Directly visualizing the momentum-forbidden dark excitons and their dynamics in atomically thin semiconductors

Structure of the moiré exciton captured by imaging its electron and hole

Interlayer excitons (ILXs) - electron-hole pairs bound across two atomically thin layered semiconductors - have emerged as attractive platforms to study exciton condensation^1-4, single-photon emission and other quantum information applications^5-7. Yet, despite extensive optical spectroscopic investigations^8-12, critical information about their size, valley configuration and the influence of the moiré potential remains unknown. Here, in a WSe₂/MoS₂ heterostructure, we captured images of the time-resolved and momentum-resolved distribution of both of the particles that bind to form the ILX: the electron and the hole. We thereby obtain a direct measurement of both the ILX diameter of around 5.2 nm, comparable with the moiré-unit-cell length of 6.1 nm, and the localization of its centre of mass. Surprisingly, this large ILX is found pinned to a region of only 1.8 nm diameter within the moiré cell, smaller than the size of the exciton itself. This high degree of localization of the ILX is backed by Bethe-Salpeter equation calculations and demonstrates that the ILX can be localized within small moiré unit cells. Unlike large moiré cells, these are uniform over large regions, allowing the formation of extended arrays of localized excitations for quantum technology.

Excitons in semiconductor moiré superlattices

Semiconductor moiré superlattices represent a rapidly developing area of engineered photonic materials and a new platform to explore correlated electron states and quantum simulation. In this Review, we briefly introduce early experiments that identified new exciton resonances in transition metal dichalcogenide heterobilayers and discuss several topics including two types of transition metal dichalcogenide moiré superlattice, new optical selection rules, early evidence of moiré excitons, and how the resonant energy, dynamics and diffusion properties of moiré excitons can be controlled via the twist angle. To interpret optical spectra, it is important to measure the energy modulation within a moiré supercell. In this context, we describe a few scanning tunnelling microscopy experiments that measure the moiré potential landscape directly. Finally, we review a few recent experiments that applied excitonic optical spectroscopy to probe correlated electron phenomena in transition metal dichalcogenide moiré superlattices.

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

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

Valley-exchange coupling probed by angle-resolved photoluminescence

The optical properties of monolayer transition metal dichalcogenides are dominated by tightly-bound excitons. They form at distinct valleys in reciprocal space, and can interact via the valley-exchange coupling, modifying their dispersion considerably. Here, we predict that angle-resolved photoluminescence can be used to probe the changes of the excitonic dispersion. The exchange-coupling leads to a unique angle dependence of the emission intensity for both circularly and linearly-polarised light. We show that these emission characteristics can be strongly tuned by an external magnetic field due to the valley-specific Zeeman-shift. We propose that angle-dependent photoluminescence measurements involving both circular and linear optical polarisation as well as magnetic fields should act as strong verification of the role of valley-exchange coupling on excitonic dispersion and its signatures in optical spectra.

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.

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.

Time- and momentum-resolved image-potential states of 2H-MoS2 surface

Rydberg-like image potential states (IPSs) form special series surface states on metal and semiconducting surfaces. Here, using time-resolved and momentum-resolved multi-photon photoemission (mPPE), we measured the energy positions, band dispersion, and carrier lifetimes of IPSs at the 2H-MoS₂ surface. The energy minima of the IPSs (n = 1 and 2) were located at 0.77 and 0.21 eV below the vacuum level. In addition, the effective masses of these two IPSs are close to the rest mass of the free electron, clearly showing nearly-free-electron character. These properties suggest a good screening effect in the MoS₂ parallel to the surface. The multi-photon resonances between the valence band and IPS (n = 1) are observed, showing a k_‖-momentum-dependent behavior. Our time-resolved mPPE measurements show that the lifetime of photoexcited electrons in the IPS (n = 1) is about 33 fs.

Time-of-flight photoelectron momentum microscopy with 80-500 MHz photon sources: electron-optical pulse picker or bandpass pre-filter

The small time gaps of synchrotron radiation in conventional multi-bunch mode (100-500 MHz) or laser-based sources with high pulse rate (∼80 MHz) are prohibitive for time-of-flight (ToF) based photoelectron spectroscopy. Detectors with time resolution in the 100 ps range yield only 20-100 resolved time slices within the small time gap. Here we present two techniques of implementing efficient ToF recording at sources with high repetition rate. A fast electron-optical beam blanking unit with GHz bandwidth, integrated in a photoelectron momentum microscope, allows electron-optical `pulse-picking' with any desired repetition period. Aberration-free momentum distributions have been recorded at reduced pulse periods of 5 MHz (at MAX II) and 1.25 MHz (at BESSY II). The approach is compared with two alternative solutions: a bandpass pre-filter (here a hemispherical analyzer) or a parasitic four-bunch island-orbit pulse train, coexisting with the multi-bunch pattern on the main orbit. Chopping in the time domain or bandpass pre-selection in the energy domain can both enable efficient ToF spectroscopy and photoelectron momentum microscopy at 100-500 MHz synchrotrons, highly repetitive lasers or cavity-enhanced high-harmonic sources. The high photon flux of a UV-laser (80 MHz, <1 meV bandwidth) facilitates momentum microscopy with an energy resolution of 4.2 meV and an analyzed region-of-interest (ROI) down to <800 nm. In this novel approach to `sub-µm-ARPES' the ROI is defined by a small field aperture in an intermediate Gaussian image, regardless of the size of the photon spot.

Phonon-Assisted Intervalley Scattering Determines Ultrafast Exciton Dynamics in MoSe_{2} Bilayers

While valleys (energy extrema) are present in all band structures of solids, their preeminent role in determining exciton resonances and dynamics in atomically thin transition metal dichalcogenides (TMDC) is unique. Using two-dimensional coherent electronic spectroscopy, we find that exciton decoherence occurs on a much faster timescale in MoSe_{2} bilayers than that in the monolayers. We further identify two population relaxation channels in the bilayer, a coherent and an incoherent one. Our microscopic model reveals that phonon-emission processes facilitate scattering events from the K valley to other lower-energy Γ and Λ valleys in the bilayer. Our combined experimental and theoretical studies unequivocally establish different microscopic mechanisms that determine exciton quantum dynamics in TMDC monolayers and bilayers. Understanding exciton quantum dynamics provides critical guidance to the manipulation of spin-valley degrees of freedom in TMDC bilayers.

Time-resolved ARPES Determination of a Quasi-Particle Band Gap and Hot Electron Dynamics in Monolayer MoS2

The electronic structure and dynamics of 2D transition metal dichalcogenide (TMD) monolayers provide important underpinnings both for understanding the many-body physics of electronic quasi-particles and for applications in advanced optoelectronic devices. However, extensive experimental investigations of semiconducting monolayer TMDs have yielded inconsistent results for a key parameter, the quasi-particle band gap (QBG), even for measurements carried out on the same layer and substrate combination. Here, we employ sensitive time- and angle-resolved photoelectron spectroscopy (trARPES) for a high-quality large-area MoS₂ monolayer to capture its momentum-resolved equilibrium and excited-state electronic structure in the weak-excitation limit. For monolayer MoS₂ on graphite, we obtain QBG values of ≈2.10 eV at 80 K and of ≈2.03 eV at 300 K, results well-corroborated by the scanning tunneling spectroscopy (STS) measurements on the same material.

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.

Inhibited nonradiative decay at all exciton densities in monolayer semiconductors

Most optoelectronic devices operate at high photocarrier densities, where all semiconductors suffer from enhanced nonradiative recombination. Nonradiative processes proportionately reduce photoluminescence (PL) quantum yield (QY), a performance metric that directly dictates the maximum device efficiency. Although transition metal dichalcogenide (TMDC) monolayers exhibit near-unity PL QY at low exciton densities, nonradiative exciton-exciton annihilation (EEA) enhanced by van-Hove singularity (VHS) rapidly degrades their PL QY at high exciton densities and limits their utility in practical applications. Here, by applying small mechanical strain (less than 1%), we circumvented VHS resonance and markedly suppressed EEA in monolayer TMDCs, resulting in near-unity PL QY at all exciton densities despite the presence of a high native defect density. Our findings can enable light-emitting devices that retain high efficiency at all brightness levels.

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.

The 2021 ultrafast spectroscopic probes of condensed matter roadmap

In the 60 years since the invention of the laser, the scientific community has developed numerous fields of research based on these bright, coherent light sources, including the areas of imaging, spectroscopy, materials processing and communications. Ultrafast spectroscopy and imaging techniques are at the forefront of research into the light-matter interaction at the shortest times accessible to experiments, ranging from a few attoseconds to nanoseconds. Light pulses provide a crucial probe of the dynamical motion of charges, spins, and atoms on picosecond, femtosecond, and down to attosecond timescales, none of which are accessible even with the fastest electronic devices. Furthermore, strong light pulses can drive materials into unusual phases, with exotic properties. In this roadmap we describe the current state-of-the-art in experimental and theoretical studies of condensed matter using ultrafast probes. In each contribution, the authors also use their extensive knowledge to highlight challenges and predict future trends.

Suppression of the vacuum space-charge effect in fs-photoemission by a retarding electrostatic front lens

The performance of time-resolved photoemission experiments at fs-pulsed photon sources is ultimately limited by the e-e Coulomb interaction, downgrading energy and momentum resolution. Here, we present an approach to effectively suppress space-charge artifacts in momentum microscopes and photoemission microscopes. A retarding electrostatic field generated by a special objective lens repels slow electrons, retaining the k-image of the fast photoelectrons. The suppression of space-charge effects scales with the ratio of the photoelectron velocities of fast and slow electrons. Fields in the range from -20 to -1100 V/mm for E_kin = 100 eV to 4 keV direct secondaries and pump-induced slow electrons back to the sample surface. Ray tracing simulations reveal that this happens within the first 40 to 3 μm above the sample surface for E_kin = 100 eV to 4 keV. An optimized front-lens design allows switching between the conventional accelerating and the new retarding mode. Time-resolved experiments at E_kin = 107 eV using fs extreme ultraviolet probe pulses from the free-electron laser FLASH reveal that the width of the Fermi edge increases by just 30 meV at an incident pump fluence of 22 mJ/cm² (retarding field -21 V/mm). For an accelerating field of +2 kV/mm and a pump fluence of only 5 mJ/cm², it increases by 0.5 eV (pump wavelength 1030 nm). At the given conditions, the suppression mode permits increasing the slow-electron yield by three to four orders of magnitude. The feasibility of the method at high energies is demonstrated without a pump beam at E_kin = 3830 eV using hard x rays from the storage ring PETRA III. The approach opens up a previously inaccessible regime of pump fluences for photoemission experiments.

Experimental measurement of the intrinsic excitonic wave function

An exciton, a two-body composite quasiparticle formed of an electron and hole, is a fundamental optical excitation in condensed matter systems. Since its discovery nearly a century ago, a measurement of the excitonic wave function has remained beyond experimental reach. Here, we directly image the excitonic wave function in reciprocal space by measuring the momentum distribution of electrons photoemitted from excitons in monolayer tungsten diselenide. By transforming to real space, we obtain a visual of the distribution of the electron around the hole in an exciton. Further, by also resolving the energy coordinate, we confirm the elusive theoretical prediction that the photoemitted electron exhibits an inverted energy-momentum dispersion relationship reflecting the valence band where the partner hole remains, rather than that of conduction band states of the electron.

Excitonic Complexes in n-Doped WS2 Monolayer

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

Proximity control of interlayer exciton-phonon hybridization in van der Waals heterostructures

Van der Waals stacking has provided unprecedented flexibility in shaping many-body interactions by controlling electronic quantum confinement and orbital overlap. Theory has predicted that also electron-phonon coupling critically influences the quantum ground state of low-dimensional systems. Here we introduce proximity-controlled strong-coupling between Coulomb correlations and lattice dynamics in neighbouring van der Waals materials, creating new electrically neutral hybrid eigenmodes. Specifically, we explore how the internal orbital 1s-2p transition of Coulomb-bound electron-hole pairs in monolayer tungsten diselenide resonantly hybridizes with lattice vibrations of a polar capping layer of gypsum, giving rise to exciton-phonon mixed eigenmodes, called excitonic Lyman polarons. Tuning orbital exciton resonances across the vibrational resonances, we observe distinct anticrossing and polarons with adjustable exciton and phonon compositions. Such proximity-induced hybridization can be further controlled by quantum designing the spatial wavefunction overlap of excitons and phonons, providing a promising new strategy to engineer novel ground states of two-dimensional systems.

Here, the authors demonstrate proximity-controlled strong-coupling between Coulomb correlations and lattice dynamics in neighbouring van der Waals materials (WSe₂ and a gypsum layer), creating electrically neutral hybrid exciton-phonon eigenmodes called excitonic Lyman polarons.

Real-time GW-BSE investigations on spin-valley exciton dynamics in monolayer transition metal dichalcogenide

We develop an ab initio nonadiabatic molecular dynamics (NAMD) method based on GW plus real-time Bethe-Salpeter equation (GW + rtBSE-NAMD) for the spin-resolved exciton dynamics. From investigations on MoS₂, we provide a comprehensive picture of spin-valley exciton dynamics where the electron-phonon (e-ph) scattering, spin-orbit interaction (SOI), and electron-hole (e-h) interactions come into play collectively. In particular, we provide a direct evidence that e-h exchange interaction plays a dominant role in the fast valley depolarization within a few picoseconds, which is in excellent agreement with experiments. Moreover, there are bright-to-dark exciton transitions induced by e-ph scattering and SOI. Our study proves that e-h many-body effects are essential to understand the spin-valley exciton dynamics in transition metal dichalcogenides and the newly developed GW + rtBSE-NAMD method provides a powerful tool for exciton dynamics in extended systems with time, space, momentum, energy, and spin resolution.

Time-Dependent Screening Explains the Ultrafast Excitonic Signal Rise in 2D Semiconductors

We calculate the time evolution of the transient reflection signal in an MoS₂ monolayer on a SiO₂/Si substrate using first-principles out-of-equilibrium real-time methods. Our simulations provide a simple and intuitive physical picture for the delayed, yet ultrafast, evolution of the signal whose rise time depends on the excess energy of the pump laser: at laser energies above the A- and B-exciton, the pump pulse excites electrons and holes far away from the K valleys in the first Brillouin zone. Electron-phonon and hole-phonon scattering lead to a gradual relaxation of the carriers toward small Active Excitonic Regions around K, enhancing the dielectric screening. The accompanying time-dependent band gap renormalization dominates over Pauli blocking and the excitonic binding energy renormalization. This explains the delayed buildup of the transient reflection signal of the probe pulse, in excellent agreement with recent experimental data. Our results show that the observed delay is not a unique signature of an exciton formation process but rather caused by coordinated carrier dynamics and its influence on the screening.

Efficient phonon cascades in WSe2 monolayers

Energy relaxation of photo-excited charge carriers is of significant fundamental interest and crucial for the performance of monolayer transition metal dichalcogenides in optoelectronics. The primary stages of carrier relaxation affect a plethora of subsequent physical mechanisms. Here we measure light scattering and emission in tungsten diselenide monolayers close to the laser excitation energy (down to ~0.6 meV). We reveal a series of periodic maxima in the hot photoluminescence intensity, stemming from energy states higher than the A-exciton state. We find a period ~15 meV for 7 peaks below (Stokes) and 5 peaks above (anti-Stokes) the laser excitation energy, with a strong temperature dependence. These are assigned to phonon cascades, whereby carriers undergo phonon-induced transitions between real states above the free-carrier gap with a probability of radiative recombination at each step. We infer that intermediate states in the conduction band at the Λ-valley of the Brillouin zone participate in the cascade process of tungsten diselenide monolayers. This provides a fundamental understanding of the first stages of carrier-phonon interaction, useful for optoelectronic applications of layered semiconductors.