Trion Photoluminescence and Trion Stability in Atomically Thin Semiconductors.

The optical response of doped monolayer semiconductors is governed by trions, i.e. photoexcited electron-hole pairs bound to doping charges. While their photoluminescence (PL) signatures have been identified in experiments, a microscopic model consistently capturing bright and dark trion peaks is still lacking. In this work, we derive a generalized trion PL formula on a quantum-mechanical footing, considering direct and phonon-assisted recombination mechanisms. We show the trion energy landscape in WSe_{2} by solving the trion Schrödinger equation. We reveal that the mass imbalance between equal charges results in less stable trions exhibiting a small binding energy and, interestingly, a large energetic offset from exciton peaks in PL spectra. Furthermore, we compute the temperature-dependent PL spectra for n- and p-doped monolayers and predict yet unobserved signatures originating from trions with an electron at the Λ point. Our work presents an important step toward a microscopic understanding of the internal structure of trions determining their stability and optical fingerprint.

Electrical control of hybrid exciton transport in a van der Waals heterostructure.

Interactions between out-of-plane dipoles in bosonic gases enable the long-range propagation of excitons. The lack of direct control over collective dipolar properties has so far limited the degrees of tunability and the microscopic understanding of exciton transport. In this work we modulate the layer hybridization and interplay between many-body interactions of excitons in a van der Waals heterostructure with an applied vertical electric field. By performing spatiotemporally resolved measurements supported by microscopic theory, we uncover the dipole-dependent properties and transport of excitons with different degrees of hybridization. Moreover, we find constant emission quantum yields of the transporting species as a function of excitation power with radiative decay mechanisms dominating over nonradiative ones, a fundamental requirement for efficient excitonic devices. Our findings provide a complete picture of the many-body effects in the transport of dilute exciton gases, and have crucial implications for studying emerging states of matter such as Bose-Einstein condensation and optoelectronic applications based on exciton propagation.

Electrically tunable dipolar interactions between layer-hybridized excitons.

Transition-metal dichalcogenide bilayers exhibit a rich exciton landscape including layer-hybridized excitons, i.e. excitons which are of partly intra- and interlayer nature. In this work, we study hybrid exciton-exciton interactions in naturally stacked WSe2 homobilayers. In these materials, the exciton landscape is electrically tunable such that the low-energy states can be rendered more or less interlayer-like depending on the strength of the external electric field. Based on a microscopic and material-specific many-particle theory, we reveal two intriguing interaction regimes: a low-dipole regime at small electric fields and a high-dipole regime at larger fields, involving interactions between hybrid excitons with a substantially different intra- and interlayer composition in the two regimes. While the low-dipole regime is characterized by weak inter-excitonic interactions between intralayer-like excitons, the high-dipole regime involves mostly interlayer-like excitons which display a strong dipole-dipole repulsion and give rise to large spectral blue-shifts and a highly anomalous diffusion. Overall, our microscopic study sheds light on the remarkable electrical tunability of hybrid exciton-exciton interactions in atomically thin semiconductors and can guide future experimental studies in this growing field of research.

Fermi Pressure and Coulomb Repulsion Driven Rapid Hot Plasma Expansion in a van der Waals Heterostructure.

Transition metal dichalcogenide heterostructures provide a versatile platform to explore electronic and excitonic phases. As the excitation density exceeds the critical Mott density, interlayer excitons are ionized into an electron-hole plasma phase. The transport of the highly non-equilibrium plasma is relevant for high-power optoelectronic devices but has not been carefully investigated previously. Here, we employ spatially resolved pump-probe microscopy to investigate the spatial-temporal dynamics of interlayer excitons and hot-plasma phase in a MoSe2/WSe2 twisted bilayer. At the excitation density of ∼1014 cm-2, well exceeding the Mott density, we find a surprisingly rapid initial expansion of hot plasma to a few microns away from the excitation source within ∼0.2 ps. Microscopic theory reveals that this rapid expansion is mainly driven by Fermi pressure and Coulomb repulsion, while the hot carrier effect has only a minor effect in the plasma phase.

Ultrafast hot electron-hole plasma photoluminescence in two-dimensional semiconductors.

The transition metal dichalcogenide family of semiconducting two-dimensional materials has recently shown a prominent potential to be an ideal platform to study the exciton Mott transition into electron-hole plasma and liquid phases due to their strong Coulomb interactions. Here, we show that pulsed laser excitation at high pump fluences can induce this exciton Mott transition to an electron-hole plasma in mono and few-layer transition metal dichalcogenides at room temperature. The formation of an electron-hole plasma leads to a broadband light emission spanning from the near infrared to the visible region. In agreement with our theoretical calculations, the photoluminescence emission at high energies displays an exponential decay that directly reflects the electronic temperature - a characteristic fingerprint of unbound electron-hole pair recombination. Furthermore, two-pulse excitation correlation measurements were performed to study the dynamics of electronic cooling, which shows two decay time components, one of less than 100 fs and a slower component of few ps associated with the electron-phonon and phonon-lattice bath thermalizations, respectively. Our work may shed light on further studies of the exciton Mott transition into other two-dimensional materials and their heterostructures and its applications in nanolasers and other optoelectronic devices.

Flat-Band-Induced Many-Body Interactions and Exciton Complexes in a Layered Semiconductor.

Interactions among a collection of particles generate many-body effects in solids that result in striking modifications of material properties. The heavy carrier mass that yields strong interactions and gate control of carrier density over a wide range makes two-dimensional semiconductors an exciting playground to explore many-body physics. The family of III-VI metal monochalcogenides emerges as a new platform for this purpose because of its excellent optical properties and the flat valence band dispersion. In this work, we present a complete study of charge-tunable excitons in few-layer InSe by photoluminescence spectroscopy. From the optical spectra, we establish that free excitons in InSe are more likely to be captured by ionized donors leading to the formation of bound exciton complexes. Surprisingly, a pronounced red shift of the exciton energy accompanied by a decrease of the exciton binding energy upon hole-doping reveals a significant band gap renormalization induced by the presence of the Fermi reservoir.

Ultrafast Nanoscopy of High-Density Exciton Phases in WSe2.

The density-driven transition of an exciton gas into an electron-hole plasma remains a compelling question in condensed matter physics. In two-dimensional transition metal dichalcogenides, strongly bound excitons can undergo this phase change after transient injection of electron-hole pairs. Unfortunately, unavoidable nanoscale inhomogeneity in these materials has impeded quantitative investigation into this elusive transition. Here, we demonstrate how ultrafast polarization nanoscopy can capture the Mott transition through the density-dependent recombination dynamics of electron-hole pairs within a WSe2 homobilayer. For increasing carrier density, an initial monomolecular recombination of optically dark excitons transitions continuously into a bimolecular recombination of an unbound electron-hole plasma above 7 × 1012 cm-2. We resolve how the Mott transition modulates over nanometer length scales, directly evidencing the strong inhomogeneity in stacked monolayers. Our results demonstrate how ultrafast polarization nanoscopy could unveil the interplay of strong electronic correlations and interlayer coupling within a diverse range of stacked and twisted two-dimensional materials.

Dark exciton anti-funneling in atomically thin semiconductors.

Transport of charge carriers is at the heart of current nanoelectronics. In conventional materials, electronic transport can be controlled by applying electric fields. Atomically thin semiconductors, however, are governed by excitons, which are neutral electron-hole pairs and as such cannot be controlled by electrical fields. Recently, strain engineering has been introduced to manipulate exciton propagation. Strain-induced energy gradients give rise to exciton funneling up to a micrometer range. Here, we combine spatiotemporal photoluminescence measurements with microscopic theory to track the way of excitons in time, space and energy. We find that excitons surprisingly move away from high-strain regions. This anti-funneling behavior can be ascribed to dark excitons which possess an opposite strain-induced energy variation compared to bright excitons. Our findings open new possibilities to control transport in exciton-dominated materials. Overall, our work represents a major advance in understanding exciton transport that is crucial for technological applications of atomically thin 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.

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.

Momentum-Resolved Observation of Exciton Formation Dynamics in Monolayer WS2.

The dynamics of momentum-dark exciton formation in transition metal dichalcogenides is difficult to measure experimentally, as many momentum-indirect exciton states are not accessible to optical interband spectroscopy. Here, we combine a tunable pump, high-harmonic probe laser source with a 3D momentum imaging technique to map photoemitted electrons from monolayer WS2. This provides momentum-, energy- and time-resolved access to excited states on an ultrafast time scale. The high temporal resolution of the setup allows us to trace the early-stage exciton dynamics on its intrinsic time scale and observe the formation of a momentum-forbidden dark KΣ exciton a few tens of femtoseconds after optical excitation. By tuning the excitation energy, we manipulate the temporal evolution of the coherent excitonic polarization and observe its influence on the dark exciton formation. The experimental results are in excellent agreement with a fully microscopic theory, resolving the temporal and spectral dynamics of bright and dark excitons in WS2.

Phonon-assisted exciton dissociation in transition metal dichalcogenides.

Monolayers of transition metal dichalcogenides (TMDs) have been established in the last years as promising materials for novel optoelectronic devices. However, the performance of such devices is often limited by the dissociation of tightly bound excitons into free electrons and holes. While previous studies have investigated tunneling at large electric fields, we focus in this work on phonon-assisted exciton dissociation that is expected to be the dominant mechanism at small fields. We present a microscopic model based on the density matrix formalism providing access to time- and momentum-resolved exciton dynamics including phonon-assisted dissociation. We track the pathway of excitons from optical excitation via thermalization to dissociation, identifying the main transitions and dissociation channels. Furthermore, we find intrinsic limits for the quantum efficiency and response time of a TMD-based photodetector and investigate their tunability with externally accessible knobs, such as excitation energy, substrate screening, temperature and strain. Our work provides microscopic insights in fundamental mechanisms behind exciton dissociation and can serve as a guide for the optimization of TMD-based optoelectronic devices.

The Art of Constructing Black Phosphorus Nanosheet Based Heterostructures: From 2D to 3D.

Assembling different kinds of 2D nanosheets into heterostructures presents a promising way of designing novel artificial materials with new and improved functionalities by combining the unique properties of each component. In the past few years, black phosphorus nanosheets (BPNSs) have been recognized as a highly feasible 2D material with outstanding electronic properties, a tunable bandgap, and strong in-plane anisotropy, highlighting their suitability as a material for constructing heterostructures. In this study, recent progress in the construction of BPNS-based heterostructures ranging from 2D hybrid structures to 3D networks is discussed, emphasizing the different types of interactions (covalent or noncovalent) between individual layers. The preparation methods, optical and electronic properties, and various applications of these heterostructures-including electronic and optoelectronic devices, energy storage devices, photocatalysis and electrocatalysis, and biological applications-are discussed. Finally, critical challenges and prospective research aspects in BPNS-based heterostructures are also highlighted.

Microscopic Picture of Electron-Phonon Interaction in Two-Dimensional Halide Perovskites.

Perovskites have attracted much attention due to their remarkable optical properties. While it is well established that excitons dominate their optical response, the impact of higher excitonic states and formation of phonon sidebands in optical spectra still need to be better understood. Here, we perform a theoretical study of excitonic properties of monolayered hybrid organic perovskites-supported by temperature-dependent photoluminescence measurements. Solving the Wannier equation, we obtain microscopic access to the Rydberg-like series of excitonic states including their wave functions and binding energies. Exploiting the generalized Elliot formula, we calculate the photoluminescence spectra demonstrating a pronounced contribution of a phonon sideband for temperatures up to 50 K, in agreement with experimental measurements. Finally, we predict temperature-dependent line widths of the three energetically lowest excitonic transitions and identify the underlying phonon-driven scattering processes.

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.

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.

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.