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

Observation of phonon Stark effect

Stark effect, the electric-field analogue of magnetic Zeeman effect, is one of the celebrated phenomena in modern physics and appealing for emergent applications in electronics, optoelectronics, as well as quantum technologies. While in condensed matter it has prospered only for excitons, whether other collective excitations can display Stark effect remains elusive. Here, we report the observation of phonon Stark effect in a two-dimensional quantum system of bilayer 2H-MoS2. The longitudinal acoustic phonon red-shifts linearly with applied electric fields and can be tuned over ~1 THz, evidencing giant Stark effect of phonons. Together with many-body ab initio calculations, we uncover that the observed phonon Stark effect originates fundamentally from the strong coupling between phonons and interlayer excitons (IXs). In addition, IX-mediated electro-phonon intensity modulation up to ~1200% is discovered for infrared-active phonon A2u. Our results unveil the exotic phonon Stark effect and effective phonon engineering by IX-mediated mechanism, promising for a plethora of exciting many-body physics and potential technological innovations.

Trifluoromethylation of 2D Transition Metal Dichalcogenides: A Mild Functionalization and Tunable p-Type Doping Method

Chemical modification is a powerful strategy for tuning the electronic properties of 2D semiconductors. Here we report the electrophilic trifluoromethylation of 2D WSe2 and MoS2 under mild conditions using the reagent trifluoromethyl thianthrenium triflate (TTT). Chemical characterization and density functional theory calculations reveal that the trifluoromethyl groups bind covalently to surface chalcogen atoms as well as oxygen substitution sites. Trifluoromethylation induces p-type doping in the underlying 2D material, enabling the modulation of charge transport and optical emission properties in WSe2. This work introduces a versatile and efficient method for tailoring the optical and electronic properties of 2D transition metal dichalcogenides.

Ultralow Auger-Assisted Interlayer Exciton Annihilation in WS2/WSe2 Moiré Heterobilayers

Transition metal dichalcogenide (TMD) heterobilayers have emerged as a promising platform for exploring solid-state quantum simulators and many-body quantum phenomena. Their type II band alignment, combined with the moiré superlattice, inevitably leads to nontrivial exciton interactions and dynamics. Here, we unveil the distinct Auger annihilation processes for delocalized interlayer excitons in WS2/WSe2 moiré heterobilayers. By fitting the characteristic efficiency droop and bimolecular recombination rate, we quantitatively determine an ultralow Auger coefficient of 1.3 × 10-5 cm2 s-1, which is >100-fold smaller than that of excitons in TMD monolayers. In addition, we reveal selective exciton upconversion into the WSe2 layer, which highlights the significance of intralayer electron Coulomb interactions in dictating the microscopic scattering pathways. The distinct Auger processes arising from spatial electron-hole separation have important implications for TMD heterobilayers while endowing interlayer excitons and their strongly correlated states with unique layer degrees of freedom.

Coexisting Phases in Transition Metal Dichalcogenides: Overview, Synthesis, Applications, and Prospects

Over the past decade, significant advancements have been made in phase engineering of two-dimensional transition metal dichalcogenides (TMDCs), thereby allowing controlled synthesis of various phases of TMDCs and facile conversion between them. Recently, there has been emerging interest in TMDC coexisting phases, which contain multiple phases within one nanostructured TMDC. By taking advantage of the merits from the component phases, the coexisting phases offer enhanced performance in many aspects compared with single-phase TMDCs. Herein, this review article thoroughly expounds the latest progress and ongoing efforts on the syntheses, properties, and applications of TMDC coexisting phases. The introduction section overviews the main phases of TMDCs (2H, 3R, 1T, 1T', 1Td), along with the advantages of phase coexistence. The subsequent section focuses on the synthesis methods for coexisting phases of TMDCs, with particular attention to local patterning and random formations. Furthermore, on the basis of the versatile properties of TMDC coexisting phases, their applications in magnetism, valleytronics, field-effect transistors, memristors, and catalysis are discussed. Lastly, a perspective is presented on the future development, challenges, and potential opportunities of TMDC coexisting phases. This review aims to provide insights into the phase engineering of 2D materials for both scientific and engineering communities and contribute to further advancements in this emerging field.

Spatial Imaging and Control of Dark Excitons in Monolayer Transition Metal Dichalcogenides

Dark excitons play a vital role in exciton condensation and optical properties of monolayer transition metal dichalcogenides (MTMDs). Previous literature mainly focuses on the detection of the energy of the dark exciton, while spatial detection and control are equally important but are less studied. Here we report that for MTMD embedded in a semiconductor microcavity and under a uniform in-plane magnetic field the spatial distribution of the dark exciton can be probed by measuring that of the cavity photon for small exciton-exciton interaction energy. Further, we propose to realize the anomalous exciton Hall effect by exploiting spatially inhomogeneous coupling of the bright and dark excitons under a Gaussian excitation beam. This effect occurs regardless of the exciton-exciton interaction, which will strengthen the diffusion of excitons in the excitation region. These results provide an improved understanding of the excitons in MTMDs, thereby facilitating their potential practical applications.

Phonon Chirality Manipulation Mechanism in Transition-Metal Dichalcogenide Interlayer-Sliding Ferroelectrics

As an ideal platform, both the theoretical prediction and first experimental verification of chiral phonons are based on transition-metal dichalcogenide materials. The manipulation of phonon chirality in these materials will have a profound effect on the study of chiral phonons. In this work, we utilize the sliding ferroelectric effect to realize the phonon chirality manipulation mechanism in transition-metal dichalcogenide materials. Based on first-principles calculations, we find the different manipulation effects of interlayer sliding on the phonon chirality and Berry curvature in bilayer and four-layer MoS2 sliding ferroelectrics. These further affect the phonon angular momentum and magnetization under a temperature gradient and the phonon Hall effect under a magnetic field. Our work connects two emerging fields and opens up a new route to manipulating phonon chirality in transition-metal dichalcogenide materials through the sliding ferroelectric mechanism.

Photoluminescence upconversion in monolayer WSe2 activated by plasmonic cavities through resonant excitation of dark excitons

Anti-Stokes photoluminescence (PL) is light emission at a higher photon energy than the excitation, with applications in optical cooling, bioimaging, lasing, and quantum optics. Here, we show how plasmonic nano-cavities activate anti-Stokes PL in WSe2 monolayers through resonant excitation of a dark exciton at room temperature. The optical near-fields of the plasmonic cavities excite the out-of-plane transition dipole of the dark exciton, leading to light emission from the bright exciton at higher energy. Through statistical measurements on hundreds of plasmonic cavities, we show that coupling to the dark exciton leads to a near hundred-fold enhancement of the upconverted PL intensity. This is further corroborated by experiments in which the laser excitation wavelength is tuned across the dark exciton. We show that a precise nanoparticle geometry is key for a consistent enhancement, with decahedral nanoparticle shapes providing an efficient PL upconversion. Finally, we demonstrate a selective and reversible switching of the upconverted PL via electrochemical gating. Our work introduces the dark exciton as an excitation channel for anti-Stokes PL in WSe2 and paves the way for large-area substrates providing nanoscale optical cooling, anti-Stokes lasing, and radiative engineering of excitons.

Interplay of valley polarized dark trion and dark exciton-polaron in monolayer WSe2

The interactions between charges and excitons involve complex many-body interactions at high densities. The exciton-polaron model has been adopted to understand the Fermi sea screening of charged excitons in monolayer transition metal dichalcogenides. The results provide good agreement with absorption measurements, which are dominated by dilute bright exciton responses. Here we investigate the Fermi sea dressing of spin-forbidden dark excitons in monolayer WSe2. With a Zeeman field, the valley-polarized dark excitons show distinct p-doping dependence in photoluminescence when the carriers reach a critical density. This density can be interpreted as the onset of strongly modified Fermi sea interactions and shifts with increasing exciton density. Through valley-selective excitation and dynamics measurements, we also infer an intervalley coupling between the dark trions and exciton-polarons mediated by the many-body interactions. Our results reveal the evolution of Fermi sea screening with increasing exciton density and the impacts of polaron-polaron interactions, which lay the foundation for understanding electronic correlations and many-body interactions in 2D systems.

Tunable phononic coupling in excitonic quantum emitters

Engineering the coupling between fundamental quantum excitations is at the heart of quantum science and technologies. An outstanding case is the creation of quantum light sources in which coupling between single photons and phonons can be controlled and harnessed to enable quantum information transduction. Here we report the deterministic creation of quantum emitters featuring highly tunable coupling between excitons and phonons. The quantum emitters are formed in strain-induced quantum dots created in homobilayer WSe2. The colocalization of quantum-confined interlayer excitons and terahertz interlayer breathing-mode phonons, which directly modulates the exciton energy, leads to a uniquely strong phonon coupling to single-photon emission, with a Huang-Rhys factor reaching up to 6.3. The single-photon spectrum of interlayer exciton emission features a single-photon purity >83% and multiple phonon replicas, each heralding the creation of a phonon Fock state in the quantum emitter. Due to the vertical dipole moment of the interlayer exciton, the phonon-photon interaction is electrically tunable to be higher than the exciton and phonon decoherence rate, and hence promises to reach the strong-coupling regime. Our result demonstrates a solid-state quantum excitonic-optomechanical system at the atomic interface of the WSe2 bilayer that emits flying photonic qubits coupled with stationary phonons, which could be exploited for quantum transduction and interconnection.

Gate-Tunable Phonon Magnetic Moment in Bilayer Graphene

We develop a first-principles quantum scheme to calculate the phonon magnetic moment in solids. As a showcase example, we apply our method to study gated bilayer graphene, a material with strong covalent bonds. According to the classical theory based on the Born effective charge, the phonon magnetic moment in this system should vanish, yet our quantum mechanical calculations find significant phonon magnetic moments. Furthermore, the magnetic moment is highly tunable by changing the gate voltage. Our results firmly establish the necessity of the quantum mechanical treatment, and identify small-gap covalent materials as a promising platform for studying tunable phonon magnetic moment.

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).

Giant Out-of-Plane Exciton Emission Enhancement in Two-Dimensional Indium Selenide via a Plasmonic Nanocavity

Out-of-plane (OP) exciton-based emitters in two-dimensional semiconductor materials are attractive candidates for novel photonic applications, such as radially polarized sources, integrated photonic chips, and quantum communications. However, their low quantum efficiency resulting from forbidden transitions limits their practicality. In this work, we achieve a giant enhancement of up to 34000 for OP exciton emission in indium selenide (InSe) via a designed Ag nanocube-over-Au film plasmonic nanocavity. The large photoluminescence enhancement factor (PLEF) is attributed to the induced OP local electric field (E_z) within the nanocavity, which facilitates effective OP exciton-plasmon interaction and subsequent tremendous enhancement. Moreover, the nanoantenna effect resulting from the effective interaction improves the directivity of spontaneous radiation. Our results not only reveal an effective photoluminescence enhancement approach for OP excitons but also present an avenue for designing on-chip photonic devices with an OP dipole orientation.

Exciton dispersion and exciton-phonon interaction in solids by time-dependent density functional theory

Understanding, predicting, and ultimately controlling exciton band structure and exciton dynamics are central to diverse chemical and materials problems. Here, we have developed a first-principles method to determine exciton dispersion and exciton-phonon interaction in semiconducting and insulating solids based on time-dependent density functional theory. The first-principles method is formulated in planewave bases and pseudopotentials and can be used to compute exciton band structures, exciton charge density, ionic forces, the non-adiabatic coupling matrix between excitonic states, and the exciton-phonon coupling matrix. Based on the spinor formulation, the method enables self-consistent noncollinear calculations to capture spin-orbital coupling. Hybrid exchange-correlation functionals are incorporated to deal with long-range electron-hole interactions in solids. A sub-Hilbert space approximation is introduced to reduce the computational cost without loss of accuracy. For validations, we have applied the method to compute the exciton band structure and exciton-phonon coupling strength in transition metal dichalcogenide monolayers; both agree very well with the previous GW-Bethe-Salpeter equation and experimental results. This development paves the way for accurate determinations of exciton dynamics in a wide range of solid-state materials.

Tip-Enhanced Dark Exciton Nanoimaging and Local Strain Control in Monolayer WSe2

Dark excitons in transition-metal dichalcogenides, with their long lifetimes and strong binding energies, provide potential platforms from photonic and optoelectronic applications to quantum information science even at room temperature. However, their spatial heterogeneity and sensitivity to strain is not yet understood. Here, we combine tip-enhanced photoluminescence spectroscopy with atomic force induced strain control to nanoimage dark excitons in WSe₂ and their response to local strain. Dark exciton emission is facilitated by out-of-plane picocavity Purcell enhancement giving rise to spatially highly localized emission, providing for higher spatial resolution compared to bright exciton nanoimaging. Further, tip-antenna-induced dark exciton emission is enhanced in areas of higher strain associated with bubbles. In addition, active force control shows dark exciton emission to be more sensitive to strain with both compressive and tensile lattice deformation facilitating emission. This interplay between localized strain and Purcell effects provides novel pathways for nanomechanical exciton emission control.

Enhancing the Purity of Deterministically Placed Quantum Emitters in Monolayer WSe2

We present a method utilizing an applied electrostatic potential for suppressing the broad defect bound excitonic emission in two-dimensional materials (2DMs) which otherwise inhibits the purity of strain induced single photon emitters (SPEs). Our heterostructure consists of a WSe₂ monolayer on a polymer in which strain has been deterministically introduced via an atomic force microscope (AFM) tip. We show that by applying an electrostatic potential, the broad defect bound background is suppressed at cryogenic temperatures, resulting in a substantial improvement in single photon purity demonstrated by a 10-fold reduction of the correlation function g⁽²⁾(0) value from 0.73 to 0.07. In addition, we see a 2-fold increase in the intensity of the SPEs as well as the ability to activate/deactivate the emitters at certain wavelengths. Finally, we present an increase in the operating temperature of the SPE up to 110 K, a 50 K increase when compared with the results when no electrostatic potential is present.

Valley Relaxation of the Moiré Excitons in a WSe2/MoSe2 Heterobilayer

The moiré superlattice consisting of lattice- or angular-mismatched van der Waals heterostructures drastically changes the physical properties of constituent atomically thin materials by confinement of the exciton by the moiré potential, which is promising for next-generation quantum optics. The moiré superlattice also affects the valley degrees of freedom of the monolayer transition-metal dichalcogenides (TMDs) and the valley-dependent optical selection rule, which results in the characteristic circular polarized light emission of the moiré exciton. However, the valley relaxation process of excitons in the moiré superlattice remains to be understood. Here, we studied valley relaxation of moiré excitons in a twisted WSe₂/MoSe₂ heterobilayer by circularly polarized photoluminescence and photoluminescence excitation (PLE) spectroscopy. The experimentally observed circularly polarized emission strongly depends on the excitation power density, which contrasts with the case of two-dimensional monolayer TMDs. The excitation power-dependent circularly polarized emission suggests the characteristic valley relaxation of the moiré exciton with a small density of states in zero-dimensional systems. In addition, the resonant PLE measurement reveals the intravalley relaxation process from the triplet to singlet state of the moiré exciton via Γ₅ phonon emission. Our findings clarified the valley relaxation of the moiré excitons, which would lead to the application of the circularly polarized quantum light emitter in twisted semiconducting heterobilayers.

Single charge control of localized excitons in heterostructures with ferroelectric thin films and two-dimensional transition metal dichalcogenides

Single charge control of localized excitons (LXs) in two-dimensional transition metal dichalcogenides (TMDCs) is crucial for potential applications in quantum information processing and storage. However, traditional electrostatic doping method by applying metallic gates onto TMDCs may cause inhomogeneous charge distribution, optical quenching, and energy loss. Herein, by locally controlling the ferroelectric polarization of the ferroelectric thin film BiFeO₃ (BFO) with a scanning probe, we can deterministically manipulate the doping type of monolayer WSe₂ to achieve p-type and n-type doping. This nonvolatile approach can maintain the doping type and hold the localized excitonic charges for a long time without applied voltage. Our work demonstrated that the ferroelectric polarization of BFO can control the charges of LXs effectively. Neutral and charged LXs have been observed in different ferroelectric polarization regions, confirmed by magnetic optical measurement. Highly circular polarization degree with 90% photon emission from these quantum emitters was achieved in high magnetic fields. Controlling the single charge of LXs in a non-volatile way shows a great potential for deterministic photon emission with desired charge states for photonic long-term memory.

Superacid Treatment on Transition Metal Dichalcogenides

Superacids are strong acids with an acidity higher than pure sulfuric acid. Recently, superacid treatment of monolayer transition metal dichalcogenide (TMDC) flakes, such as MoS2 and WS2, has shown a dramatic enhancement of optical properties, such as photoluminescence (PL) intensity. The superacid molecule is bis(trifluoromethane)sulfonimide (TFSI). In this review paper, we summarize and discuss the recent works and the current understanding of the TFSI treatment, and finally, we describe the outlook of the treatment on monolayer TMDCs.

Phononic Cavity Optomechanics of Atomically Thin Crystal in Plasmonic Nanocavity

In the picture of molecular cavity optomechanics, surface-enhanced Raman scattering (SERS) can be understood as molecular oscillators parametrically coupled to plasmonic nanocavities supporting an extremely localized optical field. This enables SERS from conventional fingerprint detection toward quantum nanotechnologies associated with, e.g., frequency upconversion and optomechanically induced transparency. Here, we study a phononic cavity optomechanical system consisting of a monolayer MoS₂ placed inside a plasmonic nanogap, where the coherent phonon-plasmon interaction involves the collective oscillation from tens of thousands of unit cells of the MoS₂ crystal. We observe the selective nonlinear SERS enhancement of the system as determined by the laser-plasmon detuning, suggesting the dynamic backaction modification of the phonon populations. Anomalous superlinear power dependence of a second-order Raman-inactive phonon mode with respect to the first-order phonons is also observed, indicating the distinctive properties of the phononic nanodevice compared with the molecular system. Our results promote the development of robust phononic optomechanical nanocavities to further explore the related quantum correlation and nonlinear effects including parametric instabilities.

High-Density, Localized Quantum Emitters in Strained 2D Semiconductors

Two-dimensional chalcogenide semiconductors have recently emerged as a host material for quantum emitters of single photons. While several reports on defect- and strain-induced single-photon emission from 2D chalcogenides exist, a bottom-up, lithography-free approach to producing a high density of emitters remains elusive. Further, the physical properties of quantum emission in the case of strained 2D semiconductors are far from being understood. Here, we demonstrate a bottom-up, scalable, and lithography-free approach for creating large areas of localized emitters with high density (∼150 emitters/um²) in a WSe₂ monolayer. We induce strain inside the WSe₂ monolayer with high spatial density by conformally placing the WSe₂ monolayer over a uniform array of Pt nanoparticles with a size of 10 nm. Cryogenic, time-resolved, and gate-tunable luminescence measurements combined with near-field luminescence spectroscopy suggest the formation of localized states in strained regions that emit single photons with a high spatial density. Our approach of using a metal nanoparticle array to generate a high density of strained quantum emitters will be applied to scalable, tunable, and versatile quantum light sources.

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.

Ab initiocalculations of spin-nonconserving exciton-phonon scattering in monolayer transition metal dichalcogenides

We investigate the spin-nonconserving relaxation channel of excitons by their couplings with phonons in two-dimensional transition metal dichalcogenides usingab initioapproaches. Combining GW-Bethe-Salpeter equation method and density functional perturbation theory, we calculate the electron-phonon and exciton-phonon coupling matrix elements for the spin-flip scattering in monolayer WSe₂, and further analyze the microscopic mechanisms influencing these scattering strengths. We find that phonons could produce effective in-plane magnetic fields which flip spin of excitons, giving rise to relaxation channels complimentary to the spin-conserving relaxation. Finally, we calculate temperature-dependent spin-flip exciton-phonon relaxation times. Our method and analysis can be generalized to study other two-dimensional materials and would stimulate experimental measurements of spin-flip exciton relaxation dynamics.

Visualization of Dark Excitons in Semiconductor Monolayers for High-Sensitivity Strain Sensing

Transition-metal dichalcogenides (TMDs) are layered materials that have a semiconducting phase with many advantageous optoelectronic properties, including tightly bound excitons and spin-valley locking. In tungsten-based TMDs, spin- and momentum-forbidden transitions give rise to dark excitons that typically are optically inaccessible but represent the lowest excitonic states of the system. Dark excitons can deeply affect the transport, dynamics, and coherence of bright excitons, hampering device performance. Therefore, it is crucial to create conditions in which these excitonic states can be visualized and controlled. Here, we show that compressive strain in WS₂ enables phonon scattering of photoexcited electrons between momentum valleys, enhancing the formation of dark intervalley excitons. We show that the emission and spectral properties of momentum-forbidden excitons are accessible and strongly depend on the local strain environment that modifies the band alignment. This mechanism is further exploited for strain sensing in two-dimensional semiconductors, revealing a gauge factor exceeding 10⁴.

Excellent response to near ultraviolet light and large intervalley scatterings of electrons in 2D SnS2

Tin disulfide (SnS₂) has attracted much attention as a novel two dimensional material due to its potential applications in electronics and optoelectronics. In this work, we investigated the optical properties of ultra-thin SnS₂ film samples (∼8 nm) via spectroscopic ellipsometry, and found that SnS₂ maintains a relatively high imaginary part of the dielectric constant (ε₂) in the range of 256-377 nm indicating high optical response. The carrier transport properties of SnS₂ were investigated considering full mode-resolved electron-phonon couplings, which reveal that the intervalley scatterings between degenerate valley (peaks) states via the fifth optical branch phonons play a dominant role in electron scattering, while ZA phonons dominate the hole scattering. The calculated electron mobility is ∼50 cm² V^-1 s^-1 which is close to previously reported experimental results. By considering full el-ph interactions based on the rigid-band approximation, the maximum value of the thermoelectric figure of merit zT reaches 0.43 at 700 K. Our work not only reveals the promising applications of SnS₂ in the fields of electronics and optoelectronics, but also showcases the computational framework for precise calculations of thermoelectric performances.

Electrically Switchable Intervalley Excitons with Strong Two-Phonon Scattering in Bilayer WSe2

We report the observation of QΓ intervalley exciton in bilayer WSe₂ devices encapsulated by boron nitride. The QΓ exciton resides at ∼18 meV below the QK exciton. The QΓ and QK excitons exhibit different Stark shifts under an out-of-plane electric field due to their different interlayer dipole moments. By controlling the electric field, we can switch their energy ordering and control which exciton dominates the luminescence of bilayer WSe₂. Remarkably, both QΓ and QK excitons exhibit unusually strong two-phonon replicas, which are comparable to or even stronger than the one-phonon replicas. By detailed theoretical simulation, we reveal the existence of numerous (≥14) two-phonon scattering paths involving (nearly) resonant exciton-phonon scattering in bilayer WSe₂. To our knowledge, such electric-field-switchable intervalley excitons with strong two-phonon replicas have not been found in any other two-dimensional semiconductors. These make bilayer WSe₂ a distinctive valleytronic material with potential novel applications.

Bright and Dark Exciton Coherent Coupling and Hybridization Enabled by External Magnetic Fields

Magnetic field- and polarization-dependent measurements on bright and dark excitons in monolayer WSe₂ combined with time-dependent density functional theory calculations reveal intriguing phenomena. Magnetic fields up to 25 T parallel to the WSe₂ plane lead to a partial brightening of the energetically lower lying exciton, leading to an increase of the dephasing time. Using a broadband femtosecond pulse excitation, the bright and partially allowed excitonic state can be excited simultaneously, resulting in coherent quantum beating between these states. The magnetic fields perpendicular to the WSe₂ plane energetically shift the bright and dark excitons relative to each other, resulting in the hybridization of the states at the K and K' valleys. Our experimental results are well captured by time-dependent density functional theory calculations. These observations show that magnetic fields can be used to control the coherent dephasing and coupling of the optical excitations in atomically thin semiconductors.

Probing dark exciton navigation through a local strain landscape in a WSe2 monolayer

In WSe₂ monolayers, strain has been used to control the energy of excitons, induce funneling, and realize single-photon sources. Here, we developed a technique for probing the dynamics of free excitons in nanoscale strain landscapes in such monolayers. A nanosculpted tapered optical fiber is used to simultaneously generate strain and probe the near-field optical response of WSe₂ monolayers at 5 K. When the monolayer is pushed by the fiber, its lowest energy states shift by as much as 390 meV (>20% of the bandgap of a WSe₂ monolayer). Polarization and lifetime measurements of these red-shifting peaks indicate they originate from dark excitons. We conclude free dark excitons are funneled to high-strain regions during their long lifetime and are the principal participants in drift and diffusion at cryogenic temperatures. This insight supports proposals on the origin of single-photon sources in WSe₂ and demonstrates a route towards exciton traps for exciton condensation.

Here, the authors use a tapered optical fibre to create a dynamic, reversible strain in a suspended WSe₂ monolayer, and observe that dark excitons are funnelled to high-strain regions and are the principal participants in drift and diffusion at cryogenic temperatures.

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.

Non-equilibrium diffusion of dark excitons in atomically thin semiconductors

Atomically thin semiconductors provide an excellent platform to study intriguing many-particle physics of tightly-bound excitons. In particular, the properties of tungsten-based transition metal dichalcogenides are determined by a complex manifold of bright and dark exciton states. While dark excitons are known to dominate the relaxation dynamics and low-temperature photoluminescence, their impact on the spatial propagation of excitons has remained elusive. In our joint theory-experiment study, we address this intriguing regime of dark state transport by resolving the spatio-temporal exciton dynamics in hBN-encapsulated WSe₂ monolayers after resonant excitation. We find clear evidence of an unconventional, time-dependent diffusion during the first tens of picoseconds, exhibiting strong deviation from the steady-state propagation. Dark exciton states are initially populated by phonon emission from the bright states, resulting in creation of hot (unequilibrated) excitons whose rapid expansion leads to a transient increase of the diffusion coefficient by more than one order of magnitude. These findings are relevant for both fundamental understanding of the spatio-temporal exciton dynamics in atomically thin materials as well as their technological application by enabling rapid diffusion.

Manipulation of Exciton Dynamics in Single-Layer WSe2 Using a Toroidal Dielectric Metasurface

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 enhancement over 1 order of magnitude at both room and low temperatures. Furthermore, we could control exciton dynamics and annihilation by using temperature to tailor the spectral overlap of excitonic and toroidal resonances, allowing us to selectively enhance the Purcell effect. Our results provide rich physical insight into the strong light-matter interactions in single-layer TMDs coupled with toroidal dielectric metasurfaces, with important implications for optoelectronics and photonics applications.

Quasi-1D exciton channels in strain-engineered 2D materials

Strain engineering is a powerful tool in designing artificial platforms for high-temperature excitonic quantum devices. Combining strong light-matter interaction with robust and mobile exciton quasiparticles, two-dimensional transition metal dichalcogenides (2D TMDCs) hold great promise in this endeavor. However, realizing complex excitonic architectures based on strain-induced electronic potentials alone has proven to be exceptionally difficult so far. Here, we demonstrate deterministic strain engineering of both single-particle electronic bandstructure and excitonic many-particle interactions. We create quasi-1D transport channels to confine excitons and simultaneously enhance their mobility through locally suppressed exciton-phonon scattering. Using ultrafast, all-optical injection and time-resolved readout, we realize highly directional exciton flow with up to 100% anisotropy both at cryogenic and room temperatures. The demonstrated fundamental modification of the exciton transport properties in a deterministically strained 2D material with effectively tunable dimensionality has broad implications for both basic solid-state science and emerging technologies.

Phonon Magnetic Moment from Electronic Topological Magnetization

The traditional theory of magnetic moments for chiral phonons is based on the picture of the circular motion of the Born effective charge, typically yielding a small fractional value of the nuclear magneton. Here we investigate the adiabatic evolution of electronic states induced by the lattice vibration of a chiral phonon and obtain an electronic orbital magnetization in the form of a topological second Chern form. We find that the traditional theory needs to be refined by introducing a k resolved Born effective charge, and identify another contribution from the phonon-modified electronic energy together with the momentum-space Berry curvature. The second Chern form can diverge when there is a Yang's monopole near the parameter space of interest as illustrated by considering a phonon at the Brillouin zone corner in a gapped graphene model. We also find large magnetic moments for the optical phonon in bulk topological materials where nontopological contribution is also important. Our results agree with recent observations in experiments.

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.

Direct Visualization of Large-Scale Intrinsic Atomic Lattice Structure and Its Collective Anisotropy in Air-Sensitive Monolayer 1T'- WTe2

Probing large-scale intrinsic structure of air-sensitive 2D materials with atomic resolution is so far challenging due to their rapid oxidization and contamination. Here, by keeping the whole experiment including growth, transfer, and characterizations in an interconnected atmosphere-control environment, the large-scale intact lattice structure of air-sensitive monolayer 1T'-WTe₂ is directly visualized by atom-resolved scanning transmission electron microscopy. Benefit from the large-scale atomic mapping, collective lattice distortions are further unveiled due to the presence of anisotropic rippling, which propagates perpendicular to only one of the preferential lattice planes in the same WTe₂ monolayer. Such anisotropic lattice rippling modulates the intrinsic point defect (Te vacancy) distribution, in which they aggregate at the constrictive inner side of the undulating structure, presumably due to the ripple-induced asymmetric strain as elaborated by density functional theory. The results pave the way for atomic characterizations and defect engineering of air-sensitive 2D layered materials.

Nonclassical Exciton Diffusion in Monolayer WSe_{2}

We experimentally demonstrate time-resolved exciton propagation in a monolayer semiconductor at cryogenic temperatures. Monitoring phonon-assisted recombination of dark states, we find a highly unusual case of exciton diffusion. While at 5 K the diffusivity is intrinsically limited by acoustic phonon scattering, we observe a pronounced decrease of the diffusion coefficient with increasing temperature, far below the activation threshold of higher-energy phonon modes. This behavior corresponds neither to well-known regimes of semiclassical free-particle transport nor to the thermally activated hopping in systems with strong localization. Its origin is discussed in the framework of both microscopic numerical and semiphenomenological analytical models illustrating the observed characteristics of nonclassical propagation. Challenging the established description of mobile excitons in monolayer semiconductors, these results open up avenues to study quantum transport phenomena for excitonic quasiparticles in atomically thin van der Waals materials and their heterostructures.

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.

Propagating Chiral Phonons in Three-Dimensional Materials

Chiral phonons were initially proposed and experimentally verified in two-dimensional (2D) systems. Their intriguing effects have generated profound impacts on multiple research fields. However, all chiral phonons reported to date are constrained to be local, in the sense that their group velocities vanish identically. Here, we propose the concept of propagating 3D chiral phonons, which can transport the information on chirality and angular momentum. Guided by the necessary conditions and using first-principles calculations, we demonstrate their existence in WN₂. The chirality, group velocity, and pseudoangular momentum are analyzed. Based on their selective coupling with valley electrons and photons, we propose an experimental setup to detect the unique feature of propagating chiral phonons. Our work endows chiral phonons with a crucial character-the ability to propagate and transport quantized information, which creates a new research direction and opens up the possibility to design novel phononic quantum devices.

Interlayer exciton formation, relaxation, and transport in TMD van der Waals heterostructures

Van der Waals (vdW) heterostructures based on transition metal dichalcogenides (TMDs) generally possess a type-II band alignment that facilitates the formation of interlayer excitons between constituent monolayers. Manipulation of the interlayer excitons in TMD vdW heterostructures holds great promise for the development of excitonic integrated circuits that serve as the counterpart of electronic integrated circuits, which allows the photons and excitons to transform into each other and thus bridges optical communication and signal processing at the integrated circuit. As a consequence, numerous studies have been carried out to obtain deep insight into the physical properties of interlayer excitons, including revealing their ultrafast formation, long population recombination lifetimes, and intriguing spin-valley dynamics. These outstanding properties ensure interlayer excitons with good transport characteristics, and may pave the way for their potential applications in efficient excitonic devices based on TMD vdW heterostructures. At present, a systematic and comprehensive overview of interlayer exciton formation, relaxation, transport, and potential applications is still lacking. In this review, we give a comprehensive description and discussion of these frontier topics for interlayer excitons in TMD vdW heterostructures to provide valuable guidance for researchers in this field.

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.

Exciton-phonon coupling strength in single-layer MoSe2 at room temperature

Single-layer transition metal dichalcogenides are at the center of an ever increasing research effort both in terms of fundamental physics and applications. Exciton–phonon coupling plays a key role in determining the (opto)electronic properties of these materials. However, the exciton–phonon coupling strength has not been measured at room temperature. Here, we use two-dimensional micro-spectroscopy to determine exciton–phonon coupling of single-layer MoSe₂. We detect beating signals as a function of waiting time induced by the coupling between A excitons and A′₁ optical phonons. Analysis of beating maps combined with simulations provides the exciton–phonon coupling. We get a Huang–Rhys factor ~1, larger than in most other inorganic semiconductor nanostructures. Our technique offers a unique tool to measure exciton–phonon coupling also in other heterogeneous semiconducting systems, with a spatial resolution ~260 nm, and provides design-relevant parameters for the development of optoelectronic devices.

The exciton–phonon coupling (EXPC) affects the opto-electronic properties of atomically thin semiconductors. Here, the authors develop two-dimensional micro-spectroscopy to determine the EXPC of monolayer MoSe₂.

Room-Temperature Synthesis of 2D Janus Crystals and their Heterostructures

Janus crystals represent an exciting class of 2D materials with different atomic species on their upper and lower facets. Theories have predicted that this symmetry breaking induces an electric field and leads to a wealth of novel properties, such as large Rashba spin-orbit coupling and formation of strongly correlated electronic states. Monolayer MoSSe Janus crystals have been synthesized by two methods, via controlled sulfurization of monolayer MoSe₂ and via plasma stripping followed thermal annealing of MoS₂ . However, the high processing temperatures prevent growth of other Janus materials and their heterostructures. Here, a room-temperature technique for the synthesis of a variety of Janus monolayers with high structural and optical quality is reported. This process involves low-energy reactive radical precursors, which enables selective removal and replacement of the uppermost chalcogen layer, thus transforming classical transition metal dichalcogenides into a Janus structure. The resulting materials show clear mixed character for their excitonic transitions, and more importantly, the presented room-temperature method enables the demonstration of first vertical and lateral heterojunctions of 2D Janus TMDs. The results present significant and pioneering advances in the synthesis of new classes of 2D materials, and pave the way for the creation of heterostructures from 2D Janus layers.

Giant Valley-Polarized Rydberg Excitons in Monolayer WSe2 Revealed by Magneto-photocurrent Spectroscopy

A strong Coulomb interaction could lead to a strongly bound exciton with high-order excited states, similar to the Rydberg atom. The interaction of giant Rydberg excitons can be engineered for a correlated ordered exciton array with a Rydberg blockade, which is promising for realizing quantum simulation. Monolayer transition metal dichalcogenides, with their greatly enhanced Coulomb interaction, are an ideal platform to host the Rydberg excitons in two dimensions. Here, we employ helicity-resolved magneto-photocurrent spectroscopy to identify Rydberg exciton states up to 11s in monolayer WSe₂. Notably, the radius of the Rydberg exciton at 11s can be as large as 214 nm, orders of magnitude larger than the 1s exciton. The giant valley-polarized Rydberg exciton not only provides an exciting platform to study the strong exciton-exciton interaction and nonlinear exciton response but also allows the investigation of the different interplay between the Coulomb interaction and Landau quantization, tunable from a low- to high-magnetic-field limit.

Intense Dark Exciton Emission from Strongly Quantum-Confined CsPbBr3 Nanocrystals

Dark exciton as the lowest-energy (ground) exciton state in metal halide perovskite nanocrystals is a subject of much interest. This is because the superior performance of perovskites as the photon source combined with long lifetime of dark exciton can be attractive for many applications of exciton. However, the direct observation of the intense and long-lived dark exciton emission, indicating facile access to dark ground exciton state, has remained elusive. Here, we report the intense photoluminescence from dark exciton with microsecond lifetime in strongly confined CsPbBr₃ nanocrystals and reveal the crucial role of confinement in accessing the dark ground exciton state. This study establishes the potential of strongly quantum-confined perovskite nanostructures as the excellent platform to harvest the benefits of extremely long-lived dark exciton.

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.

Exciton g-factors in monolayer and bilayer WSe2 from experiment and theory

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. Here, we present experimental and theoretical studies of exciton energy splittings in external magnetic field in neutral and charged WSe₂ 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 for all possible spin-valley configurations of excitons in monolayer and bilayer WSe₂ including valley-indirect excitons. Our theoretical and experimental findings shed light on some of the characteristic photoluminescence peaks observed for monolayer and bilayer WSe₂. In more general terms, the theoretical aspects of our work provide additional means for the characterization of single and few-layer transition metal dichalcogenides, as well as their heterostructures, in the presence of external magnetic fields.

Routing valley exciton emission of a WS2 monolayer via delocalized Bloch modes of in-plane inversion-symmetry-broken photonic crystal slabs

The valleys of two-dimensional transition metal dichalcogenides (TMDCs) offer a new degree of freedom for information processing. To take advantage of this valley degree of freedom, on the one hand, it is feasible to control valleys by utilizing different external stimuli, such as optical and electric fields. On the other hand, nanostructures are also used to separate the valleys by near-field coupling. However, for both of the above methods, either the required low-temperature environment or low degree of coherence properties limit their further applications. Here, we demonstrate that all-dielectric photonic crystal (PhC) slabs without in-plane inversion symmetry (C2 symmetry) can separate and route valley exciton emission of a WS2 monolayer at room temperature. Coupling with circularly polarized photonic Bloch modes of such PhC slabs, valley photons emitted by a WS2 monolayer are routed directionally and are efficiently separated in the far field. In addition, far-field emissions are directionally enhanced and have long-distance spatial coherence properties.

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.