threshold, we realize the phase transition from interlayer excitons to charge-separated electron/hole plasmas, where photoexcited electrons and holes are localized to individual layers. High carrier densities up to 4 × 10¹⁴ cm^-2 can be sustained under both pulsed and continuous wave excitation conditions. These findings open the door to optical control of electronic phases in 2D heterobilayers.

Probing and Manipulating Valley Coherence of Dark Excitons in Monolayer WSe_{2}

Monolayers of semiconducting transition metal dichalcogenides are two-dimensional direct-gap systems which host tightly bound excitons with an internal degree of freedom corresponding to the valley of the constituting carriers. Strong spin-orbit interaction and the resulting ordering of the spin-split subbands in the valence and conduction bands makes the lowest-lying excitons in WX_{2} (X being S or Se) spin forbidden and optically dark. With polarization-resolved photoluminescence experiments performed on a WSe_{2} monolayer encapsulated in a hexagonal boron nitride, we show how the intrinsic exchange interaction in combination with the applied in-plane and/or out-of-plane magnetic fields enables one to probe and manipulate the valley degree of freedom of the dark excitons.

Interface charge-transfer induced intralayer excited-state biexcitons in graphene/WS2 van der Waals heterostructures

Monolayer transition metal dichalcogenides (TMDCs) are an ideal platform for multi-carrier bound states, the excitons and trions of which have been well identified and investigated. However, the formation and identification of biexcitons with certain configurations are more complicated. Here, we report a strategy to generate the hole-trion bound state, i.e. excited-state biexcitons, in a graphene/WS₂ van der Waals heterostructure, the formation of which is attributed to the charge transfer and exciton dissociation at the hetero-interface. The biexciton nature is confirmed by excitation-power dependent, helicity-resolved, and time-resolved photoluminescence measurements. This hole-trion bound state features a thermal activation energy of ∼32 meV, rendering a stable excited-state biexciton emission up to 330 K. Moreover, the emission behavior of the excited-state biexcitons can be tuned by modifying the charge transfer process at the hetero-interface via electrostatic gating. Our results will benefit to further understanding the complex multi-carrier interactions in 2D semiconductors and related heterostructures.

Gate Tunable Dark Trions in Monolayer WSe_{2}

Monolayer WSe_{2} is an intriguing material to explore dark exciton physics. We have measured the photoluminescence from dark excitons and trions in ultraclean monolayer WSe_{2} devices encapsulated by boron nitride. The dark trions can be tuned continuously between negative and positive trions with electrostatic gating. We reveal their spin-triplet configuration and distinct valley optical emission by their characteristic Zeeman splitting under a magnetic field. The dark trion binding energies are 14-16 meV, slightly lower than the bright trion binding energies (21-35 meV). The dark trion lifetime (∼1.3  ns) is two orders of magnitude longer than the bright trion lifetime (∼10  ps) and can be tuned between 0.4 and 1.3 ns by gating. Such robust, optically detectable, and gate tunable dark trions may help us realize trion transport in two-dimensional materials.

Emerging photoluminescence from the dark-exciton phonon replica in monolayer WSe2

Tungsten-based monolayer transition metal dichalcogenides host a long-lived "dark" exciton, an electron-hole pair in a spin-triplet configuration. The long lifetime and unique spin properties of the dark exciton provide exciting opportunities to explore light-matter interactions beyond electric dipole transitions. Here we demonstrate that the coupling of the dark exciton and an optically silent chiral phonon enables the intrinsic photoluminescence of the dark-exciton replica in monolayer WSe2. Gate and magnetic-field dependent PL measurements unveil a circularly-polarized replica peak located below the dark exciton by 21.6 meV, equal to E″ phonon energy from Se vibrations. First-principles calculations show that the exciton-phonon interaction selectively couples the spin-forbidden dark exciton to the intravalley spin-allowed bright exciton, permitting the simultaneous emission of a chiral phonon and a circularly-polarized photon. Our discovery and understanding of the phonon replica reveals a chirality dictated emission channel of the phonons and photons, unveiling a new route of manipulating valley-spin.

Virtual Trions in the Photoluminescence of Monolayer Transition-Metal Dichalcogenides

Photoluminescence experiments from monolayer transition-metal dichalcogenides often show that the binding energy of trions is conspicuously similar to the energy of optical phonons. This enigmatic coincidence calls into question whether phonons are involved in the radiative recombination process. We address this problem, unraveling an intriguing optical transition mechanism. Its initial state is a localized charge (electron or hole) and delocalized exciton. The final state is the localized charge, phonon, and photon. In between, the intermediate state of the system is a virtual trion formed when the localized charge captures the exciton through emission of the phonon. We analyze the difference between radiative recombinations that involve real and virtual trions (i.e., with and without a phonon), providing useful ways to distinguish between the two in experiment.