Intrinsic lifetime of higher excitonic states in tungsten diselenide monolayers

Infrared Magnetopolaritons in MoTe_{2} Monolayers and Bilayers

MoTe_{2} monolayers and bilayers are unique within the family of van der Waals materials since they pave the way toward atomically thin infrared light-matter quantum interfaces, potentially reaching the important telecommunication windows. Here, we report emergent exciton polaritons based on MoTe_{2} monolayers and bilayers in a low-temperature open microcavity in a joint experiment-theory study. Our experiments clearly evidence both the enhanced oscillator strength and enhanced luminescence of MoTe_{2} bilayers, signified by a 38% increase of the Rabi splitting and a strongly enhanced relaxation of polaritons to low-energy states. The latter is distinct from polaritons in MoTe_{2} monolayers, which feature a bottlenecklike relaxation inhibition. Both the polaritonic spin valley locking in monolayers and the spin-layer locking in bilayers are revealed via the Zeeman effect, which we map and control via the light-matter composition of our polaritonic resonances.

Shaping exciton polarization dynamics in 2D semiconductors by tailored ultrafast pulses

The ultrafast formation of strongly bound excitons in two-dimensional semiconductors provides a rich platform for studying fundamental physics as well as developing novel optoelectronic technologies. While extensive research has explored the excitonic coherence, many-body interactions, and nonlinear optical properties, the potential to study these phenomena by directly controlling their coherent polarization dynamics has not been fully realized. In this work, we use a sub-10 fs pulse shaper to study how temporal control of coherent exciton polarization affects the generation of four-wave mixing in monolayer WS e 2 under ambient conditions. By tailoring multiphoton pathway interference, we tune the nonlinear response from destructive to constructive interference, resulting in a 2.6-fold enhancement over the four-wave mixing generated by a transform-limited pulse. This demonstrates a general method for nonlinear enhancement by shaping the pulse to counteract the temporal dispersion experienced during resonant light-matter interactions. Our method allows us to excite both 1s and 2s states, showcasing a selective control over the resonant state that produces nonlinearity. By comparing our results with theory, we find that exciton-exciton interactions dominate the nonlinear response, rather than Pauli blocking. This capability to manipulate exciton polarization dynamics in atomically thin crystals lays the groundwork for exploring a wide range of resonant phenomena in condensed matter systems and opens up new possibilities for precise optical control in advanced optoelectronic devices.

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.

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).

Exciton Lifetime and Optical Line Width Profile via Exciton-Phonon Interactions: Theory and First-Principles Calculations for Monolayer MoS2

Exciton dynamics dictates the evolution of photoexcited carriers in photovoltaic and optoelectronic devices. However, interpreting their experimental signatures is a challenging theoretical problem due to the presence of both electron-phonon and many-electron interactions. We develop and apply here a first-principles approach to exciton dynamics resulting from exciton-phonon coupling in monolayer MoS₂ and reveal the highly selective nature of exciton-phonon coupling due to the internal spin structure of excitons, which leads to a surprisingly long lifetime of the lowest-energy bright A exciton. Moreover, we show that optical absorption processes rigorously require a second-order perturbation theory approach, with photon and phonon treated on an equal footing, as proposed by Toyozawa and Hopfield. Such a treatment, thus far neglected in first-principles studies, gives rise to off-diagonal exciton-phonon self-energy, which is critical for the description of dephasing mechanisms and yields exciton line widths in excellent agreement with experiment.

Interface engineering of charge-transfer excitons in 2D lateral heterostructures

The existence of bound charge transfer (CT) excitons at the interface of monolayer lateral heterojunctions has been debated in literature, but contrary to the case of interlayer excitons in vertical heterostructure their observation still has to be confirmed. Here, we present a microscopic study investigating signatures of bound CT excitons in photoluminescence spectra at the interface of hBN-encapsulated lateral MoSe₂-WSe₂ heterostructures. Based on a fully microscopic and material-specific theory, we reveal the many-particle processes behind the formation of CT excitons and how they can be tuned via interface- and dielectric engineering. For junction widths smaller than the Coulomb-induced Bohr radius we predict the appearance of a low-energy CT exciton. The theoretical prediction is compared with experimental low-temperature photoluminescence measurements showing emission in the bound CT excitons energy range. We show that for hBN-encapsulated heterostructures, CT excitons exhibit small binding energies of just a few tens meV and at the same time large dipole moments, making them promising materials for optoelectronic applications (benefiting from an efficient exciton dissociation and fast dipole-driven exciton propagation). Our joint theory-experiment study presents a significant step towards a microscopic understanding of optical properties of technologically promising 2D lateral heterostructures.

Rydberg Excitons and Trions in Monolayer MoTe2

Monolayer transition metal dichalcogenide (TMDC) semiconductors exhibit strong excitonic optical resonances, which serve as a microscopic, noninvasive probe into their fundamental properties. Like the hydrogen atom, such excitons can exhibit an entire Rydberg series of resonances. Excitons have been extensively studied in most TMDCs (MoS₂, MoSe₂, WS₂, and WSe₂), but detailed exploration of excitonic phenomena has been lacking in the important TMDC material molybdenum ditelluride (MoTe₂). Here, we report an experimental investigation of excitonic luminescence properties of monolayer MoTe₂ to understand the excitonic Rydberg series, up to 3s. We report a significant modification of emission energies with temperature (4 to 300 K), thereby quantifying the exciton-phonon coupling. Furthermore, we observe a strongly gate-tunable exciton-trion interplay for all the Rydberg states governed mainly by free-carrier screening, Pauli blocking, and band gap renormalization in agreement with the results of first-principles GW plus Bethe-Salpeter equation approach calculations. Our results help bring monolayer MoTe₂ closer to its potential applications in near-infrared optoelectronics and photonic devices.

Theoretical Quantum Model of Two-Dimensional Propagating Plexcitons

When plasmonic excitations of metallic interfaces and nanostructures interact with electronic excitations in semiconductors, new states emerge that hybridize the characteristics of the uncoupled states. The engendered properties make these hybrid states appealing for a broad range of applications, ranging from photovoltaic devices to integrated circuitry for quantum devices. Here, through quantum modeling, the coupling of surface plasmon polaritons and mobile two-dimensional excitons such as those in atomically thin semiconductors is examined with emphasis on the case of strong coupling. Our model shows that at around the energy crossing of the dispersion relationships of the uncoupled species, they strongly interact and polariton states --propagating plexcitons -- emerge. The temporal evolution of the system where surface plasmon polaritons are continuously injected into the system is simulated to gain initial insight on potential experimental realizations of these states. The results show a steady state that is dominated by the lower-energy polariton. The study theoretically further establishes the possible existence of propagating plexcitons in atomically thin semiconductors and provides important guidance for the experimental detection and characterization of such states for a wide range of optoelectronic technologies.

Efficient Quadrature Squeezing from Biexcitonic Parametric Gain in Atomically Thin Semiconductors

Modification of electromagnetic quantum fluctuations in the form of quadrature squeezing is a central quantum resource, which can be generated from nonlinear optical processes. Such a process is facilitated by coherent two-photon excitation of the strongly bound biexciton in atomically thin semiconductors. We show theoretically that interfacing an atomically thin semiconductor with an optical cavity makes it possible to harness this two-photon resonance and use the biexcitonic parametric gain to generate squeezed light with input power an order of magnitude below current state-of-the-art devices with conventional third-order nonlinear materials that rely on far off-resonant nonlinearities. Furthermore, the squeezing bandwidth is found to be in the range of several meV. These results identify atomically thin semiconductors as a promising candidate for on-chip squeezed-light sources.

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.

Visualizing Hot-Carrier Expansion and Cascaded Transport in WS2 by Ultrafast Transient Absorption Microscopy

The competition between different spatiotemporal carrier relaxation determines the carrier harvesting in optoelectronic semiconductors, which can be greatly optimized by utilizing the ultrafast spatial expansion of highly energetic carriers before their energy dissipation via carrier-phonon interactions. Here, the excited-state dynamics in layered tungsten disulfide (WS2 ) are primarily imaged in the temporal, spatial, and spectral domains by transient absorption microscopy. Ultrafast hot carrier expansion is captured in the first 1.4 ps immediately after photoexcitation, with a mean diffusivity up to 980 cm2 s-1 . This carrier diffusivity then rapidly weakens, reaching a conventional linear spread of 10.5 cm2 s-1 after 2 ps after the hot carriers cool down to the band edge and form bound excitons. The novel carrier diffusion can be well characterized by a cascaded transport model including 3D thermal transport and thermo-optical conversion, in which the carrier temperature gradient and lattice thermal transport govern the initial hot carrier expansion and long-term exciton diffusion rates, respectively. The ultrafast hot carrier expansion breaks the limit of slow exciton diffusion in 2D transition metal dichalcogenides, providing potential guidance for high-performance applications and thermal management of optoelectronic technology.

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.

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.

Broadband sum frequency generation spectroscopy of dark exciton states in hBN-encapsulated monolayer WSe2

We demonstrate that broadband sum frequency generation (SFG) spectroscopy based on a partially incoherent supercontinuum light source can elucidate dark p-series excitons in monolayer WSe₂ encapsulated between hexagonal boron nitride (hBN) slabs. The observed 2p exciton peak energy is a few meV higher than that predicted by the Rytova-Keldysh potential model, which is originated from the Berry phase effect. Interestingly, although the radiative relaxation of the 2p exciton is weaker, the 2p exciton peak is broader than the 1s and 2s peaks, which indicates its faster dephasing than the 1s and 2s excitons. Measuring the excitation intensity and temperature dependence, we clarified that this broader linewidth is not caused by excitation- or phonon-induced dephasing, but rather by exciton-electron scattering.

Enhanced nonlinear interaction of polaritons via excitonic Rydberg states in monolayer WSe2

Strong optical nonlinearities play a central role in realizing quantum photonic technologies. Exciton-polaritons, which result from the hybridization of material excitations and cavity photons, are an attractive candidate to realize such nonlinearities. While the interaction between ground state excitons generates a notable optical nonlinearity, the strength of such interactions is generally not sufficient to reach the regime of quantum nonlinear optics. Excited states, however, feature enhanced interactions and therefore hold promise for accessing the quantum domain of single-photon nonlinearities. Here we demonstrate the formation of exciton-polaritons using excited excitonic states in monolayer tungsten diselenide (WSe2) embedded in a microcavity. The realized excited-state polaritons exhibit an enhanced nonlinear response ∼[Formula: see text] which is ∼4.6 times that for the ground-state exciton. The demonstration of enhanced nonlinear response from excited exciton-polaritons presents the potential of generating strong exciton-polariton interactions, a necessary building block for solid-state quantum photonic technologies.

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.

Excitons in Bilayer MoS_{2} Displaying a Colossal Electric Field Splitting and Tunable Magnetic Response

van der Waals heterostructures composed of transition metal dichalcogenide monolayers (TMDCs) are characterized by their truly rich excitonic properties which are determined by their structural, geometric, and electronic properties: In contrast to pure monolayers, electrons and holes can be hosted in different materials, resulting in highly tunable dipolar many-particle complexes. However, for genuine spatially indirect excitons, the dipolar nature is usually accompanied by a notable quenching of the exciton oscillator strength. Via electric and magnetic field dependent measurements, we demonstrate that a slightly biased pristine bilayer MoS_{2} hosts strongly dipolar excitons, which preserve a strong oscillator strength. We scrutinize their giant dipole moment, and shed further light on their orbital and valley physics via bias-dependent magnetic field measurements.

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

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

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.

Exciton-Scattering-Induced Dephasing in Two-Dimensional Semiconductors

Enhanced Coulomb interactions in monolayer transition metal dichalcogenides cause tightly bound electron-hole pairs (excitons) that dominate their linear and nonlinear optical response. The latter includes bleaching, energy renormalizations, and higher-order Coulomb correlation effects like biexcitons and excitation-induced dephasing. While the first three are extensively studied, no theoretical footing for excitation-induced dephasing in exciton-dominated semiconductors is available so far. In this Letter, we present microscopic calculations based on excitonic Heisenberg equations of motion and identify the coupling of optically pumped excitons to exciton-exciton scattering continua as the leading mechanism responsible for an optical-power-dependent linewidth broadening (excitation-induced dephasing) and sideband formation. Performing time-, momentum-, and energy-resolved simulations, we quantitatively evaluate the exciton-induced dephasing for the most common monolayer transition metal dichalcogenides and find an excellent agreement with recent experiments.

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.

Phonon-Assisted Photoluminescence from Indirect Excitons in Monolayers of Transition-Metal Dichalcogenides

The photoluminescence (PL) spectrum of transition-metal dichalcogenides (TMDs) shows a multitude of emission peaks below the bright exciton line, and not all of them have been explained yet. Here, we study the emission traces of phonon-assisted recombinations of indirect excitons. To this end, we develop a microscopic theory describing simultaneous exciton, phonon, and photon interaction and including consistent many-particle dephasing. We explain the drastically different PL below the bright exciton in tungsten- and molybdenum-based materials as the result of different configurations of bright and momentum-dark states. In good agreement with experiments, our calculations predict that WSe₂ exhibits clearly visible low-temperature PL signals stemming from the phonon-assisted recombination of momentum-dark K-K' excitons.

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.

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.