Exciton Diffusion and Halo Effects in Monolayer Semiconductors

Excitonic transport driven by repulsive dipolar interaction in a van der Waals heterostructure

Dipolar bosonic gases are currently the focus of intensive research due to their interesting many-body physics in the quantum regime. Their experimental embodiments range from Rydberg atoms to GaAs double quantum wells and van der Waals heterostructures built from transition metal dichalcogenides. Although quantum gases are very dilute, mutual interactions between particles could lead to exotic many-body phenomena such as Bose-Einstein condensation and high-temperature superfluidity. Here, we report the effect of repulsive dipolar interactions on the dynamics of interlayer excitons in the dilute regime. By using spatial and time-resolved photoluminescence imaging, we observe the dynamics of exciton transport, enabling a direct estimation of the exciton mobility. The presence of interactions significantly modifies the diffusive transport of excitons, effectively acting as a source of drift force and enhancing the diffusion coefficient by one order of magnitude. The repulsive dipolar interactions combined with the electrical control of interlayer excitons opens up appealing new perspectives for excitonic devices.

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.

Ultrafast Interlayer Charge Transfer between Bilayer PtSe2 and Monolayer WS2

Interlayer charge transfer (CT) between PtSe₂ and WS₂ is studied experimentally. Layer-selective pump-probe and photoluminescence quenching measurements reveal ultrafast interlayer CT in the heterostructure formed by bilayer PtSe₂ and monolayer WS₂, confirming its type-II band alignment. The CT facilitates the formation of the interlayer excitons with a lifetime of several hundred ps to 1 ns, a diffusion coefficient of 0.9 cm² s^-1, and a diffusion length reaching 200 nm. These results demonstrate the integration of PtSe₂ with other materials in van der Waals heterostructures with novel charge-transfer properties and help develop fundamental understanding on the performance of various optoelectronic devices based on heterostructures involving PtSe₂.

Electron Dynamics in a Two-Dimensional Nanobubble: A Two-Level System Based on Spatial Density

Nanobubbles formed in monolayers of transition metal dichalcogenides (TMDCs) on top of a substrate feature localized potentials in which electrons can be captured. We show that the captured electronic density can exhibit a nontrivial spatiotemporal dynamics, whose movements can be mapped to states in a two-level system illustrated as points of an electronic Poincaré sphere. These states can be fully controlled, i.e, initialized and switched, by multiple electronic wave packets. Our results could be the foundation for novel implementations of quantum circuits.

Boosting quantum yields in two-dimensional semiconductors via proximal metal plates

Monolayer transition metal dichalcogenides (1L-TMDs) have tremendous potential as atomically thin, direct bandgap semiconductors that can be used as convenient building blocks for quantum photonic devices. However, the short exciton lifetime due to the defect traps and the strong exciton-exciton interaction in TMDs has significantly limited the efficiency of exciton emission from this class of materials. Here, we show that exciton-exciton interaction in 1L-WS₂ can be effectively screened using an ultra-flat Au film substrate separated by multilayers of hexagonal boron nitride. Under this geometry, induced dipolar exciton-exciton interaction becomes quadrupole-quadrupole interaction because of effective image dipoles formed within the metal. The suppressed exciton-exciton interaction leads to a significantly improved quantum yield by an order of magnitude, which is also accompanied by a reduction in the exciton-exciton annihilation (EEA) rate, as confirmed by time-resolved optical measurements. A theoretical model accounting for the screening of the dipole-dipole interaction is in a good agreement with the dependence of EEA on exciton densities. Our results suggest that fundamental EEA processes in the TMD can be engineered through proximal metallic screening, which represents a practical approach towards high-efficiency 2D light emitters.

The short exciton lifetime and strong exciton-exciton interaction in transition metal dichalcogenides limit the efficiency of exciton emission. Here, the authors show that exciton-exciton interaction in monolayer WS₂ can be screened using proximal metal plates, leading to an improved quantum yield.

Mechanistic insight into the chemical treatments of monolayer transition metal disulfides for photoluminescence enhancement

There is a growing interest in obtaining high quality monolayer transition metal disulfides for optoelectronic applications. Surface treatments using a range of chemicals have proven effective to improve the photoluminescence yield of these materials. However, the underlying mechanism for the photoluminescence enhancement is not clear, which prevents a rational design of passivation strategies. Here, a simple and effective approach to significantly enhance the photoluminescence is demonstrated by using a family of cation donors, which we show to be much more effective than commonly used p-dopants. We develop a detailed mechanistic picture for the action of these cation donors and demonstrate that one of them, bis(trifluoromethane)sulfonimide lithium salt (Li-TFSI), enhances the photoluminescence of both MoS2 and WS2 to a level double that of the currently best performing super-acid trifluoromethanesulfonimide (H-TFSI) treatment. In addition, the ionic salts used in our treatments are compatible with greener solvents and are easier to handle than super-acids, providing the possibility of performing treatments during device fabrication. This work sets up rational selection rules for ionic chemicals to passivate transition metal disulfides and increases their potential in practical optoelectronic applications.

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.

Signatures of Dimensionality and Symmetry in Exciton Band Structure: Consequences for Exciton Dynamics and Transport

Exciton dynamics, lifetimes, and scattering are directly related to the exciton dispersion or band structure. Here, we present a general theory for exciton band structure within both ab initio and model Hamiltonian approaches. We show that contrary to common assumption, the exciton band structure contains nonanalytical discontinuities-a feature which is impossible to obtain from the electronic band structure alone. These discontinuities are purely quantum phenomena, arising from the exchange scattering of electron-hole pairs. We show that the degree of these discontinuities depends on materials' symmetry and dimensionality, with jump discontinuities occurring in 3D and different orders of removable discontinuities in 2D and 1D, whose details depend on the exciton degeneracy and material thickness. We connect these features to the early stages of exciton dynamics, radiative lifetimes, and diffusion constants, in good correspondence with recent experimental observations, revealing that the discontinuities in the band structure lead to ultrafast ballistic transport and suggesting that measured exciton diffusion and dynamics are influenced by the underlying exciton dispersion.

Motional narrowing, ballistic transport, and trapping of room-temperature exciton polaritons in an atomically-thin semiconductor

Monolayer transition metal dichalcogenide crystals (TMDCs) hold great promise for semiconductor optoelectronics because their bound electron-hole pairs (excitons) are stable at room temperature and interact strongly with light. When TMDCs are embedded in an optical microcavity, excitons can hybridise with cavity photons to form exciton polaritons, which inherit useful properties from their constituents. The ability to manipulate and trap polaritons on a microchip is critical for applications. Here, we create a non-trivial potential landscape for polaritons in monolayer WS₂, and demonstrate their trapping and ballistic propagation across tens of micrometers. We show that the effects of dielectric disorder, which restrict the diffusion of WS₂ excitons and broaden their spectral resonance, are dramatically reduced for polaritons, leading to motional narrowing and preserved partial coherence. Linewidth narrowing and coherence are further enhanced in the trap. Our results demonstrate the possibility of long-range dissipationless transport and efficient trapping of TMDC polaritons in ambient conditions.

Zitterbewegung of Moiré Excitons in Twisted MoS_{2}/WSe_{2} Heterobilayers

The moiré pattern observed in stacked noncommensurate crystal lattices, such as heterobilayers of transition metal dichalcogenides, produces a periodic modulation of their band gap. Excitons subjected to this potential landscape exhibit a band structure that gives rise to a quasiparticle dubbed the moiré exciton. In the case of MoS_{2}/WSe_{2} heterobilayers, the moiré trapping potential has honeycomb symmetry and, consequently, the moiré exciton band structure is the same as that of a Dirac-Weyl fermion, whose mass can be further tuned down to zero with a perpendicularly applied field. Here we show that, analogously to other Dirac-like particles, the moiré exciton exhibits a trembling motion, also known as Zitterbewegung, whose long timescales are compatible with current experimental techniques for exciton dynamics. This promotes the study of the dynamics of moiré excitons in van der Waals heterostructures as an advantageous solid-state platform to probe Zitterbewegung, broadly tunable by gating and interlayer twist angle.

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.

Electrical tuning of optically active interlayer excitons in bilayer MoS2

Interlayer (IL) excitons, comprising electrons and holes residing in different layers of van der Waals bonded two-dimensional semiconductors, have opened new opportunities for room-temperature excitonic devices. So far, two-dimensional IL excitons have been realized in heterobilayers with type-II band alignment. However, the small oscillator strength of the resulting IL excitons and difficulties with producing heterostructures with definite crystal orientation over large areas have challenged the practical applicability of this design. Here, following the theoretical prediction and recent experimental confirmation of the existence of IL excitons in bilayer MoS₂, we demonstrate the electrical control of such excitons up to room temperature. We find that the IL excitonic states preserve their large oscillator strength as their energies are manipulated by the electric field. We attribute this effect to the mixing of the pure IL excitons with intralayer excitons localized in a single layer. By applying an electric field perpendicular to the bilayer MoS₂ crystal plane, excitons with IL character split into two peaks with an X-shaped field dependence as a clear fingerprint of the shift of the monolayer bands with respect to each other. Finally, we demonstrate the full control of the energies of IL excitons distributed homogeneously over a large area of our device.

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.

Valley-selective optical Stark effect of exciton-polaritons in a monolayer semiconductor

Selective breaking of degenerate energy levels is a well-known tool for coherent manipulation of spin states. Though most simply achieved with magnetic fields, polarization-sensitive optical methods provide high-speed alternatives. Exploiting the optical selection rules of transition metal dichalcogenide monolayers, the optical Stark effect allows for ultrafast manipulation of valley-coherent excitons. Compared to excitons in these materials, microcavity exciton-polaritons offer a promising alternative for valley manipulation, with longer lifetimes, enhanced valley coherence, and operation across wider temperature ranges. Here, we show valley-selective control of polariton energies in WS₂ using the optical Stark effect, extending coherent valley manipulation to the hybrid light-matter regime. Ultrafast pump-probe measurements reveal polariton spectra with strong polarization contrast originating from valley-selective energy shifts. This demonstration of valley degeneracy breaking at picosecond timescales establishes a method for coherent control of valley phenomena in exciton-polaritons.

Microcavity exciton-polaritons in atomically thin semiconductors are a promising platform for valley manipulation. Here, the authors show valley-selective control of polariton energies in monolayer WS2 using the optical Stark effect, thereby extending coherent valley manipulation to a hybrid light-matter regime

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.

Rational Passivation of Sulfur Vacancy Defects in Two-Dimensional Transition Metal Dichalcogenides

Structural defects vary the optoelectronic properties of monolayer transition metal dichalcogenides, leading to concerted efforts to control defect type and density via materials growth or postgrowth passivation. Here, we explore a simple chemical treatment that allows on-off switching of low-lying, defect-localized exciton states, leading to tunable emission properties. Using steady-state and ultrafast optical spectroscopy, supported by ab initio calculations, we show that passivation of sulfur vacancy defects, which act as exciton traps in monolayer MoS₂ and WS₂, allows for controllable and improved mobilities and an increase in photoluminescence up to 275-fold, more than twice the value achieved by other chemical treatments. Our findings suggest a route for simple and rational defect engineering strategies for tunable and switchable electronic and excitonic properties through passivation.

Local Energy Landscape Drives Long-Range Exciton Diffusion in Two-Dimensional Halide Perovskite Semiconductors

Halide perovskites are versatile semiconductors with applications including photovoltaics and light-emitting devices, having modular optoelectronic properties realizable through composition and dimensionality tuning. Layered Ruddlesden-Popper perovskites are particularly interesting due to their unique 2D character and charge carrier dynamics. However, long-range energy transport through exciton diffusion in these materials is not understood or realized. Here, local time-resolved luminescence mapping techniques are employed to visualize exciton transport in exfoliated flakes of the BA2MAn-1PbnI3n+1 perovskite family. Two distinct transport regimes are uncovered, depending on the temperature range. Above 100 K, diffusion is mediated by thermally activated hopping processes between localized states. At lower temperatures, a nonuniform energy landscape emerges in which transport is dominated by downhill energy transfer to lower-energy states, leading to long-range transport over hundreds of nanometers. Efficient, long-range, and switchable downhill transfer offers exciting possibilities for controlled directional long-range transport in these 2D materials for new applications.

Transport Modeling of Locally Photogenerated Excitons in Halide Perovskites

Excitons have fundamental impacts on optoelectronic properties of semiconductors. Halide perovskites, with long carrier lifetimes and ionic crystal structures, may support highly mobile excitons because the dipolar nature of excitons suppresses phonon scattering. Inspired by recent experimental progress, we perform device modeling to rigorously analyze exciton formation and transport in methylammonium lead triiodide under local photoexcitation by using a finite element method. Mobile excitons, coexisting with free carriers, can dominate photocurrent generation at low temperatures. The simulation results are in excellent agreement with the experimentally observed strong temperature and gate dependence of carrier diffusion. This work signifies that efficient exciton transport can substantially influence charge transport in the family of perovskite materials.

Excitons in a reconstructed moiré potential in twisted WSe2/WSe2 homobilayers

Moiré superlattices in twisted van der Waals materials have recently emerged as a promising platform for engineering electronic and optical properties. A major obstacle to fully understanding these systems and harnessing their potential is the limited ability to correlate direct imaging of the moiré structure with optical and electronic properties. Here we develop a secondary electron microscope technique to directly image stacking domains in fully functional van der Waals heterostructure devices. After demonstrating the imaging of AB/BA and ABA/ABC domains in multilayer graphene, we employ this technique to investigate reconstructed moiré patterns in twisted WSe₂/WSe₂ bilayers and directly correlate the increasing moiré periodicity with the emergence of two distinct exciton species in photoluminescence measurements. These states can be tuned individually through electrostatic gating and feature different valley coherence properties. We attribute our observations to the formation of an array of two intralayer exciton species that reside in alternating locations in the superlattice, and open up new avenues to realize tunable exciton arrays in twisted van der Waals heterostructures, with applications in quantum optoelectronics and explorations of novel many-body systems.

Effective Negative Diffusion of Singlet Excitons in Organic Semiconductors

Using diffraction-limited ultrafast imaging techniques, we investigate the propagation of singlet and triplet excitons in single-crystal tetracene. Instead of an expected broadening, the distribution of singlet excitons narrows on a nanosecond time scale after photoexcitation. This narrowing results in an effective negative diffusion in which singlet excitons migrate toward the high-density region, eventually leading to a singlet exciton distribution that is smaller than the laser excitation spot. Modeling the excited-state dynamics demonstrates that the origin of the anomalous diffusion is rooted in nonlinear triplet-triplet annihilation (TTA). We anticipate that this is a general phenomenon that can be used to study exciton diffusion and nonlinear TTA rates in semiconductors relevant for organic optoelectronics.

Switchable, Tunable, and Directable Exciton Funneling in Periodically Wrinkled WS2

The extreme elastic strain of monolayer transition metal dichalcogenides provides an ideal platform to achieve efficient exciton funneling via local strain modulation; however, studies conducted thus far have focused on the use of substrates with fixed strain profiles. We prepared 1L-WS₂ on a flexible substrate such that the formation of topographic wrinkles could be switched on or off, and the depth or the direction of the wrinkle could be modified by external strain, thereby providing full control of the periodic undulation of the band gap profile of 1L-WS₂ in the range 0-57 meV. Nanoscale photoluminescence (PL) imaging unambiguously evinced that the photoexcited excitons of 1L-WS₂ were accumulated at the top regions of the wrinkles with less band gap than the valley region. Our results of broad tunability of the two-dimensional (2D) exciton funneling suggest a promising route to control exciton drift for enhanced optoelectronic performances and future 2D exciton devices.

Giant enhancement of exciton diffusivity in two-dimensional semiconductors

Two-dimensional (2D) semiconductors bear great promise for application in optoelectronic devices, but the low diffusivity of excitons stands as a notable challenge for device development. Here, we demonstrate that the diffusivity of excitons in monolayer MoS2 can be improved from 1.5 ± 0.5 to 22.5 ± 2.5 square centimeters per second with the presence of trapped charges. This is manifested by a spatial expansion of photoluminescence when the incident power reaches a threshold value to enable the onset of exciton Mott transition. The trapped charges are estimated to be in a scale of 1010 per square centimeter and do not affect the emission features and recombination dynamics of the excitons. The result indicates that trapped charges provide an attractive strategy to screen exciton scattering with phonons and impurities/defects. Pointing towards a new pathway to control exciton transport and many-body interactions in 2D semiconductors.

Neutral Exciton Diffusion in Monolayer MoS2

Monolayer transition metal dichalcogenides (TMDCs) are promising materials for next generation optoelectronic devices. The exciton diffusion length is a critical parameter that reflects the quality of exciton transport in monolayer TMDCs and limits the performance of many excitonic devices. Although diffusion lengths of a few hundred nanometers have been reported in the literature for as-exfoliated monolayers, these measurements are convoluted by neutral and charged excitons (trions) that coexist at room temperature due to natural background doping. Untangling the diffusion of neutral excitons and trions is paramount to understand the fundamental limits and potential of new optoelectronic device architectures made possible using TMDCs. In this work, we measure the diffusion lengths of neutral excitons and trions in monolayer MoS₂ by tuning the background carrier concentration using a gate voltage and utilizing both steady state and transient spectroscopy. We observe diffusion lengths of 1.5 μm and 300 nm for neutral excitons and trions, respectively, at an optical power density of 0.6 W cm^-2_.

Complex diffusion-based kinetics of photoluminescence in semiconductor nanoplatelets

We present a diffusion-based simulation and theoretical models for explanation of the photoluminescence (PL) emission intensity in semiconductor nanoplatelets. It is shown that the shape of the PL intensity curves can be reproduced by the interplay of recombination, diffusion and trapping of excitons. The emission intensity at short times is purely exponential and is defined by recombination. At long times, it is governed by the release of excitons from surface traps and is characterized by a power-law tail. We show that the crossover from one limit to another is controlled by diffusion properties. This intermediate region exhibits a rich behaviour depending on the value of diffusivity. The proposed approach reproduces all the features of experimental curves measured for different nanoplatelet systems.

Skew Scattering and Side Jump Drive Exciton Valley Hall Effect in Two-Dimensional Crystals

Exciton valley Hall effect is the spatial separation of the valley-tagged excitons by a drag force. Usually, the effect is associated with the anomalous velocity acquired by the particles due to the Berry curvature of the Bloch bands. Here we show that the anomalous velocity plays no role in the exciton valley Hall effect, which is governed by the side-jump and skew scattering. We develop a microscopic theory of the exciton valley Hall effect in the presence of a synthetic electric field and phonon drag and calculate all relevant contributions to the valley Hall current also demonstrating the cancellation of the anomalous velocity. The sensitivity of the effect to the origin of the drag force and to the scattering processes is shown. We extend the drift-diffusion model to account for the valley Hall effect and calculate the exciton density and valley polarization profiles.

Fast and Anomalous Exciton Diffusion in Two-Dimensional Hybrid Perovskites

Two-dimensional hybrid perovskites are currently in the spotlight of condensed matter and nanotechnology research due to their intriguing optoelectronic and vibrational properties with emerging potential for light-harvesting and light-emitting applications. While it is known that these natural quantum wells host tightly bound excitons, the mobilities of these fundamental optical excitations at the heart of the optoelectronic applications are barely explored. Here, we directly monitor the diffusion of excitons through ultrafast emission microscopy from liquid helium to room temperature in hBN-encapsulated two-dimensional hybrid perovskites. We find very fast diffusion with characteristic hallmarks of free exciton propagation for all temperatures above 50 K. In the cryogenic regime, we observe nonlinear, anomalous behavior with an exceptionally rapid expansion of the exciton cloud followed by a very slow and even negative effective diffusion. We discuss our findings in view of efficient exciton-phonon coupling, highlighting two-dimensional hybrids as promising platforms for basic research and optoelectronic applications.

Moiré potential impedes interlayer exciton diffusion in van der Waals heterostructures

The properties of van der Waals heterostructures are drastically altered by a tunable moiré superlattice arising from periodically varying atomic alignment between the layers. Exciton diffusion represents an important channel of energy transport in transition metal dichalcogenides (TMDs). While early studies performed on TMD heterobilayers suggested that carriers and excitons exhibit long diffusion, a rich variety of scenarios can exist. In a moiré crystal with a large supercell and deep potential, interlayer excitons may be completely localized. As the moiré period reduces at a larger twist angle, excitons can tunnel between supercells and diffuse over a longer lifetime. The diffusion should be the longest in commensurate heterostructures where the moiré superlattice is completely absent. Here, we experimentally demonstrate the rich phenomena of interlayer exciton diffusion in WSe2/MoSe2 heterostructures by comparing several samples prepared with chemical vapor deposition and mechanical stacking with accurately controlled twist angles.

Energy Transport of Hybrid Charge-Transfer Excitons

We investigate the energy transport in an organic-inorganic hybrid platform formed between semiconductors that support stable room-temperature excitons. We find that following photoexcitation, fast-moving hot hybrid charge-transfer excitons (HCTEs) are formed in about 36 ps via scattering with optical phonons at the interface between j-aggregates of organic dye and inorganic monolayer MoS₂. Once the energy falls below the optical phonon energy, the excess kinetic energy is relaxed slowly via acoustic phonon scattering, resulting in energy transport that is dominated by fast-moving hot HCTEs that transition into cold HCTEs in about 110 ps. We model the exciton-phonon interactions using Fröhlich and deformation potential theory and attribute the prolonged transport of hot HCTEs to phonon bottleneck. We find that the measured diffusivity of HCTEs in both hot and cold regions of transport was higher than the diffusivity of MoS₂ A exciton and verify these results by conducting the experiments with different excitation energies. This work not only provides significant insight into the initial energy transport of HCTEs at organic-inorganic hybrid interfaces but also contributes to the formulation of a complete physical picture of the energy dynamics in hybrid materials, which are poised to advance applications in energy conversion and optoelectronic devices.

Correlated Exciton Fluctuations in a Two-Dimensional Semiconductor on a Metal

Excitons in nanoscale materials can exhibit fluorescence fluctuations. Intermittency is pervasive in zero-dimensional emitters such as single molecules and quantum dots. In contrast, two-dimensional semiconductors are generally regarded as stable light sources. Noise contains, however, valuable information about a material. Here, we demonstrate fluorescence fluctuations in a monolayer semiconductor due to sensitivity to its nanoscopic environment focusing on the case of a metal film. The fluctuations are spatially correlated over tens of micrometers and follow power-law statistics, with simultaneous changes in emission intensity and lifetime. At low temperatures, an additional spectral contribution from interface trap states emerges with fluctuations that are correlated with neutral excitons and anticorrelated with trions. Mastering exciton fluctuations has implications for light-emitting devices such as single-photon sources and could lead to novel excitonic sensors. The quantification of fluorescence fluctuations, including imaging, unlocks a set of promising tools to characterize and exploit two-dimensional semiconductors and their interfaces.

Remote Lightening and Ultrafast Transition: Intrinsic Modulation of Exciton Spatiotemporal Dynamics in Monolayer MoS2

Devices operating with excitons have promising prospects for overcoming the dilemma of response time and integration in current generation of electron- or/and photon-based elements and devices. Although the intrinsic properties including edges, grain boundaries, and defects of atomically thin semiconductors have been demonstrated as a powerful tool to adjust the bandgap and exciton energy, investigating the intrinsic modulation of spatiotemporal dynamics still remains challenging on account of the short exciton diffusion length. Here, we achieve the attractive remote lightening phenomenon, in which the emission region could be far away (up to 14.6 μm) from the excitation center, by utilizing a femtosecond laser with ultrahigh peak power as excitation source and the edge region with high photoluminescence efficiency as a bright emitter. Furthermore, the ultrafast transition between exciton and trion is demonstrated, which provides insight into the intrinsic modulation on populations of exciton and trion states. The complete cascaded physical scenario of exciton spatiotemporal dynamics is eventually established. This work can refresh our perspective on the spatial nonuniformities of CVD-grown atomically thin semiconductors and provide important implications for developing durable and stable excitonic devices in the future.

Twist-angle-dependent interlayer exciton diffusion in WS2-WSe2 heterobilayers

The nanoscale periodic potentials introduced by moiré patterns in semiconducting van der Waals heterostructures have emerged as a platform for designing exciton superlattices. However, our understanding of the motion of excitons in moiré potentials is still limited. Here we investigated interlayer exciton dynamics and transport in WS₂-WSe₂ heterobilayers in time, space and momentum domains using transient absorption microscopy combined with first-principles calculations. We found that the exciton motion is modulated by twist-angle-dependent moiré potentials around 100 meV and deviates from normal diffusion due to the interplay between the moiré potentials and strong exciton-exciton interactions. Our experimental results verified the theoretical prediction of energetically favourable K-Q interlayer excitons and showed exciton-population dynamics that are controlled by the twist-angle-dependent energy difference between the K-Q and K-K excitons. These results form a basis to investigate exciton and spin transport in van der Waals heterostructures, with implications for the design of quantum communication devices.

Light-matter interaction in van der Waals hetero-structures

Even if individual two-dimensional materials own various interesting and unexpected properties, the stacking of such layers leads to van der Waals solids which unite the characteristics of two dimensions with novel features originating from the interlayer interactions. In this topical review, we cover fabrication and characterization of van der Waals hetero-structures with a focus on hetero-bilayers made of monolayers of semiconducting transition metal dichalcogenides. Experimental and theoretical techniques to investigate those hetero-bilayers are introduced. Most recent findings focusing on different transition metal dichalcogenides hetero-structures are presented and possible optical transitions between different valleys, appearance of moiré patterns and signatures of moiré excitons are discussed. The fascinating and fast growing research on van der Waals hetero-bilayers provide promising insights required for their application as emerging quantum-nano materials.

Quantum Interference Effect on Exciton Transport in Monolayer Semiconductors

We study theoretically weak localization of excitons in atomically thin transition metal dichalcogenides. The constructive interference of excitonic de Broglie waves on the trajectories forming closed loops results in a decrease of the exciton diffusion coefficient. We calculate the interference contribution to the diffusion coefficient for the experimentally relevant situation of exciton scattering by acoustic phonons and static disorder. For the acoustic phonon scattering, the quantum interference becomes more and more important with increasing the temperature. Our estimates show that the quantum contribution to the diffusion coefficient is considerable for the state-of-the-art monolayer and bilayer transition metal dichalcogenides.

Polariton-Polariton Interactions Revealed in a One-dimensional Whispering Gallery Microcavity

Coulomb interactions are essential to the dynamics and optical properties of exciton-polaritons. Here, we report an experimental observation of polariton-polariton interactions far beyond theory in a one-dimensional whispering gallery microcavity. Based on the unique half-light half-matter nature, we were able to clarify the effects of excitons, quantum confinement, and nonthermalized polariton distribution in the measurements of the polaritonic interactions. Spectacularly, our position-scan and power-scan investigations both revealed that the polariton-polariton interaction strength is up to 2 orders of magnitude larger than theoretical predictions. These results suggest that polaritonic interactions are far more complicated than the expectation and should be re-examined in polariton physics and devices involving polaritonic interactions.

Negative effective excitonic diffusion in monolayer transition metal dichalcogenides

While exciton relaxation in monolayers of transition metal dichalcogenides (TMDs) has been intensively studied, spatial exciton diffusion has received only a little attention - in spite of being a key process for optoelectronics and having already shown interesting unconventional behaviours (e.g. spatial halos). Here, we study the spatiotemporal dynamics in TMD monolayers and track optically excited excitons in time, momentum, and space. In particular, we investigate the temperature-dependent exciton diffusion including the remarkable exciton landscape constituted by bright and dark states. Based on a fully quantum mechanical approach, we show at low temperatures an unexpected negative effective diffusion characterized by a shrinking of the spatial exciton distributions. This phenomenon can be traced back to the existence of dark exciton states in TMD monolayers and is a result of an interplay between spatial exciton diffusion and intervalley exciton-phonon scattering.

Direct Visualization of Exciton Transport in Defective Few-Layer WS2 by Ultrafast Microscopy

As defects usually limit the exciton diffusion in 2D transition metal dichalcogenides (TMDCs), the interaction knowledge of defects and exciton transport is crucial for achieving efficient TMDC-based devices. A direct visualization of defect-modulated exciton transport is developed in few-layer WS₂ by ultrafast transient absorption microscopy. Atomic-scale defects are introduced by argon plasma treatment and identified by aberration-corrected scanning transmission electron microscopy. Neutral excitons can be captured by defects to form bound excitons in 7.75-17.88 ps, which provide a nonradiative relaxation channel, leading to decreased exciton lifetime and diffusion coefficient. The exciton diffusion length of defective sample has a drastic reduction from 349.44 to 107.40 nm. These spatially and temporally resolved measurements reveal the interaction mechanism between defects and exciton transport dynamics in 2D TMDCs, giving a guideline for designing high-performance TMDC-based devices.

Imaging material functionality through three-dimensional nanoscale tracking of energy flow

The ability of energy carriers to move between atoms and molecules underlies biochemical and material function. Understanding and controlling energy flow, however, requires observing it on ultrasmall and ultrafast spatio-temporal scales, where energetic and structural roadblocks dictate the fate of energy carriers. Here, we developed a non-invasive optical scheme that leverages non-resonant interferometric scattering to track tiny changes in material polarizability created by energy carriers. We thus map evolving energy carrier distributions in four dimensions of spacetime with few-nanometre lateral precision and directly correlate them with material morphology. We visualize exciton, charge and heat transport in polyacene, silicon and perovskite semiconductors and elucidate how disorder affects energy flow in three dimensions. For example, we show that morphological boundaries in polycrystalline metal halide perovskites possess lateral- and depth-dependent resistivities, blocking lateral transport for surface but not bulk carriers. We also reveal strategies for interpreting energy transport in disordered environments that will direct the design of defect-tolerant materials for the semiconductor industry of tomorrow.

Valley-polarized exciton currents in a van der Waals heterostructure

Valleytronics is an appealing alternative to conventional charge-based electronics that aims at encoding data in the valley degree of freedom, that is, the information as to which extreme of the conduction or valence band carriers are occupying. The ability to create and control valley currents in solid-state devices could therefore enable new paradigms for information processing. Transition metal dichalcogenides (TMDCs) are a promising platform for valleytronics due to the presence of two inequivalent valleys with spin-valley locking¹ and a direct bandgap^2,3, which allows optical initialization and readout of the valley state^4,5. Recent progress on the control of interlayer excitons in these materials^6-8 could offer an effective way to realize optoelectronic devices based on the valley degree of freedom. Here, we show the generation and transport over mesoscopic distances of valley-polarized excitons in a device based on a type-II TMDC heterostructure. Engineering of the interlayer coupling results in enhanced diffusion of valley-polarized excitons, which can be controlled and switched electrically. Furthermore, using electrostatic traps, we can increase the exciton concentration by an order of magnitude, reaching densities in the order of 10¹² cm^-2, opening the route to achieving a coherent quantum state of valley-polarized excitons via Bose-Einstein condensation.

Spatially Resolved Photogenerated Exciton and Charge Transport in Emerging Semiconductors

We review recent advances in the characterization of electronic forms of energy transport in emerging semiconductors. The approaches described all temporally and spatially resolve the evolution of initially localized populations of photogenerated excitons or charge carriers. We first provide a comprehensive background for describing the physical origin and nature of electronic energy transport both microscopically and from the perspective of the observer. We introduce the new family of far-field, time-resolved optical microscopies developed to directly resolve not only the extent of this transport but also its potentially temporally and spatially dependent rate. We review a representation of examples from the recent literature, including investigation of energy flow in colloidal quantum dot solids, organic semiconductors, organic-inorganic metal halide perovskites, and 2D transition metal dichalcogenides. These examples illustrate how traditional parameters like diffusivity are applicable only within limited spatiotemporal ranges and how the techniques at the core of this review,especially when taken together, are revealing a more complete picture of the spatiotemporal evolution of energy transport in complex semiconductors, even as a function of their structural heterogeneities.

Electrical control of interlayer exciton dynamics in atomically thin heterostructures

A van der Waals heterostructure built from atomically thin semiconducting transition metal dichalcogenides (TMDs) enables the formation of excitons from electrons and holes in distinct layers, producing interlayer excitons with large binding energy and a long lifetime. By employing heterostructures of monolayer TMDs, we realize optical and electrical generation of long-lived neutral and charged interlayer excitons. We demonstrate that neutral interlayer excitons can propagate across the entire sample and that their propagation can be controlled by excitation power and gate electrodes. We also use devices with ohmic contacts to facilitate the drift motion of charged interlayer excitons. The electrical generation and control of excitons provide a route for achieving quantum manipulation of bosonic composite particles with complete electrical tunability.

Exciton Propagation and Halo Formation in Two-Dimensional Materials

The interplay of optics, dynamics, and transport is crucial for the design of novel optoelectronic devices, such as photodetectors and solar cells. In this context, transition-metal dichalcogenides (TMDs) have received much attention. Here, strongly bound excitons dominate optical excitation, carrier dynamics, and diffusion processes. While the first two have been intensively studied, there is a lack of fundamental understanding of nonequilibrium phenomena associated with exciton transport that is of central importance (e.g., for high-efficiency light harvesting). In this work, we provide microscopic insights into the interplay of exciton propagation and many-particle interactions in TMDs. On the basis of a fully quantum mechanical approach and in excellent agreement with photoluminescence measurements, we show that Auger recombination and emission of hot phonons act as a heating mechanism giving rise to strong spatial gradients in excitonic temperature. The resulting thermal drift leads to an unconventional exciton diffusion characterized by spatial exciton halos.

Probing and Manipulating Carrier Interlayer Diffusion in van der Waals Multilayer by Constructing Type-I Heterostructure

van der Waals multilayer heterostructures have drawn increasing attention due to the potential for achieving high-performance photonic and optoelectronic devices. However, the carrier interlayer transportation behavior in multilayer structures, which is essential for determining the device performance, remains unrevealed. Here, we report a general strategy for studying and manipulating the carrier interlayer transportation in van der Waals multilayers by constructing type-I heterostructures, with a desired narrower bandgap monolayer acting as a carrier extraction layer. For heterostructures comprised of multilayer PbI₂ and monolayer WS₂, we find similar interlayer diffusion coefficients of ∼0.039 and ∼0.032 cm² s^-1 for electrons and holes in the PbI₂ multilayer by fitting the time-resolved carrier dynamics based on the diffusion model. Because of the balanced carrier interlayer diffusion and the injection process at the heterointerface, the photoluminescence emission of the bottom WS₂ monolayer is greatly enhanced by up to 106-fold at an optimized PbI₂ thickness of the heterostructure. Our results provide valuable information on carrier interlayer transportation in van der Waals multilayer structures and pave the way for utilizing carrier behaviors to improve device performances.

Dielectric disorder in two-dimensional materials

Understanding and controlling disorder is key to nanotechnology and materials science. Traditionally, disorder is attributed to local fluctuations of inherent material properties such as chemical and structural composition, doping or strain. Here, we present a fundamentally new source of disorder in nanoscale systems that is based entirely on the local changes of the Coulomb interaction due to fluctuations of the external dielectric environment. Using two-dimensional semiconductors as prototypes, we experimentally monitor dielectric disorder by probing the statistics and correlations of the exciton resonances, and theoretically analyse the influence of external screening and phonon scattering. Even moderate fluctuations of the dielectric environment are shown to induce large variations of the bandgap and exciton binding energies up to the 100 meV range, often making it a dominant source of inhomogeneities. As a consequence, dielectric disorder has strong implications for both the optical and transport properties of nanoscale materials and their heterostructures.

Optical valley Hall effect for highly valley-coherent exciton-polaritons in an atomically thin semiconductor

Spin-orbit coupling is a fundamental mechanism that connects the spin of a charge carrier with its momentum. In the optical domain, an analogous synthetic spin-orbit coupling is accessible by engineering optical anisotropies in photonic materials. Both yield the possibility of creating devices that directly harness spin and polarization as information carriers. Atomically thin transition metal dichalcogenides promise intrinsic spin-valley Hall features for free carriers, excitons and photons. Here we demonstrate spin- and valley-selective propagation of exciton-polaritons in a monolayer of MoSe₂ that is strongly coupled to a microcavity photon mode. In a wire-like device we trace the flow and helicity of exciton-polaritons expanding along its channel. By exciting a coherent superposition of K and K' tagged polaritons, we observe valley-selective expansion of the polariton cloud without either an external magnetic field or coherent Rayleigh scattering. The observed optical valley Hall effect occurs on a macroscopic scale, offering the potential for applications in spin-valley-locked photonic devices.

Effective detection of spatio-temporal carrier dynamics by carrier capture

The spatio-temporal dynamics of electrons moving in a 2D plane is challenging to detect when the required resolution shrinks simultaneously to nanometer length and subpicosecond time scale. We propose a detection scheme relying on phonon-induced carrier capture from 2D unbound states into the bound states of an embedded quantum dot. This capture process happens locally and here we explore if this locality is sufficient to use the carrier capture process as detection of the ultrafast diffraction of electrons from an obstacle in the 2D plane. As an example we consider an electronic wave packet traveling in a semiconducting monolayer of the transition metal dichalcogenide MoSe₂, and we study the scattering-induced dynamics using a single particle Lindblad approach. Our results offer a new way to high resolution detection of the spatio-temporal carrier dynamics.

Scanning Tunneling Microscope-Induced Excitonic Luminescence of a Two-Dimensional Semiconductor

The long sought-after goal of locally and spectroscopically probing the excitons of two-dimensional (2D) semiconductors is attained using a scanning tunneling microscope (STM). Excitonic luminescence from monolayer molybdenum diselenide (MoSe_{2}) on a transparent conducting substrate is electrically excited in the tunnel junction of an STM under ambient conditions. By comparing the results with photoluminescence measurements, the emission mechanism is identified as the radiative recombination of bright A excitons. STM-induced luminescence is observed at bias voltages as low as those that correspond to the energy of the optical band gap of MoSe_{2}. The proposed excitation mechanism is resonance energy transfer from the tunneling current to the excitons in the semiconductor, i.e., through virtual photon coupling. Additional mechanisms (e.g., charge injection) may come into play at bias voltages that are higher than the electronic band gap. Photon emission quantum efficiencies of up to 10^{-7} photons per electron are obtained, despite the lack of any participating plasmons. Our results demonstrate a new technique for investigating the excitonic and optoelectronic properties of 2D semiconductors and their heterostructures at the nanometer scale.

Spatio-temporal dynamics in graphene

Temporally and spectrally resolved dynamics of optically excited carriers in graphene has been intensively studied theoretically and experimentally, whereas carrier diffusion in space has attracted much less attention. Understanding the spatio-temporal carrier dynamics is of key importance for optoelectronic applications, where carrier transport phenomena play an important role. In this work, we provide a microscopic access to the time-, momentum-, and space-resolved dynamics of carriers in graphene. We determine the diffusion coefficient to be D≈ 360 cm² s^-1 and reveal the impact of carrier-phonon and carrier-carrier scattering on the diffusion process. In particular, we show that phonon-induced scattering across the Dirac cone gives rise to back-diffusion counteracting the spatial broadening of the carrier distribution.

Upconverted electroluminescence via Auger scattering of interlayer excitons in van der Waals heterostructures

The intriguing physics of carrier-carrier interactions, which likewise affect the operation of light emitting devices, stimulate the research on semiconductor structures at high densities of excited carriers, a limit reachable at large pumping rates or in systems with long-lived electron-hole pairs. By electrically injecting carriers into WSe₂/MoS₂ type-II heterostructures which are indirect in real and k-space, we establish a large population of typical optically silent interlayer excitons. Here, we reveal their emission spectra and show that the emission energy is tunable by an applied electric field. When the population is further increased by suppressing the radiative recombination rate with the introduction of an hBN spacer between WSe₂ and MoS₂, Auger-type and exciton-exciton annihilation processes become important. These processes are traced by the observation of an up-converted emission demonstrating that excitons gaining energy in non-radiative Auger processes can be recovered and recombine radiatively.

Electrical suppression of all nonradiative recombination pathways in monolayer semiconductors

Defects in conventional semiconductors substantially lower the photoluminescence (PL) quantum yield (QY), a key metric of optoelectronic performance that directly dictates the maximum device efficiency. Two-dimensional transition-metal dichalcogenides (TMDCs), such as monolayer MoS2, often exhibit low PL QY for as-processed samples, which has typically been attributed to a large native defect density. We show that the PL QY of as-processed MoS2 and WS2 monolayers reaches near-unity when they are made intrinsic through electrostatic doping, without any chemical passivation. Surprisingly, neutral exciton recombination is entirely radiative even in the presence of a high native defect density. This finding enables TMDC monolayers for optoelectronic device applications as the stringent requirement of low defect density is eased.

Quantitative optical assessment of photonic and electronic properties in halide perovskite

The development of high efficiency solar cells relies on the management of electronic and optical properties that need to be accurately measured. As the conversion efficiencies increase, there is a concomitant electronic and photonic contribution that affects the overall performances. Here we show an optical method to quantify several transport properties of semiconducting materials and the use of multidimensional imaging techniques allows decoupling and quantifying the electronic and photonic contributions. Example of application is shown on halide perovskite thin film for which a large range of transport properties is given in the literature. We therefore optically measure pure carrier diffusion properties and evidence the contribution of optical effects such as the photon recycling as well as the photon propagation where emitted light is laterally transported without being reabsorbed. This latter effect has to be considered to avoid overestimated transport properties such as carrier mobility, diffusion length or diffusion coefficient.