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

Access to the full three-dimensional Brillouin zone with time resolution, using a new tool for pump-probe angle-resolved photoemission spectroscopy

Here, we report the first time- and angle-resolved photoemission spectroscopy (TR-ARPES) with the new Fermiologics "FeSuMa" analyzer. The new experimental setup has been commissioned at the Artemis laboratory of the UK Central Laser Facility. We explain here some of the advantages of the FeSuMa for TR-ARPES and discuss how its capabilities relate to those of hemispherical analyzers and momentum microscopes. We have integrated the FeSuMa into an optimized pump-probe beamline that permits photon-energy (i.e., kz)-dependent scanning, using probe energies generated from high harmonics in a gas jet. The advantages of using the FeSuMa in this situation include the possibility of taking advantage of its "fisheye" mode of operation.

Electron Spectroscopy and Microscopy: A Window into the Surface Electronic Properties of Polycrystalline Metal Halide Perovskites

In the past years, an increasing number of experimental techniques have emerged to address the need to unveil the chemical, structural, and electronic properties of perovskite thin films with high vertical and lateral spatial resolutions. One of these is angle-resolved photoemission electron spectroscopy which can provide direct access to the electronic band structure of perovskites, with the aim of overcoming elusive and controversial information due to the complex data interpretation of purely optical spectroscopic techniques. This perspective looks at the information that can be gleaned from the direct measurement of the electronic band structure of single crystal perovskites and the challenges that remain to be overcame to extend this technique to heterogeneous polycrystalline metal halide perovskites.

Revealing hidden spin polarization in centrosymmetric van der Waals materials on ultrafast timescales

One of the key challenges for spintronic and quantum technologies is to achieve active control of the spin angular momentum of electrons in nanoscale materials on ultrafast, femtosecond timescales. While conventional ferromagnetic materials and materials supporting spin texture suffer both from conceptional limitations in miniaturization and inefficiency of optical and electronic manipulation, non-magnetic centrosymmetric layered materials with hidden spin polarization may offer an alternative pathway to manipulate the spin degree of freedom by external stimuli. Here we demonstrate an approach for generating transient spin polarization on a femtosecond timescale in the otherwise spin-unpolarized band structure of the centrosymmetric 2H-stacked group VI transition metal dichalcogenide WSe2. Using ultrafast optical excitation of a fullerene layer grown on top of WSe2, we trigger an ultrafast interlayer electron transfer from the fullerene layer into the WSe2 crystal. The resulting transient charging of the C60/WSe2 interface leads to a substantial interfacial electric field that by means of spin-layer-valley locking ultimately creates ultrafast spin polarization without the need of an external magnetic field. Our findings open a novel pathway for true optical engineering of spin functionalities such as the sub-picosecond generation and manipulation of ultrafast spin currents in 2D heterostructures.

Layer-dependent ultrafast carrier dynamics of PdSe2 investigated by photoemission electron microscopy

For atomically thin two-dimensional materials, variations in layer thickness can result in significant changes in the electronic energy band structure and physicochemical properties, thereby influencing the carrier dynamics and device performance. In this work, we employ time- and energy-resolved photoemission electron microscopy to reveal the ultrafast carrier dynamics of PdSe2 with different layer thicknesses. We find that for few-layer PdSe2 with a semiconductor phase, an ultrafast hot carrier cooling on a timescale of approximately 0.3 ps and an ultrafast defect trapping on a timescale of approximately 1.3 ps are unveiled, followed by a slower decay of approximately tens of picoseconds. However, for bulk PdSe2 with a semimetal phase, only an ultrafast hot carrier cooling and a slower decay of approximately tens of picoseconds are observed, while the contribution of defect trapping is suppressed with the increase of layer number. Theoretical calculations of the electronic energy band structure further confirm the transition from a semiconductor to a semimetal. Our work demonstrates that TR- and ER-PEEM with ultrahigh spatiotemporal resolution and wide-field imaging capability has great advantages in revealing the intricate details of ultrafast carrier dynamics of nanomaterials.

Thickness-dependent electronic relaxation dynamics in solution-phase redox-exfoliated MoS2 heterostructures

Electronic relaxation dynamics of solution-phase redox-exfoliated molybdenum disulfide (MoS2) monolayer and multilayer ensembles are described. MoS2 was exfoliated using polyoxometalate (POM) reductants. This process yields a colloidal heterostructure consisting of MoS2 2D sheet multilayers with surface-bound POM complexes. Using two-dimensional electronic spectroscopy, transient bleaching and photoinduced absorption signals were detected at excitation/detection energies of 1.82/1.87 and 1.82/1.80 eV, respectively. Approximate 100-fs bandgap renormalization (BGR) and subsequent defect- and phonon-mediated relaxation on the picosecond timescale were resolved for several MoS2 thicknesses spanning from 1 to 2 L to ∼20 L. BGR rates were independent of sample thickness and slightly slower than observations for chemical vapor deposition-grown MoS2 monolayers. However, defect-mediated relaxation accelerated ∼10-fold with increased sample thicknesses. The relaxation rates increased from 0.33 ± 0.05 to 1.2 ± 0.1 and 3.1 ± 0.4 ps-1 for 1-2 L, 3-4 L, and 20 L fractions. The thicknesses-dependent relaxation rates for POM-MoS2 heterostructures were modeled using a saturating exponential function that showed saturation at thirteen MoS2 layers. The results suggest that the increased POM surface coverage leads to larger defect density in the POM-MoS2 heterostructure. These are the first descriptions of the influence of sample thickness on electronic relaxation rates in solution-phase redox-exfoliated POM-MoS2 heterostructures. Outcomes of this work are expected to impact the development of solution-phase exfoliation of 2D metal-chalcogenide heterostructures.

Direct Hot-Electron Transfer at the Au Nanoparticle/Monolayer Transition-Metal Dichalcogenide Interface Observed with Ultrahigh Spatiotemporal Resolution

Plasmon-induced hot-electron transfer at the metallic nanoparticle/semiconductor interface is the basis of plasmon-enhanced photocatalysis and energy harvesting. However, limited by the nanoscale size of hot spots and femtosecond time scale of hot-electron transfer, direct observation is still challenging. Herein, by using spatiotemporal-resolved photoemission electron microscopy with a two-color pump-probe beamline, we directly observed such a process with a concise system, the Au nanoparticle/monolayer transition-metal dichalcogenide (TMD) interface. The ultrafast hot-electron transfer from Au nanoparticles to monolayer TMDs and the plasmon-enhanced transfer process were directly measured and verified through an in situ comparison with the Au film/TMD interface and free TMDs. The lifetime at the Au nanoparticle/MoSe2 interface decreased from 410 to 42 fs, while the photoemission intensities exhibited a 27-fold increase compared to free MoSe2. We also measured the evolution of hot electrons in the energy distributions, indicating the hot-electron injection and decay happened in an ultrafast time scale of ∼50 fs without observable electron cooling.

A versatile laser-based apparatus for time-resolved ARPES with micro-scale spatial resolution

We present the development of a versatile apparatus for 6.2 eV laser-based time and angle-resolved photoemission spectroscopy with micrometer spatial resolution (time-resolved μ-ARPES). With a combination of tunable spatial resolution down to ∼11 μm, high energy resolution (∼11 meV), near-transform-limited temporal resolution (∼280 fs), and tunable 1.55 eV pump fluence up to 3 mJ/cm2, this time-resolved μ-ARPES system enables the measurement of ultrafast electron dynamics in exfoliated and inhomogeneous materials. We demonstrate the performance of our system by correlating the spectral broadening of the topological surface state of Bi2Se3 with the spatial dimension of the probe pulse, as well as resolving the spatial inhomogeneity contribution to the observed spectral broadening. Finally, after in situ exfoliation, we performed time-resolved μ-ARPES on a ∼30 μm flake of transition metal dichalcogenide WTe2, thus demonstrating the ability to access ultrafast electron dynamics with momentum resolution on micro-exfoliated materials.

Disentangling the multiorbital contributions of excitons by photoemission exciton tomography

Excitons are realizations of a correlated many-particle wave function, specifically consisting of electrons and holes in an entangled state. Excitons occur widely in semiconductors and are dominant excitations in semiconducting organic and low-dimensional quantum materials. To efficiently harness the strong optical response and high tuneability of excitons in optoelectronics and in energy-transformation processes, access to the full wavefunction of the entangled state is critical, but has so far not been feasible. Here, we show how time-resolved photoemission momentum microscopy can be used to gain access to the entangled wavefunction and to unravel the exciton's multiorbital electron and hole contributions. For the prototypical organic semiconductor buckminsterfullerene (C60), we exemplify the capabilities of exciton tomography and achieve unprecedented access to key properties of the entangled exciton state including localization, charge-transfer character, and ultrafast exciton formation and relaxation dynamics.

Probing electron-hole Coulomb correlations in the exciton landscape of a twisted semiconductor heterostructure

In two-dimensional semiconductors, cooperative and correlated interactions determine the material's excitonic properties and can even lead to the creation of correlated states of matter. Here, we study the fundamental two-particle correlated exciton state formed by the Coulomb interaction between single-particle holes and electrons. We find that the ultrafast transfer of an exciton's hole across a type II band-aligned semiconductor heterostructure leads to an unexpected sub-200-femtosecond upshift of the single-particle energy of the electron being photoemitted from the two-particle exciton state. While energy relaxation usually leads to an energetic downshift of the spectroscopic signature, we show that this upshift is a clear fingerprint of the correlated interaction of the electron and hole parts of the exciton. In this way, time-resolved photoelectron spectroscopy is straightforwardly established as a powerful method to access electron-hole correlations and cooperative behavior in quantum materials. Our work highlights this capability and motivates the future study of optically inaccessible correlated excitonic and electronic states of matter.

Dynamical control of nanoscale light-matter interactions in low-dimensional quantum materials

Tip-enhanced nano-spectroscopy and -imaging have significantly advanced our understanding of low-dimensional quantum materials and their interactions with light, providing a rich insight into the underlying physics at their natural length scale. Recently, various functionalities of the plasmonic tip expand the capabilities of the nanoscopy, enabling dynamic manipulation of light-matter interactions at the nanoscale. In this review, we focus on a new paradigm of the nanoscopy, shifting from the conventional role of imaging and spectroscopy to the dynamical control approach of the tip-induced light-matter interactions. We present three different approaches of tip-induced control of light-matter interactions, such as cavity-gap control, pressure control, and near-field polarization control. Specifically, we discuss the nanoscale modifications of radiative emissions for various emitters from weak to strong coupling regime, achieved by the precise engineering of the cavity-gap. Furthermore, we introduce recent works on light-matter interactions controlled by tip-pressure and near-field polarization, especially tunability of the bandgap, crystal structure, photoluminescence quantum yield, exciton density, and energy transfer in a wide range of quantum materials. We envision that this comprehensive review not only contributes to a deeper understanding of the physics of nanoscale light-matter interactions but also offers a valuable resource to nanophotonics, plasmonics, and materials science for future technological advancements.

Ultrafast Charge Transfer and Recombination Dynamics in Monolayer-Multilayer WSe2 Junctions Revealed by Time-Resolved Photoemission Electron Microscopy

The ultrafast carrier dynamics of junctions between two chemically identical, but electronically distinct, transition metal dichalcogenides (TMDs) remains largely unknown. Here, we employ time-resolved photoemission electron microscopy (TR-PEEM) to probe the ultrafast carrier dynamics of a monolayer-to-multilayer (1L-ML) WSe2 junction. The TR-PEEM signals recorded for the individual components of the junction reveal the sub-ps carrier cooling dynamics of 1L- and 7L-WSe2, as well as few-ps exciton-exciton annihilation occurring on 1L-WSe2. We observe ultrafast interfacial hole (h) transfer from 1L- to 7L-WSe2 on an ∼0.2 ps time scale. The resultant excess h density in 7L-WSe2 decays by carrier recombination across the junction interface on an ∼100 ps time scale. Reminiscent of the behavior at a depletion region, the TR-PEEM image reveals the h density accumulation on the 7L-WSe2 interface, with a decay length ∼0.60 ± 0.17 μm. These charge transfer and recombination dynamics are in agreement with ab initio quantum dynamics. The computed orbital densities reveal that charge transfer occurs from the basal plane, which extends over both 1L and ML regions, to the upper plane localized on the ML region. This mode of charge transfer is distinctive to chemically homogeneous junctions of layered materials and constitutes an additional carrier deactivation pathway that should be considered in studies of 1L-TMDs found alongside their ML, a common occurrence in exfoliated samples.

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.

Ultrafast Interlayer Charge Transfer Outcompeting Intralayer Valley Relaxation in Few-Layer 2D Heterostructures

While 2D transition metal dichalcogenides (TMDs) feature interesting layer-tunable multivalley band structures, their preeminent role in determining the photoexcitation charge transfer dynamics in 2D heterostructures (HSs) is yet to be unraveled, as previous charge transfer studies on TMD HSs have been mostly focused on monolayers with a direct bandgap at the K valley. By ultrafast transient absorption spectroscopy and deliberately designed few-layer WSe2/WS2 HSs, we have observed an ultrafast interlayer electron transfer from photoexcited few-layer WSe2 to WS2, prior to intralayer relaxation to lower lying dark valleys. More interestingly, we have identified an unconventional ∼0.5 ps electron back-transfer process after the initial interlayer electron transfer in HSs with WSe2 layers ≥ 3, regenerating indirect intralayer excitons. The result reveals an ielectron and valley relaxation pathway mediated by interlayer charge transfer in 2D HSs, faster than intralayer relaxation. It also sheds light on the origin of generally observed robust ultrafast interlayer charge transfer in TMD HSs and provides guidance toward optoelectronic and valleytronic devices using few-layer TMDs.

Strongly Localized Moiré Exciton in Twisted Homobilayers

Artificially molding exciton flux is the cornerstone for developing promising excitonic devices. In the emerging hetero/homobilayers, the spatial separated charges prolong exciton lifetimes and create out-plane dipoles, facilitating electrically control exciton flux on a large scale, and the nanoscale periodic moiré potentials arising from twist-angle or/and lattice mismatch can substantially alter exciton dynamics, which are mainly proved in the heterostructures. However, the spatially indirect excitons dynamics in homobilayers without lattice mismatch remain elusive. Here the nonequilibrium dynamics of indirect exciton in homobilayers are systematically investigated. The homobilayers with slightly twist-angle can induce a deep moiré potential (>50 meV) in the energy landscape of indirect excitons, resulting in a strongly localized moiré excitons insulating the transport dynamics from phonons and disorder. These findings provide insights into the exciton dynamics and many-body physics in moiré superlattices modulated energy landscape, with implications for designing excitonic devices operating at room temperature.

Mechanical, electronic, optical, piezoelectric and ferroic properties of strained graphene and other strained monolayers and multilayers: an update

This is an update of a previous review (Naumiset al2017Rep. Prog. Phys.80096501). Experimental and theoretical advances for straining graphene and other metallic, insulating, ferroelectric, ferroelastic, ferromagnetic and multiferroic 2D materials were considered. We surveyed (i) methods to induce valley and sublattice polarisation (P) in graphene, (ii) time-dependent strain and its impact on graphene's electronic properties, (iii) the role of local and global strain on superconductivity and other highly correlated and/or topological phases of graphene, (iv) inducing polarisationPon hexagonal boron nitride monolayers via strain, (v) modifying the optoelectronic properties of transition metal dichalcogenide monolayers through strain, (vi) ferroic 2D materials with intrinsic elastic (σ), electric (P) and magnetic (M) polarisation under strain, as well as incipient 2D multiferroics and (vii) moiré bilayers exhibiting flat electronic bands and exotic quantum phase diagrams, and other bilayer or few-layer systems exhibiting ferroic orders tunable by rotations and shear strain. The update features the experimental realisations of a tunable two-dimensional Quantum Spin Hall effect in germanene, of elemental 2D ferroelectric bismuth, and 2D multiferroic NiI2. The document was structured for a discussion of effects taking place in monolayers first, followed by discussions concerning bilayers and few-layers, and it represents an up-to-date overview of exciting and newest developments on the fast-paced field of 2D materials.

Ultrafast many-body bright-dark exciton transition in anatase TiO2

The momentum-forbidden dark excitons can have a pivotal role in quantum information processing, Bose-Einstein condensation, and light-energy harvesting. Anatase TiO2 with an indirect band gap is a prototypical platform to study bright to momentum-forbidden dark exciton transition. Here, we examine, by GW plus the real-time Bethe-Salpeter equation combined with the nonadiabatic molecular dynamics (GW + rtBSE-NAMD), the many-body transition that occurs within 100 fs from the optically excited bright to the strongly bound momentum-forbidden dark excitons in anatase TiO2. Comparing with the single-particle picture in which the exciton transition is considered to occur through electron-phonon scattering, within the GW + rtBSE-NAMD framework, the many-body electron-hole Coulomb interaction activates additional exciton relaxation channels to notably accelerate the exciton transition in competition with other radiative and nonradiative processes. The existence of dark excitons and ultrafast bright-dark exciton transitions sheds insights into applications of anatase TiO2 in optoelectronic devices and light-energy harvesting as well as the formation process of dark excitons in semiconductors.

Reveal Ultrafast Electron Relaxation across Sub-bands of Tellurium by Time- and Energy-Resolved Photoemission Microscopy

Exploring ultrafast carrier dynamics is crucial for the materials' fundamental properties and device design. In this work, we employ time- and energy-resolved photoemission electron microscopy with tunable pump wavelengths from visible to near-infrared to reveal the ultrafast carrier dynamics of the elemental semiconductor tellurium. We find that two discrete sub-bands around the Γ point of the conduction band are involved in excited-state electron ultrafast relaxation and reveal that hot electrons first go through ultrafast intra sub-band cooling on a time scale of about 0.3 ps and then transfer from the higher sub-band to the lower one on a time scale of approximately 1 ps. Additionally, theoretical calculations reveal that the lower one has flat-band characteristics, possessing a large density of states and a long electron lifetime. Our work demonstrates that TR- and ER-PEEM with broad tunable pump wavelengths are powerful techniques in revealing the details of ultrafast carrier dynamics in time and energy domains.

Probing the Formation of Dark Interlayer Excitons via Ultrafast Photocurrent

Optically dark excitons determine a wide range of properties of photoexcited semiconductors yet are hard to access via conventional time-resolved spectroscopies. Here, we develop a time-resolved ultrafast photocurrent technique (trPC) to probe the formation dynamics of optically dark excitons. The nonlinear nature of the trPC makes it particularly sensitive to the formation of excitons occurring at the femtosecond time scale after the excitation. As a proof of principle, we extract the interlayer exciton formation time of 0.4 ps at 160 μJ/cm2 fluence in a MoS2/MoSe2 heterostructure and show that this time decreases with fluence. In addition, our approach provides access to the dynamics of carriers and their interlayer transport. Overall, our work establishes trPC as a technique to study dark excitons in various systems that are hard to probe by other approaches.

Ultrafast Electronic Dynamics in Anisotropic Indirect Interlayer Excitonic States of Monolayer WSe2/ReS2 Heterojunctions

Understanding ultrafast electronic dynamics of the interlayer excitonic states in atomically thin transition metal dichalcogenides is of importance in engineering valleytronics and developing excitonic integrated circuits. In this work, we experimentally explored the ultrafast dynamics of indirect interlayer excitonic states in monolayer type II WSe2/ReS2 heterojunctions using time-resolved photoemission electron microscopy, which reveals its anisotropic behavior. The ultrafast cooling and decay of excited-state electrons exhibit significant linear dichroism. The ab initio theoretical calculations provide unambiguous evidence that this linear dichroism result is primarily associated with the anisotropic nonradiative recombination of indirect interlayer excitonic states. Measuring time-resolved photoemission energy spectra, we have further revealed the ultrafast evolution of excited-state electrons in anisotropic indirect interlayer excitonic states. The findings have important implications for controlling the interlayer moiré excitonic effects and designing anisotropic optoelectronic devices.

Recent Advances in Moiré Superlattice Systems by Angle-Resolved Photoemission Spectroscopy

The last decade has witnessed a flourish in 2D materials including graphene and transition metal dichalcogenides (TMDs) as atomic-scale Legos. Artificial moiré superlattices via stacking 2D materials with a twist angle and/or a lattice mismatch have recently become a fertile playground exhibiting a plethora of emergent properties beyond their building blocks. These rich quantum phenomena stem from their nontrivial electronic structures that are effectively tuned by the moiré periodicity. Modern angle-resolved photoemission spectroscopy (ARPES) can directly visualize electronic structures with decent momentum, energy, and spatial resolution, thus can provide enlightening insights into fundamental physics in moiré superlattice systems and guides for designing novel devices. In this review, first, a brief introduction is given on advanced ARPES techniques and basic ideas of band structures in a moiré superlattice system. Then ARPES research results of various moiré superlattice systems are highlighted, including graphene on substrates with small lattice mismatches, twisted graphene/TMD moiré systems, and high-order moiré superlattice systems. Finally, it discusses important questions that remain open, challenges in current experimental investigations, and presents an outlook on this field of research.

Sequential order dependent dark-exciton modulation in bi-layered TMD heterostructure

We report the emergence of dark-excitons in transition-metal-dichalcogenide (TMD) heterostructures that strongly rely on the stacking sequence, i.e., momentum-dark K-Q exciton located exclusively at the top layer of the heterostructure. The feature stems from band renormalization and is distinct from those of typical neutral excitons or trions, regardless of materials, substrates, and even homogeneous bilayers, which is further confirmed by scanning tunneling spectroscopy. To understand the unusual stacking sequence, we introduce the excitonic Elliot formula by imposing strain exclusively on the top layer that could be a consequence of the stacking process. We further find that the intensity ratio of Q- to K-excitons in the same layer is inversely proportional to laser power, unlike for conventional K-K excitons. This can be a metric for engineering the intensity of dark K-Q excitons in TMD heterostructures, which could be useful for optical power switches in solar panels.

Observation of ultrafast interfacial Meitner-Auger energy transfer in a Van der Waals heterostructure

Atomically thin layered van der Waals heterostructures feature exotic and emergent optoelectronic properties. With growing interest in these novel quantum materials, the microscopic understanding of fundamental interfacial coupling mechanisms is of capital importance. Here, using multidimensional photoemission spectroscopy, we provide a layer- and momentum-resolved view on ultrafast interlayer electron and energy transfer in a monolayer-WSe2/graphene heterostructure. Depending on the nature of the optically prepared state, we find the different dominating transfer mechanisms: while electron injection from graphene to WSe2 is observed after photoexcitation of quasi-free hot carriers in the graphene layer, we establish an interfacial Meitner-Auger energy transfer process following the excitation of excitons in WSe2. By analysing the time-energy-momentum distributions of excited-state carriers with a rate-equation model, we distinguish these two types of interfacial dynamics and identify the ultrafast conversion of excitons in WSe2 to valence band transitions in graphene. Microscopic calculations find interfacial dipole-monopole coupling underlying the Meitner-Auger energy transfer to dominate over conventional Förster- and Dexter-type interactions, in agreement with the experimental observations. The energy transfer mechanism revealed here might enable new hot-carrier-based device concepts with van der Waals heterostructures.

Ultrafast Hidden Spin Polarization Dynamics of Bright and Dark Excitons in 2H-WSe_{2}

We performed spin-, time- and angle-resolved extreme ultraviolet photoemission spectroscopy of excitons prepared by photoexcitation of inversion-symmetric 2H-WSe_{2} with circularly polarized light. The very short probing depth of XUV photoemission permits selective measurement of photoelectrons originating from the top-most WSe_{2} layer, allowing for direct measurement of hidden spin polarization of bright and momentum-forbidden dark excitons. Our results reveal efficient chiroptical control of bright excitons' hidden spin polarization. Following optical photoexcitation, intervalley scattering between nonequivalent K-K^{'} valleys leads to a decay of bright excitons' hidden spin polarization. Conversely, the ultrafast formation of momentum-forbidden dark excitons acts as a local spin polarization reservoir, which could be used for spin injection in van der Waals heterostructures involving multilayer transition metal dichalcogenides.

Coherent-Phonon-Driven Intervalley Scattering and Rabi Oscillation in Multivalley 2D Materials

Resolving the complete electron scattering dynamics mediated by coherent phonons is crucial for understanding electron-phonon couplings beyond equilibrium. Here we present a time-resolved theoretical investigation on strongly coupled ultrafast electron and phonon dynamics in monolayer WSe_{2}, with a focus on the intervalley scattering from the optically "bright" K state to "dark" Q state. We find that the strong coherent lattice vibration along the longitudinal acoustic phonon mode [LA(M)] can drastically promote K-to-Q transition on a timescale of ∼400  fs, comparable with previous experimental observation on thermal-phonon-mediated electron dynamics. Further, this coherent-phonon-driven intervalley scattering occurs in an unconventional steplike manner and further induces an electronic Rabi oscillation. By constructing a two-level model and quantitatively comparing with ab initio dynamic simulations, we uncover the critical role of nonadiabatic coupling effects. Finally, a new strategy is proposed to effectively tune the intervalley scattering rates by varying the coherent phonon amplitude, which could be realized via light-induced nonlinear phononics that we hope will spark experimental investigation.

Excitation-Dependent High-Lying Excitonic Exchange via Interlayer Energy Transfer from Lower-to-Higher Bandgap 2D Material

High light absorption (∼15%) and strong photoluminescence (PL) emission in monolayer (1L) transition metal dichalcogenides (TMDs) make them ideal candidates for optoelectronic device applications. Competing interlayer charge transfer (CT) and energy transfer (ET) processes control the photocarrier relaxation pathways in TMD heterostructures (HSs). In TMDs, long-distance ET can survive up to several tens of nm, unlike the CT process. Our experiment shows that an efficient ET occurs from the 1Ls WSe₂-to-MoS₂ with an interlayer hexagonal boron nitride (hBN), due to the resonant overlapping of the high-lying excitonic states between the two TMDs, resulting in enhanced HS MoS₂ PL emission. This type of unconventional ET from the lower-to-higher optical bandgap material is not typical in the TMD HSs. With increasing temperature, the ET process becomes weaker due to the increased electron-phonon scattering, destroying the enhanced MoS₂ emission. Our work provides new insight into the long-distance ET process and its effect on the photocarrier relaxation pathways.

Strain-induced dark exciton generation in rippled monolayer MoS2

Recently, it has been revealed that dark excitons play a significant role in optically controlled information processing due to their much longer radiative lifetimes than those of bright ones. For the realizable implementation of the features, it is important to understand and manipulate conditions in which dark excitons could exist. We adopt strain-engineered rippling as a new parameter for the modification of the electronic structure of monolayer MoS₂ and demonstrate the efficient conversion of bright to dark excitons via a first-principles study. For rippled monolayer MoS₂ above a strain of ∼6.8%, we show that the spin order of the conduction band is reversed and the spin forbidden dark exciton then goes below the bright one.

High-flux wavelength tunable XUV source in the 12-40.8 eV photon energy range with adjustable energy and time resolution for Tr-ARPES applications

High-order harmonic generation (HHG) has a broad spectrum covering vacuum ultraviolet to extreme ultraviolet (XUV) bands, which is useful for applications involving material analyses at different information depths. Such an HHG light source is perfect for time- and angle-resolved photoemission spectroscopy. Here, we demonstrate a high-photon flux HHG source driven by a two-color field. Applying a fused silica compression stage to reduce the driving pulse width, we obtained a high XUV photon flux of 2 × 10¹² phs/s @21.6 eV on target. We designed a classical diffraction mounted (CDM) grating monochromator that can achieve a wide range of photon energy from 12 to 40.8 eV, while the time resolution is improved by reducing the pulse front tilt after the harmonic selection. We designed a spatial filtering method to adjust the time resolution using the CDM monochromator and significantly reduced the pulse front tilt of the XUV pulses. We also demonstrate a detailed prediction of the energy resolution broadening which is caused by the space charge effect.

Spin-polarized spatially indirect excitons in a topological insulator

The exciton, a bound state of an electron and a hole, is a fundamental quasiparticle induced by coherent light-matter interactions in semiconductors. When the electrons and holes are in distinct spatial locations, spatially indirect excitons are formed with a much longer lifetime and a higher condensation temperature. One of the ultimate frontiers in this field is to create long-lived excitonic topological quasiparticles by driving exciton states with topological properties, to simultaneously leverage both topological effects and correlation^1,2. Here we reveal the existence of a transient excitonic topological surface state (TSS) in a topological insulator, Bi₂Te₃. By using time-, spin- and angle-resolved photoemission spectroscopy, we directly follow the formation of a long-lived exciton state as revealed by an intensity buildup below the bulk-TSS mixing point and an anomalous band renormalization of the continuously connected TSS in the momentum space. Such a state inherits the spin-polarization of the TSS and is spatially indirect along the z axis, as it couples photoinduced surface electrons and bulk holes in the same momentum range, which ultimately leads to an excitonic state of the TSS. These results establish Bi₂Te₃ as a possible candidate for the excitonic condensation of TSSs³ and, in general, opens up a new paradigm for exploring the momentum space emergence of other spatially indirect excitons, such as moiré and quantum well excitons^4-6, and for the study of non-equilibrium many-body topological physics.

Momentum-Resolved Exciton Coupling and Valley Polarization Dynamics in Monolayer WS_{2}

Using time- and angle-resolved photoemission, we present momentum- and energy-resolved measurements of exciton coupling in monolayer WS_{2}. We observe strong intravalley coupling between the B_{1s} exciton and A_{n>1} states. Our measurements indicate that the dominant valley depolarization mechanism conserves the exciton binding energy and momentum. While this conservation is consistent with Coulomb exchange-driven valley depolarization, we do not observe a momentum or energy dependence to the depolarization rate as would be expected for the exchange-based mechanism.

Interlayer exciton landscape in WS2/tetracene heterostructures

The vertical stacking of two-dimensional materials into heterostructures gives rise to a plethora of intriguing optoelectronic properties and presents an unprecedented potential for technological development. While much progress has been made combining different monolayers of transition metal dichalcogenides (TMDs), little is known about TMD-based heterostructures including organic layers of molecules. Here, we present a joint theory-experiment study on a TMD/tetracene heterostructure demonstrating clear signatures of spatially separated interlayer excitons in low temperature photoluminescence spectra. Here, the Coulomb-bound electrons and holes are localized either in the TMD or in the molecule layer, respectively. We reveal both in theory and experiment signatures of the entire intra- and interlayer exciton landscape in the photoluminescence spectra. In particular, we find both in theory and experiment a pronounced transfer of intensity from the intralayer TMD exciton to a series of energetically lower interlayer excitons with decreasing temperature. In addition, we find signatures of phonon-sidebands stemming from these interlayer exciton states. Our findings shed light on the microscopic nature of interlayer excitons in TMD/molecule heterostructures and could have important implications for technological applications of these materials.

Time- and angle-resolved photoemission spectroscopy (TR-ARPES) of TMDC monolayers and bilayers

Many unique properties in two-dimensional (2D) materials and their heterostructures rely on charge excitation, scattering, transfer, and relaxation dynamics across different points in the momentum space. Understanding these dynamics is crucial in both the fundamental study of 2D physics and their incorporation in optoelectronic and quantum devices. A direct method to probe charge carrier dynamics with momentum resolution is time- and angle-resolved photoemission spectroscopy (TR-ARPES). Such measurements have been challenging, since photoexcited carriers in many 2D monolayers reside at high crystal momenta, requiring probe photon energies in the extreme UV (EUV) regime. These challenges have been recently addressed by development of table-top pulsed EUV sources based on high harmonic generation, and the successful integration into a TR-ARPES and/or time-resolved momentum microscope. Such experiments will allow direct imaging of photoelectrons with superior time, energy, and crystal momentum resolution, with unique advantage over traditional optical measurements. Recently, TR-ARPES experiments of 2D transition metal dichalcogenide (TMDC) monolayers and bilayers have created unprecedented opportunities to reveal many intrinsic dynamics of 2D materials, such as bandgap renormalization, charge carrier scattering, relaxation, and wavefunction localization in moiré patterns. This perspective aims to give a short review of recent discoveries and discuss the challenges and opportunities of such techniques in the future.

Quantum interference between dark-excitons and zone-edged acoustic phonons in few-layer WS2

Fano resonance which describes a quantum interference between continuum and discrete states, provides a unique method for studying strongly interacting physics. Here, we report a Fano resonance between dark excitons and zone-edged acoustic phonons in few-layer WS₂ by using the resonant Raman technique. The discrete phonons with large momentum at the M-point of the Brillouin zone and the continuum dark exciton states related to the optically forbidden transition at K and Q valleys are coupled by the exciton-phonon interactions. We observe rich Fano resonance behaviors across layers and modes defined by an asymmetry-parameter q: including constructive interference with two mirrored asymmetry Fano peaks (weak coupling, q > 1 and q < - 1), and destructive interference with Fano dip (strong coupling, ∣q∣ < < 1). Our results provide new insight into the exciton-phonon quantum interference in two-dimensional semiconductors, where such interferences play a key role in their transport, optical, and thermodynamic properties.

Charge Transfer Dynamics in MoSe2/hBN/WSe2 Heterostructures

Ultrafast charge transfer processes provide a facile way to create interlayer excitons in directly contacted transition metal dichalcogenide (TMD) layers. More sophisticated heterostructures composed of TMD/hBN/TMD enable new ways to control interlayer exciton properties and achieve novel exciton phenomena, such as exciton insulators and condensates, where longer lifetimes are desired. In this work, we experimentally study the charge transfer dynamics in a heterostructure composed of a 1 nm thick hBN spacer between MoSe₂ and WSe₂ monolayers. We observe the hole transfer from MoSe₂ to WSe₂ through the hBN barrier with a time constant of 500 ps, which is over 3 orders of magnitude slower than that between TMD layers without a spacer. Furthermore, we observe strong competition between the interlayer charge transfer and intralayer exciton-exciton annihilation processes at high excitation densities. Our work opens possibilities to understand charge transfer pathways in TMD/hBN/TMD heterostructures for the efficient generation and control of interlayer excitons.

'Molecular Beam Epitaxy' on Organic Semiconductor Single Crystals: Characterization of Well-Defined Molecular Interfaces by Synchrotron Radiation X-ray Diffraction Techniques

Epitaxial growth, often termed "epitaxy", is one of the most essential techniques underpinning semiconductor electronics, because crystallinities of the materials seriously dominate operation efficiencies of the electronic devices such as power gain/consumption, response speed, heat loss, and so on. In contrast to already well-established epitaxial growth methodologies for inorganic (covalent or ionic) semiconductors, studies on inter-molecular (van der Waals) epitaxy for organic semiconductors is still in the initial stage. In the present review paper, we briefly summarize recent works on the epitaxial inter-molecular junctions built on organic semiconductor single-crystal surfaces, particularly on single crystals of pentacene and rubrene. Experimental methodologies applicable for the determination of crystal structures of such organic single-crystal-based molecular junctions are also illustrated.

Confined Monolayer Ag As a Large Gap 2D Semiconductor and Its Momentum Resolved Excited States

2D materials have intriguing quantum phenomena that are distinctively different from their bulk counterparts. Recently, epitaxially synthesized wafer-scale 2D metals, composed of elemental atoms, are attracting attention not only for their potential applications but also for exotic quantum effects such as superconductivity. By mapping momentum-resolved electronic states using time-resolved and angle-resolved photoemission spectroscopy (ARPES), we reveal that monolayer Ag confined between bilayer graphene and SiC is a large gap (>1 eV) 2D semiconductor, consistent with ab initio GW calculations. The measured valence band dispersion matches the GW quasiparticle band structure. However, the conduction band dispersion shows an anomalously large effective mass of 2.4 m₀. Possible mechanisms for this large enhancement in the "apparent mass" are discussed.

Exciton Manifolds in Highly Ambipolar Doped WS2

The disentanglement of single and many particle properties in 2D semiconductors and their dependencies on high carrier concentration is challenging to experimentally study by pure optical means. We establish an electrolyte gated WS2 monolayer field-effect structure capable of shifting the Fermi level from the valence into the conduction band that is suitable to optically trace exciton binding as well as the single-particle band gap energies in the weakly doped regime. Combined spectroscopic imaging ellipsometry and photoluminescence spectroscopies spanning large n- and p-type doping with charge carrier densities up to 1014 cm-2 enable to study screening phenomena and doping dependent evolution of the rich exciton manifold whose origin is controversially discussed in literature. We show that the two most prominent emission bands in photoluminescence experiments are due to the recombination of spin-forbidden and momentum-forbidden charge neutral excitons activated by phonons. The observed interband transitions are redshifted and drastically weakened under electron or hole doping. This field-effect platform is not only suitable for studying exciton manifold but is also suitable for combined optical and transport measurements on degenerately doped atomically thin quantum materials at cryogenic temperatures.

Superacid Treatment on Transition Metal Dichalcogenides

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

Resonant Coherent Raman Scattering from WSe2

Low-dimensional transition-metal dichalcogenides (TMDs) continue to comprise a subject of intense research because of their unique optical and electronic properties that may be harnessed in modern devices. Intense photoluminescence (PL) from few-/monolayer TMDs rendered PL-based micro- and nanospectroscopic characterization ideal in the quest to understand the correlation between structure and function in these materials. Nonlinear optical methods are by comparison far less utilized for this purpose. In this work, we describe an approach based on electronically resonant four-wave-mixing that allows spatio-spectral characterization of excitons in monolayer WSe₂. Due to the coherent nature of the response that we exploit to trace exciton resonances, and recent demonstrations of electronic four-wave-mixing-based nanoimaging and nanospectroscopy, our present work is an important step toward characterizing TMDs on the nano-femto scale using light.

Formation of moiré interlayer excitons in space and time

Moiré superlattices in atomically thin van der Waals heterostructures hold great promise for extended control of electronic and valleytronic lifetimes^1-7, the confinement of excitons in artificial moiré lattices^8-13 and the formation of exotic quantum phases^14-18. Such moiré-induced emergent phenomena are particularly strong for interlayer excitons, where the hole and the electron are localized in different layers of the heterostructure^19,20. To exploit the full potential of correlated moiré and exciton physics, a thorough understanding of the ultrafast interlayer exciton formation process and the real-space wavefunction confinement is indispensable. Here we show that femtosecond photoemission momentum microscopy provides quantitative access to these key properties of the moiré interlayer excitons. First, we elucidate that interlayer excitons are dominantly formed through femtosecond exciton-phonon scattering and subsequent charge transfer at the interlayer-hybridized Σ valleys. Second, we show that interlayer excitons exhibit a momentum fingerprint that is a direct hallmark of the superlattice moiré modification. Third, we reconstruct the wavefunction distribution of the electronic part of the exciton and compare the size with the real-space moiré superlattice. Our work provides direct access to interlayer exciton formation dynamics in space and time and reveals opportunities to study correlated moiré and exciton physics for the future realization of exotic quantum phases of matter.

Ultrafast Momentum-Resolved Hot Electron Dynamics in the Two-Dimensional Topological Insulator Bismuthene

Two-dimensional quantum spin Hall (QSH) insulators are a promising material class for spintronic applications based on topologically protected spin currents in their edges. Yet, they have not lived up to their technological potential, as experimental realizations are scarce and limited to cryogenic temperatures. These constraints have also severely restricted characterization of their dynamical properties. Here, we report on the electron dynamics of the novel room-temperature QSH candidate bismuthene after photoexcitation using time- and angle-resolved photoemission spectroscopy. We map the transiently occupied conduction band and track the full relaxation pathway of hot photocarriers. Intriguingly, we observe photocarrier lifetimes much shorter than those in conventional semiconductors. This is ascribed to the presence of topological in-gap states already established by local probes. Indeed, we find spectral signatures consistent with these earlier findings. Demonstration of the large band gap and the view into photoelectron dynamics mark a critical step toward optical control of QSH functionalities.

Through the Lens of a Momentum Microscope: Viewing Light-Induced Quantum Phenomena in 2D Materials

Van der Waals (vdW) materials at their 2D limit are diverse, flexible, and unique laboratories to study fundamental quantum phenomena and their future applications. Their novel properties rely on their pronounced Coulomb interactions, variety of crystal symmetries and spin-physics, and the ease of incorporation of different vdW materials to form sophisticated heterostructures. In particular, the excited state properties of many 2D semiconductors and semi-metals are relevant for their technological applications, particularly those that can be induced by light. In this paper, the recent advances made in studying out-of-equilibrium, light-induced, phenomena in these materials are reviewed using powerful, surface-sensitive, time-resolved photoemission-based techniques, with a particular emphasis on the emerging multi-dimensional photoemission spectroscopy technique of time-resolved momentum microscopy. The advances this technique has enabled in studying the nature and dynamics of occupied excited states in these materials are discussed. Then, the future research directions opened by these scientific and instrumental advancements are projected for studying the physics of 2D materials and the opportunities to engineer their band-structure and band-topology by laser fields.

Unconventional excitonic states with phonon sidebands in layered silicon diphosphide

Complex correlated states emerging from many-body interactions between quasiparticles (electrons, excitons and phonons) are at the core of condensed matter physics and material science. In low-dimensional materials, quantum confinement affects the electronic, and subsequently, optical properties for these correlated states. Here, by combining photoluminescence, optical reflection measurements and ab initio theoretical calculations, we demonstrate an unconventional excitonic state and its bound phonon sideband in layered silicon diphosphide (SiP₂), where the bound electron-hole pair is composed of electrons confined within one-dimensional phosphorus-phosphorus chains and holes extended in two-dimensional SiP₂ layers. The excitonic state and emergent phonon sideband show linear dichroism and large energy redshifts with increasing temperature. Our ab initio many-body calculations confirm that the observed phonon sideband results from the correlated interaction between excitons and optical phonons. With these results, we propose layered SiP₂ as a platform for the study of excitonic physics and many-particle effects.

Far-from-Equilibrium Electron-Phonon Interactions in Optically Excited Graphene

Comprehending far-from-equilibrium many-body interactions is one of the major goals of current ultrafast condensed matter physics research. Here, a particularly interesting but barely understood situation occurs during a strong optical excitation, where the electron and phonon systems can be significantly perturbed and the quasiparticle distributions cannot be described with equilibrium functions. In this work, we use time- and angle-resolved photoelectron spectroscopy to study such far-from-equilibrium many-body interactions for the prototypical material graphene. In accordance with theoretical simulations, we find remarkable transient renormalizations of the quasiparticle self-energy caused by the photoinduced nonequilibrium conditions. These observations can be understood by ultrafast scatterings between nonequilibrium electrons and strongly coupled optical phonons, which signify the crucial role of ultrafast nonequilibrium dynamics on many-body interactions. Our results advance the understanding of many-body physics in extreme conditions, which is important for any endeavor to optically manipulate or create non-equilibrium states of matter.

Design of coherent wideband radiation process in a Nd3+-doped high entropy glass system

We discover that the spatially coherent radiation within a certain frequency range can be obtained without a common nonlinear optical process. Conventionally, the emission spectra were obtained by de-exciting excited centers from real excited energy levels to the ground state. Our findings are achieved by deploying a high-entropy glass system (HEGS) doped with neodymium ions. The HEGS exhibits a much broader infrared absorption than common glass systems, which can be attributed to be high-frequency optical branch phonons or allowable multi-phonon processes caused by phonon broadening in the system. A broadened phonon-assisted wideband radiation (BPAWR) is induced if the pump laser is absorbed by the system. The subsequent low-threshold self-absorption coherence modulation (SACM) can be controlled by changing excitation wavelengths, sample size, and doping concentrations. The SACM can be red-shifted through the emission of phonons of the excited species and be blue-shifted by absorbing phonons before they are de-excited. There is a time delay up to 1.66 ns between the pump pulse and the BPAWR when measured after traveling through a 35 mm long sample, which is much longer than the Raman process. The BPAWR-SACM can amplify the centered non-absorption band with a gain up to 26.02 dB. These results reveal that the shift of the novel radiation is determined by the frequency of the non-absorption band near the absorption region, and therefore the emission shifts can be modulated by changing the absorption spectrum. When used in fiber lasers, the BPAWR-SACM process may help to achieve tunability.

Photoexcitation Dynamics and Long-Lived Excitons in Strain-Engineered Transition Metal Dichalcogenides

Strain-engineering in 2D transition metal dichalcogenide (TMD) semiconductors has garnered intense research interest in tailoring the optical properties via strain-induced modifications of the electronic bands in TMDs, while its impact on the exciton dynamics remains less understood. To address this, an extensive study of transient optical absorption (TA) of both W- and Mo-based single-crystalline monolayer TMDs grown by a recently developed laser-assisted evaporation method is performed. All spectral features of the monolayers as grown on fused silica substrates exhibit appreciable redshifts relating to the existence of strain due to growth conditions. Moreover, these systems exhibit a dramatic slowing down of exciton dynamics (100s of picoseconds to few nanoseconds) with an increase in carrier densities, which strongly contrasts with the monolayers in their freestanding form as well as in comparison with more traditionally grown TMDs. The observations are related to the modifications of the electronic bands as expected from the strain and associated population of the intervalley dark excitons that can now interplay with intravalley excitations. These findings are consistent across both the Mo- and W-based TMD families, providing key information about the influence of the growth conditions on the nature of optical excitations and fostering emerging optoelectronic applications of monolayer TMDs.

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

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

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

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

Dark-Exciton Driven Energy Funneling into Dielectric Inhomogeneities in Two-Dimensional Semiconductors

The optoelectronic and transport properties of two-dimensional transition metal dichalcogenide semiconductors (2D TMDs) are highly susceptible to external perturbation, enabling precise tailoring of material function through postsynthetic modifications. Here, we show that nanoscale inhomogeneities known as nanobubbles can be used for both strain and, less invasively, dielectric tuning of exciton transport in bilayer tungsten diselenide (WSe₂). We use ultrasensitive spatiotemporally resolved optical scattering microscopy to directly image exciton transport, revealing that dielectric nanobubbles are surprisingly efficient at funneling and trapping excitons at room temperature, even though the energies of the bright excitons are negligibly affected. Our observations suggest that exciton funneling in dielectric inhomogeneities is driven by momentum-indirect (dark) excitons whose energies are more sensitive to dielectric perturbations than bright excitons. These results reveal a new pathway to control exciton transport in 2D semiconductors with exceptional spatial and energetic precision using dielectric engineering of dark state energetic landscapes.

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.

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.