Giant Stark splitting of an exciton in bilayer MoS2

Resolving polarization switching pathways of sliding ferroelectricity in trilayer 3R-MoS2

Sliding ferroelectricity, an emerging type of hysteretic behaviour with strong potential for memory-related applications, involves dynamically switching the polarization associated with the stacking arrangement in two-dimensional van der Waals materials. Because different stacking configurations can share a degenerate net polarization, it has remained a challenge to resolve the intermediate stacking configuration and the polarization switching pathway in multi-interface devices. In this work, we present an optical approach to resolve the polarization degeneracy in a trilayer 3R-MoS2 over different switching cycles. By performing reflection contrast spectroscopy in dual-gated devices, we identify distinct responses of inter- and intralayer excitons in all four possible stacking configurations (ABC, ABA, BAB and CBA). Diffraction-limited spatial resolution makes it possible to image the switching of the stacking configurations. We find that the switching pathway is influenced not only by the competition among pinning centres-which localize domain walls at different interfaces-but also by a free-carrier screening effect linked to chemical doping. These findings highlight the importance of managing domain walls, pinning centres and doping levels in sliding ferroelectric devices, offering insights for further development in sensing and computing applications.

Circular Dichroism and Interlayer Exciton Hall Effect in Transition Metal Dichalcogenides Homobilayers

In van der Waals (vdW) architectures of transition metal dichalcogenides (TMDCs), the coupling between interlayer exciton and quantum degrees of freedom opens unprecedented opportunities for excitonic physics. Taking the MoSe2 homobilayer as representative, we identify that the interlayer registry defines the nature and dynamics of the lowest-energy interlayer exciton. The large layer polarization (Pn) is proved, which ensures the formation of layer-resolved interlayer excitons. In particular, sliding ferroelectric polarization couples to the dipole orientation of the interlayer exciton, thus achieving the long-sought electric control of excitonic states. In line with the phase winding of the Bloch states under C3 rotational symmetry, we clarify the valley optical circular dichroism, enriching the exciton valleytronics. We also elucidate the Hall effect of the layer- and valley-polarized interlayer excitons, which advances our understanding of the spatial transport properties of the composite particles and provides new insights into the exciton-based applications.

Anomalous Polarons in Two-Dimensional Organometallic Perovskite Ferroelectric

The concept of ferroelectric polarons is proposed to partially explain the exceptional optoelectronic properties observed in lead halide perovskites (LHPs). It is intriguing but unclear how this proposal, which involves local or transient polarizations, applies in general to 2D LHPs with long-range ferroelectricity. Here, this work presents a pioneering time-domain experimental investigation of polarons in ferroelectric (IA)2(MA)2Pb3Br10 (IMPB; IA is isoamylammonium and MA is methylammonium) using transient absorption spectroscopy. Compared to non-ferroelectric LHPs, IMPB exhibits several distinct polaronic properties closely associated with macroscopic polarizations of ferroelectricity, including a prolonged polaron formation time (≈1.1 ps), a Stark splitting of the bleaching (≈63 meV), and a giant polaron Mott density (≈7.6 × 1018 cm-3). These findings broaden the realm of 2D polaron systems and reveal the decisive role of static/unidirectional polarizations on polaron physics in 2D LHPs.

Bright dipolar excitons in twisted black phosphorus homostructures

Bright dipolar excitons, which contain electrical dipoles and have high oscillator strength, are an ideal platform for studying correlated quantum phenomena. They usually rely on carrier tunneling between two quantum wells or two layers to hybridize with nondipolar excitons to gain oscillator strength. In this work, we uncovered a new type of bright infrared dipolar exciton by stacking 90°-twisted black phosphorus (BP) structures. These excitons, inherent to the reconstructed band structure, exhibit high oscillator strength. Most importantly, they inherit the linear polarization from BP, which allows light polarization to be used to select the dipole direction. Moreover, the dipole moment and resonance energy can be widely tuned by the thickness of the BP. Our results demonstrate a useful platform for exploring tunable correlated dipolar excitons.

Large-Area Epitaxial Growth of Transition Metal Dichalcogenides

Over the past decade, research on atomically thin two-dimensional (2D) transition metal dichalcogenides (TMDs) has expanded rapidly due to their unique properties such as high carrier mobility, significant excitonic effects, and strong spin-orbit couplings. Considerable attention from both scientific and industrial communities has fully fueled the exploration of TMDs toward practical applications. Proposed scenarios, such as ultrascaled transistors, on-chip photonics, flexible optoelectronics, and efficient electrocatalysis, critically depend on the scalable production of large-area TMD films. Correspondingly, substantial efforts have been devoted to refining the synthesizing methodology of 2D TMDs, which brought the field to a stage that necessitates a comprehensive summary. In this Review, we give a systematic overview of the basic designs and significant advancements in large-area epitaxial growth of TMDs. We first sketch out their fundamental structures and diverse properties. Subsequent discussion encompasses the state-of-the-art wafer-scale production designs, single-crystal epitaxial strategies, and techniques for structure modification and postprocessing. Additionally, we highlight the future directions for application-driven material fabrication and persistent challenges, aiming to inspire ongoing exploration along a revolution in the modern semiconductor industry.

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

Electrically tunable layer-hybridized trions in doped WSe2 bilayers

Doped van der Waals heterostructures host layer-hybridized trions, i.e. charged excitons with layer-delocalized constituents holding promise for highly controllable optoelectronics. Combining a microscopic theory with photoluminescence (PL) experiments, we demonstrate the electrical tunability of the trion energy landscape in naturally stacked WSe2 bilayers. We show that an out-of-plane electric field modifies the energetic ordering of the lowest lying trion states, which consist of layer-hybridized Λ -point electrons and layer-localized K-point holes. At small fields, intralayer-like trions yield distinct PL signatures in opposite doping regimes characterized by weak Stark shifts in both cases. Above a doping-asymmetric critical field, interlayer-like species are energetically favored and produce PL peaks with a pronounced Stark red-shift and a counter-intuitively large intensity arising from efficient phonon-assisted recombination. Our work presents an important step forward in the microscopic understanding of layer-hybridized trions in van der Waals heterostructures and paves the way towards optoelectronic applications based on electrically controllable atomically-thin semiconductors.

Observation of phonon Stark effect

Stark effect, the electric-field analogue of magnetic Zeeman effect, is one of the celebrated phenomena in modern physics and appealing for emergent applications in electronics, optoelectronics, as well as quantum technologies. While in condensed matter it has prospered only for excitons, whether other collective excitations can display Stark effect remains elusive. Here, we report the observation of phonon Stark effect in a two-dimensional quantum system of bilayer 2H-MoS2. The longitudinal acoustic phonon red-shifts linearly with applied electric fields and can be tuned over ~1 THz, evidencing giant Stark effect of phonons. Together with many-body ab initio calculations, we uncover that the observed phonon Stark effect originates fundamentally from the strong coupling between phonons and interlayer excitons (IXs). In addition, IX-mediated electro-phonon intensity modulation up to ~1200% is discovered for infrared-active phonon A2u. Our results unveil the exotic phonon Stark effect and effective phonon engineering by IX-mediated mechanism, promising for a plethora of exciting many-body physics and potential technological innovations.

Highly tunable ground and excited state excitonic dipoles in multilayer 2H-MoSe2

The fundamental properties of an exciton are determined by the spin, valley, energy, and spatial wavefunctions of the Coulomb-bound electron and hole. In van der Waals materials, these attributes can be widely engineered through layer stacking configuration to create highly tunable interlayer excitons with static out-of-plane electric dipoles, at the expense of the strength of the oscillating in-plane dipole responsible for light-matter coupling. Here we show that interlayer excitons in bi- and tri-layer 2H-MoSe2 crystals exhibit electric-field-driven coupling with the ground (1s) and excited states (2s) of the intralayer A excitons. We demonstrate that the hybrid states of these distinct exciton species provide strong oscillator strength, large permanent dipoles (up to 0.73 ± 0.01 enm), high energy tunability (up to ~200 meV), and full control of the spin and valley characteristics such that the exciton g-factor can be manipulated over a large range (from -4 to +14). Further, we observe the bi- and tri-layer excited state (2s) interlayer excitons and their coupling with the intralayer excitons states (1s and 2s). Our results, in good agreement with a coupled oscillator model with spin (layer)-selectivity and beyond standard density functional theory calculations, promote multilayer 2H-MoSe2 as a highly tunable platform to explore exciton-exciton interactions with strong light-matter interactions.

Hybrid Moiré Excitons and Trions in Twisted MoTe2-MoSe2 Heterobilayers

We report experimental and theoretical studies of MoTe2-MoSe2 heterobilayers with rigid moiré superlattices controlled by the twist angle. Using an effective continuum model that combines resonant interlayer electron tunneling with stacking-dependent moiré potentials, we identify the nature of moiré excitons and the dependence of their energies, oscillator strengths, and Landé g-factors on the twist angle. Within the same framework, we interpret distinct signatures of bound complexes among electrons and moiré excitons in nearly collinear heterostacks. Our work provides a fundamental understanding of hybrid moiré excitons and trions in MoTe2-MoSe2 heterobilayers and establishes the material system as a prime candidate for optical studies of correlated phenomena in moiré lattices.

Giant Faraday rotation in atomically thin semiconductors

Faraday rotation is a fundamental effect in the magneto-optical response of solids, liquids and gases. Materials with a large Verdet constant find applications in optical modulators, sensors and non-reciprocal devices, such as optical isolators. Here, we demonstrate that the plane of polarization of light exhibits a giant Faraday rotation of several degrees around the A exciton transition in hBN-encapsulated monolayers of WSe2 and MoSe2 under moderate magnetic fields. This results in the highest known Verdet constant of -1.9 × 107 deg T-1 cm-1 for any material in the visible regime. Additionally, interlayer excitons in hBN-encapsulated bilayer MoS2 exhibit a large Verdet constant (VIL ≈ +2 × 105 deg T-1 cm-2) of opposite sign compared to A excitons in monolayers. The giant Faraday rotation is due to the giant oscillator strength and high g-factor of the excitons in atomically thin semiconducting transition metal dichalcogenides. We deduce the complete in-plane complex dielectric tensor of hBN-encapsulated WSe2 and MoSe2 monolayers, which is vital for the prediction of Kerr, Faraday and magneto-circular dichroism spectra of 2D heterostructures. Our results pose a crucial advance in the potential usage of two-dimensional materials in ultrathin optical polarization devices.

Ultraviolet interlayer excitons in bilayer WSe2

Interlayer excitons in van der Waals heterostructures are fascinating for applications like exciton condensation, excitonic devices and moiré-induced quantum emitters. The study of these charge-transfer states has almost exclusively focused on band edges, limiting the spectral region to the near-infrared regime. Here we explore the above-gap analogues of interlayer excitons in bilayer WSe2 and identify both neutral and charged species emitting in the ultraviolet. Even though the transitions occur far above the band edge, the states remain metastable, exhibiting linewidths as narrow as 1.8 meV. These interlayer high-lying excitations have switchable dipole orientations and hence show prominent Stark splitting. The positive and negative interlayer high-lying trions exhibit significant binding energies of 20-30 meV, allowing for a broad tunability of transitions via electric fields and electrostatic doping. The Stark splitting of these trions serves as a highly accurate, built-in sensor for measuring interlayer electric field strengths, which are exceedingly difficult to quantify otherwise. Such excitonic complexes are further sensitive to the interlayer twist angle and offer opportunities to explore emergent moiré physics under electrical control. Our findings more than double the accessible energy range for applications based on interlayer excitons.

High-throughput computational stacking reveals emergent properties in natural van der Waals bilayers

Stacking of two-dimensional (2D) materials has emerged as a facile strategy for realising exotic quantum states of matter and engineering electronic properties. Yet, developments beyond the proof-of-principle level are impeded by the vast size of the configuration space defined by layer combinations and stacking orders. Here we employ a density functional theory (DFT) workflow to calculate interlayer binding energies of 8451 homobilayers created by stacking 1052 different monolayers in various configurations. Analysis of the stacking orders in 247 experimentally known van der Waals crystals is used to validate the workflow and determine the criteria for realisable bilayers. For the 2586 most stable bilayer systems, we calculate a range of electronic, magnetic, and vibrational properties, and explore general trends and anomalies. We identify an abundance of bistable bilayers with stacking order-dependent magnetic or electrical polarisation states making them candidates for slidetronics applications.

Exciton Polaritons in Emergent Two-Dimensional Semiconductors

The "marriage" of light (i.e., photon) and matter (i.e., exciton) in semiconductors leads to the formation of hybrid quasiparticles called exciton polaritons with fascinating quantum phenomena such as Bose-Einstein condensation (BEC) and photon blockade. The research of exciton polaritons has been evolving into an era with emergent two-dimensional (2D) semiconductors and photonic structures for their tremendous potential to break the current limitations of quantum fundamental study and photonic applications. In this Perspective, the basic concepts of 2D excitons, optical resonators, and the strong coupling regime are introduced. The research progress of exciton polaritons is reviewed, and important discoveries (especially the recent ones of 2D exciton polaritons) are highlighted. Subsequently, the emergent 2D exciton polaritons are discussed in detail, ranging from the realization of the strong coupling regime in various photonic systems to the discoveries of attractive phenomena with interesting physics and extensive applications. Moreover, emerging 2D semiconductors, such as 2D perovskites (2DPK) and 2D antiferromagnetic (AFM) semiconductors, are surveyed for the manipulation of exciton polaritons with distinct control degrees of freedom (DOFs). Finally, the outlook on the 2D exciton polaritons and their nonlinear interactions is presented with our initial numerical simulations. This Perspective not only aims to provide an in-depth overview of the latest fundamental findings in 2D exciton polaritons but also attempts to serve as a valuable resource to prospect explorations of quantum optics and topological photonic applications.

Tuning and exploiting interlayer coupling in two-dimensional van der Waals heterostructures

Two-dimensional (2D) layered materials can stack into new material systems, with van der Waals (vdW) interaction between the adjacent constituent layers. This stacking process of 2D atomic layers creates a new degree of freedom-interlayer interface between two adjacent layers-that can be independently studied and tuned from the intralayer degree of freedom. In such heterostructures (HSs), the physical properties are largely determined by the vdW interaction between the individual layers,i.e.interlayer coupling, which can be effectively tuned by a number of means. In this review, we summarize and discuss a number of such approaches, including stacking order, electric field, intercalation, and pressure, with both their experimental demonstrations and theoretical predictions. A comprehensive overview of the modulation on structural, optical, electrical, and magnetic properties by these four approaches are also presented. We conclude this review by discussing several prospective research directions in 2D HSs field, including fundamental physics study, property tuning techniques, and future applications.

Observation of quadrupolar and dipolar excitons in a semiconductor heterotrilayer

Van der Waals (vdW) materials have opened up many avenues for discovery through layer assembly, as epitomized by interlayer dipolar excitons that exhibit electrically tunable luminescence, lasing and exciton condensation. Extending interlayer excitons to more vdW layers, however, raises fundamental questions concerning coherence within excitons and coupling between moiré superlattices at multiple interfaces. Here, by assembling angle-aligned WSe2/WS2/WSe2 heterotrilayers, we demonstrate the emergence of quadrupolar excitons. We confirm the exciton's quadrupolar nature by the decrease in its energy of 12 meV from coherent hole tunnelling between the two outer layers, its tunable static dipole moment under an external electric field and the reduced exciton-exciton interactions. At high exciton density, we also see signatures of a phase of oppositely aligned dipolar excitons, consistent with a staggered dipolar phase predicted to be driven by attractive dipolar interactions. Our demonstration paves the way for discovering emergent exciton orderings for three vdW layers and beyond.

Coherent ultrafast photoemission from a single quantized state of a one-dimensional emitter

Femtosecond laser-driven photoemission source provides an unprecedented femtosecond-resolved electron probe not only for atomic-scale ultrafast characterization but also for free-electron radiation sources. However, for conventional metallic electron source, intense lasers may induce a considerable broadening of emitting energy level, which results in large energy spread (>600 milli-electron volts) and thus limits the spatiotemporal resolution of electron probe. Here, we demonstrate the coherent ultrafast photoemission from a single quantized energy level of a carbon nanotube. Its one-dimensional body can provide a sharp quantized electronic excited state, while its zero-dimensional tip can provide a quantized energy level act as a narrow photoemission channel. Coherent resonant tunneling electron emission is evidenced by a negative differential resistance effect and a field-driven Stark splitting effect. The estimated energy spread is ~57 milli-electron volts, which suggests that the proposed carbon nanotube electron source may promote electron probe simultaneously with subangstrom spatial resolution and femtosecond temporal resolution.

Coherent Phonons in van der Waals MoSe2/WSe2 Heterobilayers

The increasing role of two-dimensional (2D) devices requires the development of new techniques for ultrafast control of physical properties in 2D van der Waals (vdW) nanolayers. A special feature of heterobilayers assembled from vdW monolayers is femtosecond separation of photoexcited electrons and holes between the neighboring layers, resulting in the formation of Coulomb force. Using laser pulses, we generate a 0.8 THz coherent breathing mode in MoSe2/WSe2 heterobilayers, which modulates the thickness of the heterobilayer and should modulate the photogenerated electric field in the vdW gap. While the phonon frequency and decay time are independent of the stacking angle between the MoSe2 and WSe2 monolayers, the amplitude decreases at intermediate angles, which is explained by a decrease in the photogenerated electric field between the layers. The modulation of the vdW gap by coherent phonons enables a new technology for the generation of THz radiation in 2D nanodevices with vdW heterobilayers.

Exciton Superposition across Moiré States in a Semiconducting Moiré Superlattice

Moiré superlattices of semiconducting transition metal dichalcogenides enable unprecedented spatial control of electron wavefunctions, leading to emerging quantum states. The breaking of translational symmetry further introduces a new degree of freedom: high symmetry moiré sites of energy minima behaving as spatially separated quantum dots. We demonstrate the superposition between two moiré sites by constructing a trilayer WSe2/monolayer WS2 moiré heterojunction. The two moiré sites in the first layer WSe2 interfacing WS2 allow the formation of two different interlayer excitons, with the hole residing in either moiré site of the first layer WSe2 and the electron in the third layer WSe2. An electric field can drive the hybridization of either of the interlayer excitons with the intralayer excitons in the third WSe2 layer, realizing the continuous tuning of interlayer exciton hopping between two moiré sites and a superposition of the two interlayer excitons, distinctively different from the natural trilayer WSe2.

Quadrupolar excitons and hybridized interlayer Mott insulator in a trilayer moiré superlattice

Transition metal dichalcogenide (TMDC) moiré superlattices, owing to the moiré flatbands and strong correlation, can host periodic electron crystals and fascinating correlated physics. The TMDC heterojunctions in the type-II alignment also enable long-lived interlayer excitons that are promising for correlated bosonic states, while the interaction is dictated by the asymmetry of the heterojunction. Here we demonstrate a new excitonic state, quadrupolar exciton, in a symmetric WSe₂-WS₂-WSe₂ trilayer moiré superlattice. The quadrupolar excitons exhibit a quadratic dependence on the electric field, distinctively different from the linear Stark shift of the dipolar excitons in heterobilayers. This quadrupolar exciton stems from the hybridization of WSe₂ valence moiré flatbands. The same mechanism also gives rise to an interlayer Mott insulator state, in which the two WSe₂ layers share one hole laterally confined in one moiré unit cell. In contrast, the hole occupation probability in each layer can be continuously tuned via an out-of-plane electric field, reaching 100% in the top or bottom WSe₂ under a large electric field, accompanying the transition from quadrupolar excitons to dipolar excitons. Our work demonstrates a trilayer moiré system as a new exciting playground for realizing novel correlated states and engineering quantum phase transitions.

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.

Interspecies exciton interactions lead to enhanced nonlinearity of dipolar excitons and polaritons in MoS2 homobilayers

Nonlinear interactions between excitons strongly coupled to light are key for accessing quantum many-body phenomena in polariton systems. Atomically-thin two-dimensional semiconductors provide an attractive platform for strong light-matter coupling owing to many controllable excitonic degrees of freedom. Among these, the recently emerged exciton hybridization opens access to unexplored excitonic species, with a promise of enhanced interactions. Here, we employ hybridized interlayer excitons (hIX) in bilayer MoS₂ to achieve highly nonlinear excitonic and polaritonic effects. Such interlayer excitons possess an out-of-plane electric dipole as well as an unusually large oscillator strength allowing observation of dipolar polaritons (dipolaritons) in bilayers in optical microcavities. Compared to excitons and polaritons in MoS₂ monolayers, both hIX and dipolaritons exhibit ≈ 8 times higher nonlinearity, which is further strongly enhanced when hIX and intralayer excitons, sharing the same valence band, are excited simultaneously. This provides access to an unusual nonlinear regime which we describe theoretically as a mixed effect of Pauli exclusion and exciton-exciton interactions enabled through charge tunnelling. The presented insight into many-body interactions provides new tools for accessing few-polariton quantum correlations.

Signatures of Electric Field and Layer Separation Effects on the Spin-Valley Physics of MoSe2/WSe2 Heterobilayers: From Energy Bands to Dipolar Excitons

Multilayered van der Waals heterostructures based on transition metal dichalcogenides are suitable platforms on which to study interlayer (dipolar) excitons, in which electrons and holes are localized in different layers. Interestingly, these excitonic complexes exhibit pronounced valley Zeeman signatures, but how their spin-valley physics can be further altered due to external parameters-such as electric field and interlayer separation-remains largely unexplored. Here, we perform a systematic analysis of the spin-valley physics in MoSe2/WSe2 heterobilayers under the influence of an external electric field and changes of the interlayer separation. In particular, we analyze the spin (Sz) and orbital (Lz) degrees of freedom, and the symmetry properties of the relevant band edges (at K, Q, and Γ points) of high-symmetry stackings at 0° (R-type) and 60° (H-type) angles-the important building blocks present in moiré or atomically reconstructed structures. We reveal distinct hybridization signatures on the spin and the orbital degrees of freedom of low-energy bands, due to the wave function mixing between the layers, which are stacking-dependent, and can be further modified by electric field and interlayer distance variation. We find that H-type stackings favor large changes in the g-factors as a function of the electric field, e.g., from -5 to 3 in the valence bands of the Hhh stacking, because of the opposite orientation of Sz and Lz of the individual monolayers. For the low-energy dipolar excitons (direct and indirect in k-space), we quantify the electric dipole moments and polarizabilities, reflecting the layer delocalization of the constituent bands. Furthermore, our results show that direct dipolar excitons carry a robust valley Zeeman effect nearly independent of the electric field, but tunable by the interlayer distance, which can be rendered experimentally accessible via applied external pressure. For the momentum-indirect dipolar excitons, our symmetry analysis indicates that phonon-mediated optical processes can easily take place. In particular, for the indirect excitons with conduction bands at the Q point for H-type stackings, we find marked variations of the valley Zeeman (∼4) as a function of the electric field, which notably stands out from the other dipolar exciton species. Our analysis suggests that stronger signatures of the coupled spin-valley physics are favored in H-type stackings, which can be experimentally investigated in samples with twist angle close to 60°. In summary, our study provides fundamental microscopic insights into the spin-valley physics of van der Waals heterostructures, which are relevant to understanding the valley Zeeman splitting of dipolar excitonic complexes, and also intralayer excitons.

Thickness- and Twist-Angle-Dependent Interlayer Excitons in Metal Monochalcogenide Heterostructures

Interlayer excitons, or bound electron-hole pairs whose constituent quasiparticles are located in distinct stacked semiconducting layers, are being intensively studied in heterobilayers of two-dimensional semiconductors. They owe their existence to an intrinsic type-II band alignment between both layers that convert these into p-n junctions. Here, we unveil a pronounced interlayer exciton (IX) in heterobilayers of metal monochalcogenides, namely, γ-InSe on ε-GaSe, whose pronounced emission is adjustable just by varying their thicknesses given their number of layers dependent direct band gaps. Time-dependent photoluminescense spectroscopy unveils considerably longer interlayer exciton lifetimes with respect to intralayer ones, thus confirming their nature. The linear Stark effect yields a bound electron-hole pair whose separation d is just (3.6 ± 0.1) Å with d being very close to d_Se = 3.4 Å which is the calculated interfacial Se separation. The envelope of IX is twist-angle-dependent and describable by superimposed emissions that are nearly equally spaced in energy, as if quantized due to localization induced by the small moiré periodicity. These heterostacks are characterized by extremely flat interfacial valence bands making them prime candidates for the observation of magnetism or other correlated electronic phases upon carrier doping.

Highly nonlinear dipolar exciton-polaritons in bilayer MoS2

Realizing nonlinear optical response in the low photon density limit in solid-state systems has been a long-standing challenge. Semiconductor microcavities in the strong coupling regime hosting exciton-polaritons have emerged as attractive candidates in this context. However, the weak interaction between these quasiparticles has been a hurdle in this quest. Dipolar excitons provide an attractive strategy to overcome this limitation but are often hindered by their weak oscillator strength. The interlayer dipolar excitons in naturally occurring homobilayer MoS₂ alleviates this issue owing to their formation via hybridization of interlayer charge transfer exciton with intralayer B exciton. Here we demonstrate the formation of dipolar exciton polaritons in bilayer MoS₂ resulting in unprecedented nonlinear interaction strengths. A ten-fold increase in nonlinearity is observed for the interlayer dipolar excitons compared to the conventional A excitons. These highly nonlinear dipolar polaritons will likely be a frontrunner in the quest for solid-state quantum nonlinear devices.

Dipolar excitons enable large nonlinear interaction but are usually hampered by their weak oscillator strength. Here, the authors demonstrate the strong light-matter coupling of interlayer dipolar excitons having unusually large oscillator strength in bilayer MoS₂ resulting in highly nonlinear dipolar polaritons.

Capacitively and Inductively Coupled Excitons in Bilayer MoS_{2}

The coupling of intralayer A and B excitons and interlayer excitons (IE) is studied in a two-dimensional semiconductor, homobilayer MoS_{2}. It is shown that the measured optical susceptibility reveals both the magnitude and the phase of the coupling constants. The IE and B excitons couple via a 0-phase (capacitive) coupling; the IE and A excitons couple via a π-phase (inductive) coupling. The IE-B and IE-A coupling mechanisms are interpreted as hole tunneling and electron-hole exchange, respectively. The couplings imply that even in a monolayer, the A and B excitons have mixed spin states. Using the IE as a sensor, the A-B intravalley exchange coupling is determined. Finally, we realize a bright and highly tunable lowest-energy momentum-direct exciton at high electric fields.

Ultrafast pseudospin quantum beats in multilayer WSe2 and MoSe2

Layered van-der-Waals materials with hexagonal symmetry offer an extra degree of freedom to their electrons, the so-called valley index or valley pseudospin, which behaves conceptually like the electron spin. Here, we present investigations of excitonic transitions in mono- and multilayer WSe₂ and MoSe₂ materials by time-resolved Faraday ellipticity (TRFE) with in-plane magnetic fields, B_∥, of up to 9 T. In monolayer samples, the measured TRFE time traces are almost independent of B_∥, which confirms a close to zero in-plane exciton g factor g_∥, consistent with first-principles calculations. In contrast, we observe pronounced temporal oscillations in multilayer samples for B_∥ > 0. Our first-principles calculations confirm the presence of a non-zero g_∥ for the multilayer samples. We propose that the oscillatory TRFE signal in the multilayer samples is caused by pseudospin quantum beats of excitons, which is a manifestation of spin- and pseudospin layer locking in the multilayer samples.

Temperature induced modulation of resonant Raman scattering in bilayer 2H-MoS2

The temperature evolution of the resonant Raman scattering from high-quality bilayer 2H-MoS[Formula: see text] encapsulated in hexagonal BN flakes is presented. The observed resonant Raman scattering spectrum as initiated by the laser energy of 1.96 eV, close to the A excitonic resonance, shows rich and distinct vibrational features that are otherwise not observed in non-resonant scattering. The appearance of 1st and 2nd order phonon modes is unambiguously observed in a broad range of temperatures from 5 to 320 K. The spectrum includes the Raman-active modes, i.e. E[Formula: see text]([Formula: see text]) and A[Formula: see text]([Formula: see text]) along with their Davydov-split counterparts, i.e. E[Formula: see text]([Formula: see text]) and B[Formula: see text]([Formula: see text]). The temperature evolution of the Raman scattering spectrum brings forward key observations, as the integrated intensity profiles of different phonon modes show diverse trends. The Raman-active A[Formula: see text]([Formula: see text]) mode, which dominates the Raman scattering spectrum at T = 5 K quenches with increasing temperature. Surprisingly, at room temperature the B[Formula: see text]([Formula: see text]) mode, which is infrared-active in the bilayer, is substantially stronger than its nominally Raman-active A[Formula: see text]([Formula: see text]) counterpart.

Interlayer Coupling and Pressure Engineering in Bilayer MoS2

Controlling the interlayer coupling by tuning lattice parameters through pressure engineering is an important route for tailoring the optoelectronic properties of two-dimensional materials. In this work, we report a pressure-dependent study on the exciton transitions of bilayer MoS2 exfoliated on a diamond anvil surface. The applied hydrostatic pressure changes from ambient pressure up to 11.05 GPa using a diamond anvil cell device. Raman, photoluminescence, and reflectivity spectra at room temperature are analyzed to characterize the interlayer coupling of this bilayer system. With the increase of pressure, the indirect exciton emission disappears completely at about 5 GPa. Importantly, we clearly observed the interlayer exciton from the reflectivity spectra, which becomes invisible at a low pressure around 1.26 GPa. This indicates that the interlayer exciton is very sensitive to the hydrostatic pressure due to the oscillator strength transfer from the direct transition to the indirect one.

Self-Trapped Interlayer Excitons in van der Waals Heterostructures

The self-trapped state (STS) of the interlayer exciton (IX) has aroused enormous interest owing to its significant impact on the fundamental properties of the van der Waals heterostructures (vdWHs). Nevertheless, the microscopic mechanisms of STS are still controversial. Herein, we study the corrections of the binding energies of the IXs stemming from the exciton-interface optical phonon coupling in four kinds of vdWHs and find that these IXs are in the STS for the appropriate ratio of the electron and hole effective masses. We show that these self-trapped IXs could be classified into type I with the increasing binding energy in the tens of millielectronvolts range, which are very agreement with the red-shift of the IX spectra in experiments, and type II with the decreasing binding energy, which provides a possible explanation for the blue-shift and broad line width of the IX's spectra at low temperatures. Moreover, these two types of exciton states could be transformed into each other by adjusting the structural parameters of vdWHs. These results not only provide an in-depth understanding for the self-trapped mechanism but also shed light on the modulations of IXs in vdWHs.

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.

Exciton-dielectric mode coupling in MoS2 nanoflakes visualized by cathodoluminescence

Two-dimensional (2D) transition metal dichalcogenides (TMDCs), possessing unique exciton luminescence properties, have attracted significant attention for use in optical and electrical devices. TMDCs are also high refractive index materials that can strongly confine the electromagnetic field in nanoscale dimensions when patterned into nanostructures, thus resulting in complex light emission that includes exciton and dielectric resonances. Here, we use cathodoluminescence (CL) to experimentally visualize the emission modes of single molybdenum disulfide (MoS2) nanoflakes and to investigate luminescence enhancement due to dielectric resonances in nanoscale dimensions, by using a scanning transmission electron microscope. Specifically, we identify dielectric modes whose resonant wavelength is sensitive to the shape and size of the nanoflake, and exciton emission peaks whose energies are insensitive to the geometry of the flakes. Using a four-dimensional CL method and boundary element method simulations, we further theoretically and experimentally visualize the emission polarization and angular emission patterns, revealing the coupling of the exciton and dielectric resonant modes. Such nanoscopic observation provides a detailed understanding of the optical responses of MoS2 including modal couplings of excitons and dielectric resonances which play a crucial role in the development of energy conversion devices, single-photon emitters, and nanophotonic circuits with enhanced light-matter interactions.

Electrically Switchable Intervalley Excitons with Strong Two-Phonon Scattering in Bilayer WSe2

We report the observation of QΓ intervalley exciton in bilayer WSe₂ devices encapsulated by boron nitride. The QΓ exciton resides at ∼18 meV below the QK exciton. The QΓ and QK excitons exhibit different Stark shifts under an out-of-plane electric field due to their different interlayer dipole moments. By controlling the electric field, we can switch their energy ordering and control which exciton dominates the luminescence of bilayer WSe₂. Remarkably, both QΓ and QK excitons exhibit unusually strong two-phonon replicas, which are comparable to or even stronger than the one-phonon replicas. By detailed theoretical simulation, we reveal the existence of numerous (≥14) two-phonon scattering paths involving (nearly) resonant exciton-phonon scattering in bilayer WSe₂. To our knowledge, such electric-field-switchable intervalley excitons with strong two-phonon replicas have not been found in any other two-dimensional semiconductors. These make bilayer WSe₂ a distinctive valleytronic material with potential novel applications.

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.

Orbital Gating Driven by Giant Stark Effect in Tunneling Phototransistors

Conventional gating in transistors uses electric fields through external dielectrics that require complex fabrication processes. Various optoelectronic devices deploy photogating by electric fields from trapped charges in neighbor nanoparticles or dielectrics under light illumination. Orbital gating driven by giant Stark effect is demonstrated in tunneling phototransistors based on 2H-MoTe₂ without using external gating bias or slow charge trapping dynamics in photogating. The original self-gating by light illumination modulates the interlayer potential gradient by switching on and off the giant Stark effect where the d_z 2-orbitals of molybdenum atoms play the dominant role. The orbital gating shifts the electronic bands of the top atomic layer of the MoTe₂ by up to 100 meV, which is equivalent to modulation of a carrier density of 7.3 × 10¹¹ cm^-2 by electrical gating. Suppressing conventional photoconductivity, the orbital gating in tunneling phototransistors achieves low dark current, practical photoresponsivity (3357 AW^-1 ), and fast switching time (0.5 ms) simultaneously.

Spin-Selective Hole-Exciton Coupling in a V-Doped WSe2 Ferromagnetic Semiconductor at Room Temperature

While valley polarization with strong Zeeman splitting is the most prominent characteristic of two-dimensional (2D) transition metal dichalcogenide (TMD) semiconductors under magnetic fields, enhancement of the Zeeman splitting has been demonstrated by incorporating magnetic dopants into the host materials. Unlike Fe, Mn, and Co, V is a distinctive dopant for ferromagnetic semiconducting properties at room temperature with large Zeeman shifting of band edges. Nevertheless, little known is the excitons interacting with spin-polarized carriers in V-doped TMDs. Here, we report anomalous circularly polarized photoluminescence (CPL) in a V-doped WSe₂ monolayer at room temperature. Excitons couple to V-induced spin-polarized holes to generate spin-selective positive trions, leading to differences in the populations of neutral excitons and trions between left and right CPL. Using transient absorption spectroscopy, we elucidate the origin of excitons and trions that are inherently distinct for defect-mediated and impurity-mediated trions. Ferromagnetic characteristics are further confirmed by the significant Zeeman splitting of nanodiamonds deposited on the V-doped WSe₂ monolayer.

Self-Limiting Opto-Electrochemical Thinning of Transition-Metal Dichalcogenides

Two-dimensional monolayer and few-layer transition-metal dichalcogenides (TMDs) are promising for advanced electronic and photonic applications due to their extraordinary optoelectronic and mechanical properties. However, it has remained challenging to produce high-quality TMD thin films with controlled thickness and desired micropatterns, which are essential for their practical implementation in functional devices. In this work, a self-limiting opto-electrochemical thinning (sOET) technique is developed for on-demand thinning and patterning of TMD flakes at high efficiency. Benefiting from optically enhanced electrochemical reactions, sOET features a low operational optical power density of down to 70 μW μm^-2 to avoid photodamage and thermal damage to the thinned TMD flakes. Through selective optical excitation with different laser wavelengths based on the thickness-dependent band gaps of TMD materials, sOET enables precise control over the final thickness of TMD flakes. With the capability of thickness control and site-specific patterning, our sOET offers an effective route to fabricating high-quality TMD materials for a broad range of applications in nanoelectronics, nanomechanics, and nanophotonics.

Interlayer exciton mediated second harmonic generation in bilayer MoS2

Second-harmonic generation (SHG) is a non-linear optical process, where two photons coherently combine into one photon of twice their energy. Efficient SHG occurs for crystals with broken inversion symmetry, such as transition metal dichalcogenide monolayers. Here we show tuning of non-linear optical processes in an inversion symmetric crystal. This tunability is based on the unique properties of bilayer MoS2, that shows strong optical oscillator strength for the intra- but also interlayer exciton resonances. As we tune the SHG signal onto these resonances by varying the laser energy, the SHG amplitude is enhanced by several orders of magnitude. In the resonant case the bilayer SHG signal reaches amplitudes comparable to the off-resonant signal from a monolayer. In applied electric fields the interlayer exciton energies can be tuned due to their in-built electric dipole via the Stark effect. As a result the interlayer exciton degeneracy is lifted and the bilayer SHG response is further enhanced by an additional two orders of magnitude, well reproduced by our model calculations. Since interlayer exciton transitions are highly tunable also by choosing twist angle and material combination our results open up new approaches for designing the SHG response of layered materials.

Bidirectional and reversible tuning of the interlayer spacing of two-dimensional materials

Interlayer spacing is expected to influence the properties of multilayer two-dimensional (2D) materials. However, the ability to non-destructively regulate the interlayer spacing bidirectionally and reversibly is challenging. Here we report the preparation of 2D materials with tunable interlayer spacing by introducing active sites (Ce ions) in 2D materials to capture and immobilize Pt single atoms. The strong chemical interaction between active sites and Pt atoms contributes to the intercalation behavior of Pt atoms in the interlayer of 2D materials and further promotes the formation of chemical bonding between Pt atom and host materials. Taking cerium-embedded molybdenum disulfide (MoS2) as an example, intercalation of Pt atoms enables interlayer distance tuning via an electrochemical protocol, leading to interlayer spacing reversible and linear compression and expansion from 6.546 ± 0.039 Å to 5.792 ± 0.038 Å (~11 %). The electronic property evolution with the interlayer spacing variation is demonstrated by the photoluminescence (PL) spectra, delivering that the well-defined barrier between the multilayer and monolayer layered materials can be artificially designed.

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

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