Experimental measurement of the intrinsic excitonic wave function

Photo-Assisted Ferroelectric Domain Control for α-In2Se3 Artificial Synapses Inspired by Spontaneous Internal Electric Fields

α-In2Se3 semiconductor crystals realize artificial synapses by tuning in-plane and out-of-plane ferroelectricity with diverse avenues of electrical and optical pulses. While the electrically induced ferroelectricity of α-In2Se3 shows synaptic memory operation, the optically assisted synaptic plasticity in α-In2Se3 has also been preferred for polarization flipping enhancement. Here, the synaptic memory behavior of α-In2Se3 is demonstrated by applying electrical gate voltages under white light. As a result, the induced internal electric field is identified at a polarization flipped conductance channel in α-In2Se3/hexagonal boron nitride (hBN) heterostructure ferroelectric field effect transistors (FeFETs) under white light and discuss the contribution of this built-in electric field on synapse characterization. The biased dipoles in α-In2Se3 toward potentiation polarization direction by an enhanced internal built-in electric field under illumination of white light lead to improvement of linearity for long-term depression curves with proper electric spikes. Consequently, upon applying appropriate electric spikes to α-In2Se3/hBN FeFETs with illuminating white light, the recognition accuracy values significantly through the artificial learning simulation is elevated for discriminating hand-written digit number images.

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.

Time-domain observation of interlayer exciton formation and thermalization in a MoSe2/WSe2 heterostructure

Vertical heterostructures of transition metal dichalcogenides (TMDs) host interlayer excitons with electrons and holes residing in different layers. With respect to their intralayer counterparts, interlayer excitons feature longer lifetimes and diffusion lengths, paving the way for room temperature excitonic optoelectronic devices. The interlayer exciton formation process and its underlying physical mechanisms are largely unexplored. Here we use ultrafast transient absorption spectroscopy with a broadband white-light probe to simultaneously resolve interlayer charge transfer and interlayer exciton formation dynamics in a MoSe2/WSe2 heterostructure. We observe an interlayer exciton formation timescale nearly an order of magnitude (~1 ps) longer than the interlayer charge transfer time (~100 fs). Microscopic calculations attribute this relative delay to an interplay of a phonon-assisted interlayer exciton cascade and thermalization, and excitonic wave-function overlap. Our results may explain the efficient photocurrent generation observed in optoelectronic devices based on TMD heterostructures, as the interlayer excitons are able to dissociate during thermalization.

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.

Giant self-driven exciton-Floquet signatures in time-resolved photoemission spectroscopy of MoS2 from time-dependent GW approach

Time-resolved, angle-resolved photoemission spectroscopy (TR-ARPES) is a one-particle spectroscopic technique that can probe excitons (two-particle excitations) in momentum space. We present an ab initio, time-domain GW approach to TR-ARPES and apply it to monolayer MoS2. We show that photoexcited excitons may be measured and quantified as satellite bands and lead to the renormalization of the quasiparticle bands. These features are explained in terms of an exciton-Floquet phenomenon induced by an exciton time-dependent bosonic field, which are orders of magnitude stronger than those of laser field-induced Floquet bands in low-dimensional semiconductors. Our findings imply a way to engineer Floquet matter through the coherent oscillation of excitons and open the new door for mechanisms for band structure engineering.

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.

Nanoscale Periodic Trapping Sites for Interlayer Excitons Built by Deformable Molecular Crystal on 2D Crystal

The nanoscale moiré pattern formed at 2D transition-metal dichalcogenide crystal (TMDC) heterostructures provides periodic trapping sites for excitons, which is essential for realizing various exotic phases such as artificial exciton lattices, Bose-Einstein condensates, and exciton insulators. At organic molecule/TMDC heterostructures, similar periodic potentials can be formed via other degrees of freedom. Here, we utilize the structure deformability of a 2D molecular crystal as a degree of freedom to create a periodic nanoscale potential that can trap interlayer excitons (IXs). Specifically, two semiconducting molecules, PTCDI and PTCDA, which possess similar band gaps and ionization potentials but form different lattice structures on MoS₂, are investigated. The PTCDI lattice on MoS₂ is distorted geometrically, which lifts the degeneracy of the two molecules within the crystal's unit cell. The degeneracy lifting results in a spatial variation of the molecular orbital energy, with an amplitude and periodicity of ∼0.2 eV and ∼2 nm, respectively. On the other hand, no such energy variation is observed in PTCDA/MoS₂, where the PTCDA lattice is much less distorted. The periodic variation in molecular orbital energies provides effective trapping sites for IXs. For IXs formed at PTCDI/MoS₂, rapid spatial localization of the electron in the organic layer toward the interface is observed, which demonstrates the effectiveness of these interfacial IX traps.

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.

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.

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.

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.

Optical absorption of interlayer excitons in transition-metal dichalcogenide heterostructures

Interlayer excitons, electron-hole pairs bound across two monolayer van der Waals semiconductors, offer promising electrical tunability and localizability. Because such excitons display weak electron-hole overlap, most studies have examined only the lowest-energy excitons through photoluminescence. We directly measured the dielectric response of interlayer excitons, which we accessed using their static electric dipole moment. We thereby determined an intrinsic radiative lifetime of 0.40 nanoseconds for the lowest direct-gap interlayer exciton in a tungsten diselenide/molybdenum diselenide heterostructure. We found that differences in electric field and twist angle induced trends in exciton transition strengths and energies, which could be related to wave function overlap, moiré confinement, and atomic reconstruction. Through comparison with photoluminescence spectra, this study identifies a momentum-indirect emission mechanism. Characterization of the absorption is key for applications relying on light-matter interactions.

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.

Real-Time GW: Toward an Ab Initio Description of the Ultrafast Carrier and Exciton Dynamics in Two-Dimensional Materials

We demonstrate the feasibility of the time-linear scaling formulation of the GW method [Phys. Rev. Lett. 124, 076601 (2020)PRLTAO0031-900710.1103/PhysRevLett.124.076601] for ab initio simulations of optically driven two-dimensional materials. The time-dependent GW equations are derived and solved numerically in the basis of Bloch states. We address carrier multiplication and relaxation in photoexcited graphene and find deviations from the typical exponential behavior predicted by the Markovian Boltzmann approach. For a resonantly pumped semiconductor we discover a self-sustained screening cascade leading to the Mott transition of coherent excitons. Our results draw attention to the importance of non-Markovian and dynamical screening effects in out-of-equilibrium phenomena.

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.

Generation of structured coherent extreme ultraviolet beams from an MgO crystal

Short wavelength high-harmonic sources are undergoing intense development for applications in spectroscopy and microscopy. Despite recent progress in peak and average power, spatial control over coherent extreme ultraviolet (XUV) beams remains a formidable challenge due to the lack of suitable optical elements for beam shaping and control. Here we demonstrate a robust and precise approach that structures XUV high-order harmonics in space as they are emitted from a nanostructured MgO crystal. Our demonstration paves the way for bridging the numerous applications of shaped light beams from the visible to the short wavelengths, with potential uses for applications in microscopy and nanoscale machining.

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.