Formation of moiré interlayer excitons in space and time

Time-resolved momentum microscopy with fs-XUV photons at high repetition rates with flexible energy and time resolution

Time-resolved momentum microscopy is an emerging technique based on photoelectron spectroscopy for characterizing ultrafast electron dynamics and the out-of-equilibrium electronic structure of materials in the entire Brillouin zone with high efficiency. In this article, we introduce a setup for time-resolved momentum microscopy based on an energy-filtered momentum microscope coupled to a custom-made high-harmonic generation photon source driven by a multi-100 kHz commercial Yb-ultrafast laser that delivers fs pulses in the extreme ultraviolet range. The laser setup includes a nonlinear pulse compression stage employing spectral broadening in a Herriott-type bulk-based multi-pass cell. This element allows flexible tuning of the driving pulse duration, providing a versatile time-resolved momentum microscopy setup featuring two operational modes designed to enhance either the energy or time resolution. We show the capabilities of the system by tracing ultrafast electron dynamics in the conduction band valleys of a bulk crystal of the 2D semiconductor WS2. Using uncompressed driving laser pulses, we demonstrate an energy resolution better than (107 ± 2) meV, while compressed pulses lead to a time resolution better than (48.8 ± 17) fs.

Ultrafast Control over Stiffening and Softening of Coherent Interlayer Coupling in WSe2/WS2 Heterobilayers

Twisted van der Waals heterostructures have led to emerging layer-dependent correlated physics in moiré potentials. While optoelectronic controls over interlayer electronic coupling have been reported, the concomitant interlayer vibration has not yet been controlled. Here, we report experimental evidence of ultrafast optical control over the amplitude and oscillation period of interlayer breathing phonons in WSe2/WS2 heterobilayers. Femtosecond optical excitation above the Mott density in gate-tuned devices shows as large as 10% changes of stiffening and softening amplitude of coherent phonons. A theoretical model, incorporating both Buckingham and Hartree energies, is presented to elucidate the impact of charge-separated carriers generated by photoexcitation on phonon dynamics. This work, therefore, provides insights for extending optoelectronic engineering into the coherent phonons in moiré systems.

Moiré Superlattice in Two-Dimensional Materials: Fundamentals, Applications, and Recent Developments

Moiré superlattices, arising from the periodic Moiré patterns formed by two-dimensional (2D) materials stacked with a slight lattice mismatch, have attracted significant attention due to their unique electronic and optical performances. This review provides an overview of recent advances in Moiré superlattices, highlighting their formation mechanisms, structural characteristics, and emergent phenomena. First, we discuss the theoretical basis and experimental techniques employed in fabricating Moiré superlattices. Then we outline various characterization methods that enable the investigation of the structural and electronic performance of Moiré superlattices at the atomic scale. Afterward, we review the diverse range of emergent phenomena exhibited in Moiré superlattices. These phenomena include the appearance of electronic band engineering, unconventional superconductivity, and topologically nontrivial state. We explore how these phenomena arise from the interplay between the original electronic properties of the constituent materials and the Moiré pattern-induced modifications. Furthermore, we examine the potential applications of Moiré superlattices in fields such as electronics, optoelectronics, and quantum technologies. Finally, we summarize the challenges and directions in Moiré superlattice research, which include exploring more complex Moiré patterns, understanding the role of twist angle and strain engineering, and developing theoretical frameworks to describe the behaviors of Moiré systems. This review aims to provide a comprehensive understanding of the recent progress in Moiré superlattices, shedding light on their formation, performance, and potential applications. The insights gained from this research are expected to pave the way for the design and development of next-generation functional Moiré superlattices.

Polarization and Charge-Separation of Moiré Excitons in van der Waals Heterostructures

Twisted transition metal dichalcogenide (TMD) bilayers exhibit periodic moiré potentials, which can trap excitons at certain high-symmetry sites. At small twist angles, TMD lattices undergo an atomic reconstruction, altering the moiré potential landscape via the formation of large domains, potentially separating the charges in-plane and leading to the formation of intralayer charge-transfer (CT) excitons. Here, we employ a microscopic, material-specific theory to investigate the intralayer charge-separation in atomically reconstructed MoSe2-WSe2 heterostructures. We identify three distinct and twist-angle-dependent exciton regimes including localized Wannier-like excitons, polarized excitons, and intralayer CT excitons. We calculate the moiré site hopping for these excitons and predict a fundamentally different twist-angle-dependence compared to regular Wannier excitons - presenting an experimentally accessible key signature for the emergence of intralayer CT excitons. Furthermore, we show that the charge separation and its impact on the hopping can be efficiently tuned via dielectric engineering.

Moiré-engineered light-matter interactions in MoS2/WSe2 heterobilayers at room temperature

Moiré superlattices in van der Waals heterostructures represent a highly tunable quantum system, attracting substantial interest in both many-body physics and device applications. However, the influence of the moiré potential on light-matter interactions at room temperature has remained largely unexplored. In our study, we demonstrate that the moiré potential in MoS2/WSe2 heterobilayers facilitates the localization of interlayer exciton (IX) at room temperature. By performing reflection contrast spectroscopy, we demonstrate the importance of atomic reconstruction in modifying intralayer excitons, supported by the atomic force microscopy experiment. When decreasing the twist angle, we observe that the IX lifetime becomes longer and light emission gets enhanced, indicating that non-radiative decay channels such as defects are suppressed by the moiré potential. Moreover, through the integration of moiré superlattices with silicon single-mode cavities, we find that the devices employing moiré-trapped IXs exhibit a significantly lower threshold, one order of magnitude smaller compared to the device utilizing delocalized IXs. These findings not only encourage the exploration of many-body physics in moiré superlattices at elevated temperatures but also pave the way for leveraging these artificial quantum materials in photonic and optoelectronic applications.

Advanced Characterization of the Spatial Variation of Moiré Heterostructures and Moiré Excitons

In this short review, an overview of recent progress in deploying advanced characterization techniques is provided to understand the effects of spatial variation and inhomogeneities in moiré heterostructures over multiple length scales. Particular emphasis is placed on correlating the impact of twist angle misalignment, nano-scale disorder, and atomic relaxation on the moiré potential and its collective excitations, particularly moiré excitons. Finally, future technological applications leveraging moiré excitons are discussed.

Interlayer and Moiré excitons in atomically thin double layers: From individual quantum emitters to degenerate ensembles

Abstract

Interlayer excitons (IXs), composed of electron and hole states localized in different layers, excel in bilayers composed of atomically thin van der Waals materials such as semiconducting transition-metal dichalcogenides (TMDs) due to drastically enlarged exciton binding energies, exciting spin-valley properties, elongated lifetimes, and large permanent dipoles. The latter allows modification by electric fields and the study of thermalized bosonic quasiparticles, from the single particle level to interacting degenerate dense ensembles. Additionally, the freedom to combine bilayers of different van der Waals materials without lattice or relative twist-angle constraints leads to layer-hybridized and Moiré excitons, which can be widely engineered. This article covers fundamental aspects of IXs, including correlation phenomena as well as the consequence of Moiré superlattices with a strong focus on TMD homo- and heterobilayers.

Graphical abstract

Strain fingerprinting of exciton valley character in 2D semiconductors

Intervalley excitons with electron and hole wavefunctions residing in different valleys determine the long-range transport and dynamics observed in many semiconductors. However, these excitons with vanishing oscillator strength do not directly couple to light and, hence, remain largely unstudied. Here, we develop a simple nanomechanical technique to control the energy hierarchy of valleys via their contrasting response to mechanical strain. We use our technique to discover previously inaccessible intervalley excitons associated with K, Γ, or Q valleys in prototypical 2D semiconductors WSe2 and WS2. We also demonstrate a new brightening mechanism, rendering an otherwise "dark" intervalley exciton visible via strain-controlled hybridization with an intravalley exciton. Moreover, we classify various localized excitons from their distinct strain response and achieve large tuning of their energy. Overall, our valley engineering approach establishes a new way to identify intervalley excitons and control their interactions in a diverse class of 2D systems.

Turkish Hematologists’ Preferences for Related Donor Selection: Results of a Multicenter Survey

Allogeneic hematopoietic stem cell transplantation (allo-HSCT) is a widely utilized treatment for various hematological diseases. While selection criteria for unrelated donors are well established, there is a lack of consistency and standardization in the selection of related donors. This study investigated the current approach of hematologists to the selection of related donors at Turkish HSCT centers. The study employed a cross-sectional survey design, distributing a self-administered questionnaire to 95 adult and pediatric transplantation centers in Türkiye to investigate their approaches to related donor selection for allo-HSCT. The questionnaire collected data on various topics including the center’s experience in performing allo-HSCT, patient groups treated, number of allo-HSCT procedures conducted between 2015 and 2021, preferences for related donors, considerations in related donor selection (such as sex and past pregnancies), guidelines utilized for related donor selection, upper age limit for related donors, and the use of specialized advanced analyses for elderly donors. The response rate to the survey was 38.9%. Variability was observed across centers in terms of sex consideration and the impact of past pregnancies on related female donor rejection. Different guidelines were employed for related donor selection, with the European Bone Marrow Transplantation guidelines being the most commonly used. Regarding the upper age limit for related donors, 8.1% of centers accepted an upper age limit of 55 years, 48.7% preferred an upper age limit of 65 years, and 43.2% selected related donors aged 65 and above. The lack of standardized guidelines for related donor selection in HSCT centers leads to variability in criteria and potential risks. Collaboration among centers is essential to establish consensus and develop standardized protocols.

Interaction-Driven Quasi-Insulating Ground States of Gapped Electron-Doped Bilayer Graphene

Bernal bilayer graphene has recently been discovered to exhibit a wide range of unique ordered phases resulting from interaction-driven effects and encompassing spin and valley magnetism, correlated insulators, correlated metals, and superconductivity. This Letter reports on a novel family of correlated phases characterized by spin and valley ordering, distinct from those reported previously. These phases emerge in electron-doped bilayer graphene where the energy bands are exceptionally flat, manifested through an intriguing nonlinear current-bias behavior that occurs at the onset of the phases and is accompanied by an insulating temperature dependence. These characteristics align with the presence of charge- or spin-density-wave states that open a gap on a portion of the Fermi surface or fully gapped Wigner crystals, resulting in an exceptionally intricate phase diagram.

Twisted MoSe2 Homobilayer Behaving as a Heterobilayer

Heterostructures (HSs) formed by the transition-metal dichalcogenide materials have shown great promise in next-generation (opto)electronic applications. An artificially twisted HS allows us to manipulate the optical and electronic properties. In this work, we introduce the understanding of the energy transfer (ET) process governed by the dipolar interaction in a twisted molybdenum diselenide (MoSe2) homobilayer without any charge-blocking interlayer. We fabricated an unconventional homobilayer (i.e., HS) with a large twist angle (∼57°) by combining the chemical vapor deposition (CVD) and mechanical exfoliation (Exf.) techniques to fully exploit the lattice parameter mismatch and indirect/direct (CVD/Exf.) bandgap nature. These effectively weaken the interlayer charge transfer and allow the ET to control the carrier recombination channels. Our experimental and theoretical results explain a massive HS photoluminescence enhancement due to an efficient ET process. This work shows that the electronically decoupled MoSe2 homobilayer is coupled by the ET process, mimicking a "true" heterobilayer nature.

Infrared Interlayer Excitons in Twist-Free MoTe2/MoS2 Heterobilayers

Excitonic devices based on interlayer excitons in van der Waals heterobilayers are a promising platform for advancing photoelectric interconnection telecommunications. However, the absence of exciton emission in the crucial telecom C-band has constrained their practical applications. Here, this limitation is addressed by reporting exciton emission at 0.8 eV (1550 nm) in a chemically vapor-deposited, strictly aligned MoTe2/MoS2 heterobilayer, resulting from the direct bandgap transitions of interlayer excitons as identified by momentum-space imaging of their electrons and holes. The decay mechanisms dominated by direct radiative recombination ensure constant emission quantum yields, a basic demand for efficient excitonic devices. The atomically sharp interface enables the resolution of two narrowly-splitter transitions induced by spin-orbit coupling, further distinguished through the distinct Landé g-factors as the fingerprint of spin configurations. By electrical control, the double transitions coupling into opposite circularly-polarized photon modes, preserve or reverse the helicities of the incident light with a degree of polarization up to 90%. The Stark effect tuning extends the emission energy range by over 150 meV (270 nm), covering the telecom C-band. The findings provide a material platform for studying the excitonic complexes and significantly boost the application prospects of excitonic devices in silicon photonics and all-optical telecommunications.

Berry curvature signatures in chiroptical excitonic transitions

The topology of the electronic band structure of solids can be described by its Berry curvature distribution across the Brillouin zone. We theoretically introduce and experimentally demonstrate a general methodology based on the measurement of energy- and momentum-resolved optical transition rates, allowing to reveal signatures of Berry curvature texture in reciprocal space. By performing time- and angle-resolved photoemission spectroscopy of atomically thin WSe2 using polarization-modulated excitations, we demonstrate that excitons become an asset in extracting the quantum geometrical properties of solids. We also investigate the resilience of our measurement protocol against ultrafast scattering processes following direct chiroptical transitions.

Nonlinear Nano-Imaging of Interlayer Coupling in 2D Graphene-Semiconductor Heterostructures

The emergent electronic, spin, and other quantum properties of 2D heterostructures of graphene and transition metal dichalcogenides are controlled by the underlying interlayer coupling and associated charge and energy transfer dynamics. However, these processes are sensitive to interlayer distance and crystallographic orientation, which are in turn affected by defects, grain boundaries, or other nanoscale heterogeneities. This obfuscates the distinction between interlayer charge and energy transfer. Here, nanoscale imaging in coherent four-wave mixing (FWM) and incoherent two-photon photoluminescence (2PPL) is combined with a tip distance-dependent coupled rate equation model to resolve the underlying intra- and inter-layer dynamics while avoiding the influence of structural heterogeneities in mono- to multi-layer graphene/WSe2 heterostructures. With selective insertion of hBN spacer layers, it is shown that energy, as opposed to charge transfer, dominates the interlayer-coupled optical response. From the distinct nano-FWM and -2PPL tip-sample distance-dependent modification of interlayer and intralayer relaxation by tip-induced enhancement and quenching, an interlayer energy transfer time ofτ ET ≈ ( 0 . 35 - 0.15 + 0.65 ) $\tau _{\rm ET} \approx (0.35^{+0.65}_{-0.15})$  ps consistent with recent reports is derived. As a local probe technique, this approach highlights the ability to determine intrinsic sample properties even in the presence of large sample heterogeneity.

Resonant Band Hybridization in Alloyed Transition Metal Dichalcogenide Heterobilayers

Bandstructure engineering using alloying is widely utilized for achieving optimized performance in modern semiconductor devices. While alloying has been studied in monolayer transition metal dichalcogenides, its application in van der Waals heterostructures built from atomically thin layers is largely unexplored. Here, heterobilayers made from monolayers of WSe2 (or MoSe2) and MoxW1 - xSe2 alloy are fabricated and nontrivial tuning of the resultant bandstructure is observed as a function of concentration x. This evolution is monitored by measuring the energy of photoluminescence (PL) of the interlayer exciton (IX) composed of an electron and hole residing in different monolayers. In MoxW1 - xSe2/WSe2, a strong IX energy shift of ≈100 meV is observed for x varied from 1 to 0.6. However, for x < 0.6 this shift saturates and the IX PL energy asymptotically approaches that of the indirect bandgap in bilayer WSe2. This observation is theoretically interpreted as the strong variation of the conduction band K valley for x > 0.6, with IX PL arising from the K - K transition, while for x < 0.6, the bandstructure hybridization becomes prevalent leading to the dominating momentum-indirect K - Q transition. This bandstructure hybridization is accompanied with strong modification of IX PL dynamics and nonlinear exciton properties. This work provides foundation for bandstructure engineering in van der Waals heterostructures highlighting the importance of hybridization effects and opening a way to devices with accurately tailored electronic properties.

Conduction Band Replicas in a 2D Moiré Semiconductor Heterobilayer

Stacking monolayer semiconductors creates moiré patterns, leading to correlated and topological electronic phenomena, but measurements of the electronic structure underpinning these phenomena are scarce. Here, we investigate the properties of the conduction band in moiré heterobilayers of WS2/WSe2 using submicrometer angle-resolved photoemission spectroscopy with electrostatic gating. We find that at all twist angles the conduction band edge is the K-point valley of the WS2, with a band gap of 1.58 ± 0.03 eV. From the resolved conduction band dispersion, we deduce an effective mass of 0.15 ± 0.02 me. Additionally, we observe replicas of the conduction band displaced by reciprocal lattice vectors of the moiré superlattice. We argue that the replicas result from the moiré potential modifying the conduction band states rather than final-state diffraction. Interestingly, the replicas display an intensity pattern with reduced 3-fold symmetry, which we show implicates the pseudo vector potential associated with in-plane strain in moiré band formation.

Excitonic Thermalization Bottleneck in Twisted TMD Heterostructures

Twisted van der Waals heterostructures show intriguing interface exciton physics, including hybridization effects and emergence of moiré potentials. Recent experiments have revealed that moiré-trapped excitons exhibit remarkable dynamics, where excited states show lifetimes that are several orders of magnitude longer than in monolayers. The origin of this behavior is still under debate. Based on a microscopic many-particle approach, we investigate the phonon-driven relaxation cascade of nonequilibrium moiré excitons in the exemplary MoSe2-WSe2 heterostructure. We track exciton relaxation pathways across different moiré mini-bands and identify the phonon-scattering channels assisting the spatial redistribution of excitons into low-energy pockets of the moiré potential. We unravel a phonon bottleneck in the flat band structure at low twist angles preventing excitons from fully thermalizing into the lowest state, explaining the measured enhanced emission intensity and lifetime of excited moiré excitons. Overall, our work provides important insights into exciton relaxation dynamics in flat-band exciton materials.

Polaron-induced changes in moiré exciton propagation in twisted van der Waals heterostructures

Twisted transition metal dichalcogenides (TMDs) present an intriguing platform for exploring excitons and their transport properties. By introducing a twist angle, a moiré superlattice forms, providing a spatially dependent exciton energy landscape. Based on a microscopic many-particle theory, we investigate in this work polaron-induced changes in exciton transport properties in the exemplary MoSe2/WSe2 heterostructure. We demonstrate that polaron formation and the associated enhancement of the moiré exciton mass lead to a significant band flattening. As a result, the moiré inter-cell tunneling and the propagation velocity undergo noticeable temperature and twist-angle dependent changes. We predict a reduction of the hopping strength ranging from 80% at a twist angle of 1° to 30% at 3° at room temperature. The provided microscopic insights into the spatio-temporal exciton dynamics in presence of a moiré potential further expand the possibilities to tune charge and energy transport in 2D materials.

Low-Scaling GW Algorithm Applied to Twisted Transition-Metal Dichalcogenide Heterobilayers

The GW method is widely used for calculating the electronic band structure of materials. The high computational cost of GW algorithms prohibits their application to many systems of interest. We present a periodic, low-scaling, and highly efficient GW algorithm that benefits from the locality of the Gaussian basis and the polarizability. The algorithm enables G0W0 calculations on a MoSe2/WS2 bilayer with 984 atoms per unit cell, in 42 h using 1536 cores. This is 4 orders of magnitude faster than a plane-wave G0W0 algorithm, allowing for unprecedented computational studies of electronic excitations at the nanoscale.

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.

Unraveling the strain tuning mechanism of interlayer excitons in WSe2/MoSe2heterostructure

Atomically thin transition metal dichalcogenides (TMDs) exhibit rich excitonic physics, due to reduced dielectric screening and strong Coulomb interactions. Especially, some attractive topics in modern condensed matter physics, such as correlated insulator, superconductivity, topological excitons bands, are recently reported in stacking two monolayer (ML) TMDs. Here, we clearly reveal the tuning mechanism of tensile strain on interlayer excitons (IEXs) and intralayer excitons (IAXs) in WSe2/MoSe2heterostructure (HS) at low temperature. We utilize the cryogenic tensile strain platform to stretch the HS, and measure by micro-photoluminescence (μ-PL). The PL peaks redshifts of IEXs and IAXs in WSe2/MoSe2HS under tensile strain are well observed. The first-principles calculations by using density functional theory reveals the PL peaks redshifts of IEXs and IAXs origin from bandgap shrinkage. The calculation results also show the Mo-4d states dominating conduction band minimum shifts of the ML MoSe2plays a dominant role in the redshifts of IEXs. This work provides new insights into understanding the tuning mechanism of tensile strain on IEXs and IAXs in two-dimensional (2D) HS, and paves a way to the development of flexible optoelectronic devices based on 2D materials.

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.

Heteroepitaxy in Organic/TMD Hybrids and Challenge to Achieve it for TMD Monolayers: The Case of Pentacene on WS2 and WSe2

The intriguing photophysical properties of monolayer stacks of different transition-metal dichalcogenides (TMDs), revealing rich exciton physics including interfacial and moiré excitons, have recently prompted an extension of similar investigations to hybrid systems of TMDs and organic films, as the latter combine large photoabsorption cross sections with the ability to tailor energy levels by targeted synthesis. To go beyond single-molecule photoexcitations and exploit the excitonic signatures of organic solids, crystalline molecular films are required. Moreover, a defined registry on the substrate, ideally an epitaxy, is desirable to also achieve an excitonic coupling in momentum space. This poses a certain challenge as excitonic dipole moments of organic films are closely related to the molecular orientation and film structure, which critically depend on the support roughness. Using X-ray diffraction, optical polarization, and atomic force microscopy, we analyzed the structure of pentacene (PEN) multilayer films grown on WSe2(001) and WS2(001) and identified an epitaxial alignment. While (022)-oriented PEN films are formed on both substrates, their azimuthal orientations are quite different, showing an alignment of the molecular L-axis along the ⟨ 110 ⟩ WSe 2 and ⟨ 100 ⟩ WS 2 directions. This intrinsic epitaxial PEN growth depends, however, sensitively on the substrates surface quality. While it occurs on exfoliated TMD single crystals and multilayer flakes, it is hardly found on exfoliated monolayers, which often exhibit bubbles and wrinkles. This enhances the surface roughness and results in (001)-oriented PEN films with upright molecular orientation but without any azimuthal alignment. However, monolayer flakes can be smoothed by AFM operated in contact mode or by transferring to ultrasmooth substrates such as hBN, which again yields epitaxial PEN films. As different PEN orientations result in different characteristic film morphologies (elongated mesa islands vs pyramidal dendrites), which can be easily distinguished by AFM or optical microscopy, this provides a simple means to judge the roughness of the used TMD surface.

Ultrafast optical properties and applications of anisotropic 2D materials

Two-dimensional (2D) layered materials exhibit strong light-matter interactions, remarkable excitonic effects, and ultrafast optical response, making them promising for high-speed on-chip nanophotonics. Recently, significant attention has been directed towards anisotropic 2D materials (A2DMs) with low in-plane crystal symmetry. These materials present unique optical properties dependent on polarization and direction, offering additional degrees of freedom absent in conventional isotropic 2D materials. In this review, we discuss recent progress in understanding the fundamental aspects and ultrafast nanophotonic applications of A2DMs. We cover structural characteristics and anisotropic linear/nonlinear optical properties of A2DMs, including well-studied black phosphorus and rhenium dichalcogenides, as well as emerging quasi-one-dimensional materials. Then, we discuss fundamental ultrafast anisotropic phenomena occurring in A2DMs, such as polarization-dependent ultrafast dynamics of charge carriers and excitons, their direction-dependent spatiotemporal diffusion, photo-induced symmetry switching, and anisotropic coherent acoustic phonons. Furthermore, we review state-of-the-art ultrafast nanophotonic applications based on A2DMs, including polarization-driven active all-optical modulations and ultrafast pulse generations. This review concludes by offering perspectives on the challenges and future prospects of A2DMs in ultrafast nanophotonics.

Vitality of Intralayer Vibration in hBN for Effective Long-Range Interlayer Hole Transfer across High Barriers in MoSe2/hBN/WSe2 Heterostructures

Introducing the two-dimensional (2D) hexagonal boron nitride (hBN) between 2D transition metal dichalcogenide (TMD) layers promises convenient manipulation of the interlayer exciton (IX) and interlayer charge transfer in TMD/hBN/TMD heterostructures, while the role of inserted hBN layers during IX formation is controversial. Employing ab initio nonadiabatic molecular dynamics (NAMD) simulations and the electron-phonon coupling model, we systematically investigate interlayer hole transfer in MoSe2/WSe2 bilayers intercalated by hBN layers with various thicknesses. The conventional direct hole transfer from MoSe2 to WSe2 is decelerated by 2-3 orders of magnitude after the hBN insertion. Meanwhile, a novel channel intermediated by a deeper hole of WSe2 becomes dominant, where the intralayer shear mode of hBN plays a crucial role by reducing the energy barriers for this new channel. The unique role of hBN layers is revealed for the first time, enriching the knowledge of the underlying microscopic mechanisms and providing instructive guidance to practical van der Waals optoelectronic devices.

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.

Light-induced hexatic state in a layered quantum material

The tunability of materials properties by light promises a wealth of future applications in energy conversion and information technology. Strongly correlated materials such as transition metal dichalcogenides offer optical control of electronic phases, charge ordering and interlayer correlations by photodoping. Here, we find the emergence of a transient hexatic state during the laser-induced transformation between two charge-density wave phases in a thin-film transition metal dichalcogenide, 1T-type tantalum disulfide (1T-TaS2). Introducing tilt-series ultrafast nanobeam electron diffraction, we reconstruct charge-density wave rocking curves at high momentum resolution. An intermittent suppression of three-dimensional structural correlations promotes a loss of in-plane translational order caused by a high density of unbound topological defects, characteristic of a hexatic intermediate. Our results demonstrate the merit of tomographic ultrafast structural probing in tracing coupled order parameters, heralding universal nanoscale access to laser-induced dimensionality control in functional heterostructures and devices.

Localization and interaction of interlayer excitons in MoSe2/WSe2 heterobilayers

Transition metal dichalcogenide (TMD) heterobilayers provide a versatile platform to explore unique excitonic physics via the properties of the constituent TMDs and external stimuli. Interlayer excitons (IXs) can form in TMD heterobilayers as delocalized or localized states. However, the localization of IX in different types of potential traps, the emergence of biexcitons in the high-excitation regime, and the impact of potential traps on biexciton formation have remained elusive. In our work, we observe two types of potential traps in a MoSe2/WSe2 heterobilayer, which result in significantly different emission behavior of IXs at different temperatures. We identify the origin of these traps as localized defect states and the moiré potential of the TMD heterobilayer. Furthermore, with strong excitation intensity, a superlinear emission behavior indicates the emergence of interlayer biexcitons, whose formation peaks at a specific temperature. Our work elucidates the different excitation and temperature regimes required for the formation of both localized and delocalized IX and biexcitons and, thus, contributes to a better understanding and application of the rich exciton physics in TMD heterostructures.

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.

Toward High-Peak-to-Valley-Ratio Graphene Resonant Tunneling Diodes

The resonant tunneling diode (RTD) is one of the very few room-temperature-operating quantum devices to date that is able to exhibit negative differential resistance. However, the reported key figure of merit, the current peak-to-valley ratio (PVR), of graphene RTDs has been up to only 3.9 at room temperature thus far. This remains very puzzling, given the atomically flat interfaces of the 2D materials. By varying the active area and perimeter of RTDs based on a graphene/hexagonal boron nitride/graphene heterostructure, we discovered that the edge doping can play a dominant role in determining the resonant tunneling, and a large area-to-perimeter ratio is necessary to obtain a high PVR. The understanding enables establishing a novel design rule and results in a PVR of 14.9, which is at least a factor of 3.8 higher than previously reported graphene RTDs. Furthermore, a theory is developed allowing extraction of the edge doping depth for the first time.

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.

Electrically tunable dipolar interactions between layer-hybridized excitons

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

Fast Twist Angle Mapping of Bilayer Graphene Using Spectroscopic Ellipsometric Contrast Microscopy

Twisted bilayer graphene provides an ideal solid-state model to explore correlated material properties and opportunities for a variety of optoelectronic applications, but reliable, fast characterization of the twist angle remains a challenge. Here we introduce spectroscopic ellipsometric contrast microscopy (SECM) as a tool for mapping twist angle disorder in optically resonant twisted bilayer graphene. We optimize the ellipsometric angles to enhance the image contrast based on measured and calculated reflection coefficients of incident light. The optical resonances associated with van Hove singularities correlate well to Raman and angle-resolved photoelectron emission spectroscopy, confirming the accuracy of SECM. The results highlight the advantages of SECM, which proves to be a fast, nondestructive method for characterization of twisted bilayer graphene over large areas, unlocking process, material, and device screening and cross-correlative measurement potential for bilayer and multilayer materials.

Bosonic Delocalization of Dipolar Moiré Excitons

In superlattices of twisted semiconductor monolayers, tunable moiré potentials emerge, trapping excitons into periodic arrays. In particular, spatially separated interlayer excitons are subject to a deep potential landscape and they exhibit a permanent dipole providing a unique opportunity to study interacting bosonic lattices. Recent experiments have demonstrated density-dependent transport properties of moiré excitons, which could play a key role for technological applications. However, the intriguing interplay between exciton-exciton interactions and moiré trapping has not been well understood yet. In this work, we develop a microscopic theory of interacting excitons in external potentials allowing us to tackle this highly challenging problem. We find that interactions between moiré excitons lead to a delocalization at intermediate densities, and we show how this transition can be tuned via twist angle and temperature. The delocalization is accompanied by a modification of optical moiré resonances, which gradually merge into a single free exciton peak.

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

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

Moiré magnetic exchange interactions in twisted magnets

In addition to moiré superlattices, twisting can also generate moiré magnetic exchange interactions (MMEIs) in van der Waals magnets. However, owing to the extreme complexity and twist-angle-dependent sensitivity, all existing models fail to fully capture MMEIs and thus cannot provide an understanding of MMEI-induced physics. Here, we develop a microscopic moiré spin Hamiltonian that enables the effective description of MMEIs via a sliding-mapping approach in twisted magnets, as demonstrated in twisted bilayer CrI3. We show that the emergence of MMEIs can create a magnetic skyrmion bubble with non-conserved helicity, a 'moiré-type skyrmion bubble'. This represents a unique spin texture solely generated by MMEIs and ready to be detected under the current experimental conditions. Importantly, the size and population of skyrmion bubbles can be finely controlled by twist angle, a key step for skyrmion-based information storage. Furthermore, we reveal that MMEIs can be effectively manipulated by substrate-induced interfacial Dzyaloshinskii-Moriya interactions, modulating the twist-angle-dependent magnetic phase diagram, which solves outstanding disagreements between theories and experiments.

Nanocavity-Integrated van der Waals Heterobilayers for Nano-excitonic Transistor

Optical computing with optical transistors has emerged as a possible solution to the exponentially growing computational workloads, yet an on-chip nano-optical modulation remains a challenge due to the intrinsically noninteracting nature of photons in addition to the diffraction limit. Here, we present an all-optical approach toward nano-excitonic transistors using an atomically thin WSe₂/Mo_0.5W_0.5Se₂ heterobilayer inside a plasmonic tip-based nanocavity. Through optical wavefront shaping, we selectively modulate tip-enhanced photoluminescence (TEPL) responses of intra- and interlayer excitons in a ∼25 nm² area, demonstrating the enabling concept of an ultrathin 2-bit nano-excitonic transistor. We suggest a simple theoretical model describing the underlying adaptive TEPL modulation mechanism, which relies on the additional spatial degree of freedom provided by the presence of the plasmonic tip. Furthermore, we experimentally demonstrate a concept of a 2-trit nano-excitonic transistor, which can provide a technical basis for processing the massive amounts of data generated by emerging artificial intelligence technologies.

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.

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.