Tuning layer-hybridized moiré excitons by the quantum-confined Stark effect

Synthesis, Modulation, and Application of Two-Dimensional TMD Heterostructures

Two-dimensional (2D) transition metal dichalcogenide (TMD) heterostructures have attracted a lot of attention due to their rich material diversity and stack geometry, precise controllability of structure and properties, and potential practical applications. These heterostructures not only overcome the inherent limitations of individual materials but also enable the realization of new properties through appropriate combinations, establishing a platform to explore new physical and chemical properties at micro-nano-pico scales. In this review, we systematically summarize the latest research progress in the synthesis, modulation, and application of 2D TMD heterostructures. We first introduce the latest techniques for fabricating 2D TMD heterostructures, examining the rationale, mechanisms, advantages, and disadvantages of each strategy. Furthermore, we emphasize the importance of characteristic modulation in 2D TMD heterostructures and discuss some approaches to achieve novel functionalities. Then, we summarize the representative applications of 2D TMD heterostructures. Finally, we highlight the challenges and future perspectives in the synthesis and device fabrication of 2D TMD heterostructures and provide some feasible solutions.

Stark effect and orbital hybridization of moiré interlayer excitons in the MoSe2/WSe2 heterobilayer

In this paper, we undertake a theoretical investigation into the effects of both in-plane and out-of-plane static electric fields on moiré interlayer excitons (IXs) within a WSe2/MoSe2 heterobilayer. We thoroughly analyze a wide range of properties pertaining to the IXs, including the binding energy, Stark shift, orbital hybridization, photoluminescence (PL) spectra, and radiative lifetime. Various factors influencing IX behavior, such as the dielectric environment, spacing separation, and moiré trap effects, are examined in detail. Our results demonstrate that the in-plane electric field leads to energy splitting between states with non-zero angular momentum, such as the 2p± dark states. Consequently, we analyze IX orbital hybridization, including hybrid Rydberg states like 1s, 2p±, and 2s. In contrast, we show that an out-of-plane electric field induced by a double-gate setup causes a quadratic Stark effect on the center of mass (COM) eigenenergies, leading to energy splitting of degenerate states and resulting in orbital hybridization of COM eigenvectors. Additionally, we demonstrate that a parallel electric field brightens the 2p± dark state through a one-photon PL process, due to the hybridization phenomena between s- and p-type Rydberg states. In short, our investigation is in great agreement with previous research and can assist experimenters in designing novel optoelectronic applications, such as on-chip electro-optic modulators and TeraHertz devices.

Room Temperature, Twist Angle Independent, Momentum Direct Interlayer Excitons in van der Waals Heterostructures with Wide Spectral Tunability

Interlayer excitons (IXs) in van der Waals heterostructures with static out of plane dipole moment and long lifetime show promise in the development of exciton based optoelectronic devices and the exploration of many body physics. However, these IXs are not always observed, as the emission is very sensitive to lattice mismatch and twist angle between the constituent materials. Moreover, their emission intensity is very weak compared to that of corresponding intralayer excitons at room temperature. Here we report the room-temperature realization of twist angle independent momentum direct IX in the heterostructures of bulk PbI2 and bilayer WS2. Momentum conserving transitions combined with the large band offsets between the constituent materials enable intense IX emission at room temperature. A long lifetime (∼100 ns), noticeable Stark shift, and tunability of IX emission from 1.70 to 1.45 eV by varying the number of WS2 layers make these heterostructures promising to develop room temperature exciton based optoelectronic devices.

Twist angle-dependent interlayer hybridized exciton lifetimes in van der Waals heterostructures

The interlayer twist angle has a direct effect on exciton lifetimes in van der Waals heterostructures. At small angles, the interlayer and intralayer excitons in MoSe2/WS2 heterostructures are hybridized, resulting in hybridized excitons with long lifetimes and strong resonance. However, the study of twist-angle modulation of hybridized exciton lifetimes is still insufficient, leading to an unclear understanding of the mechanism through which the twist angle between layers influences the lifetime of hybridized excitons. Here, we observed the formation of hybridized excitons by constructing MoSe2/WS2 heterostructures with different twist angles. The exciton lifetime is found to increase from 0.5 ns to 3.3 ns when the twist angle is reduced from 12° to 1°. This work provides a new perspective on the modulation of the exciton lifetime, enabling further exploration in improving the efficiency of optoelectronic devices.

Enhancing Layer-Engineered Interlayer Exciton Emission and Valley Polarization in van der Waals Heterostructures via Strain

Layer-engineered interlayer excitons from heterostructures of transition-metal dichalcogenides (TMDCs) exhibit a rich variety of emissive states and intriguing valley spin-selection rules, the effective modulation of which is crucial for excitonic physics and related device applications. Strain or high pressure provides the possibility to tune the energy of the interlayer excitons; however, the reported emission intensity is substantially quenched, which greatly limits their practical application in optoelectronic devices. Here, via applying uniaxial strain based on polyvinyl alcohol (PVA) encapsulation technique, we report enhanced layer-engineered interlayer exciton emission intensity with largely modulated emission energy in WSe2/WS2 heterobilayer and heterotrilayer. Both momentum-direct and momentum-indirect interlayer excitons were observed, and their emission energies show an opposite shift tendency upon applied strain, which agrees with our DFT calculations. We further demonstrate that intralayer and interlayer exciton states with low phonon interactions can be modulated through the mechanical strain applied to the PVA substrate at low temperatures. Due to strain-induced breaking of the 3-fold rotational symmetry, we observe the enhanced valley polarization of interlayer excitons. Our study contributes to the understanding and modulation of the optical properties of interlayer excitons, which could be exploited for optoelectronic device applications.

Control of Hybrid Exciton Lifetime in MoSe2/WS2 Moiré Heterostructures

Hybrid excitons, characterized by their strong oscillation strength and long lifetimes, hold great potential as information carriers in semiconductors. They offer promising applications in exciton-based devices and circuits. MoSe2/WS2 heterostructures represent an ideal platform for studying hybrid excitons, but how to regulate the exciton lifetime has not yet been explored. In this study, layer hybridization is modulated by applying electric fields parallel or antiparallel to the dipole moment, enabling us to regulate the exciton lifetime from 1.36 to 4.60 ns. Furthermore, the time-resolved photoluminescence decay traces are measured at different excitation power. A hybrid exciton annihilation rate of 8.9 × 10-4 cm2 s-1 is obtained by fitting. This work reveals the effects of electric fields and excitation power on the lifetime of hybrid excitons in MoSe2/WS2 1.5° moiré heterostructures, which play important roles in high photoluminescence quantum yield optoelectronic devices based on transition-metal dichalcogenides heterostructures.

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.

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.

Correlation-driven nonequilibrium exciton site transition in a WSe2/WS2 moiré supercell

Moiré superlattices of transition metal dichalcogenides offer a unique platform to explore correlated exciton physics with optical spectroscopy. Whereas the spatially modulated potentials evoke that the exciton resonances are distinct depending on a site in a moiré supercell, there have been no clear demonstration how the moiré excitons trapped in different sites dynamically interact with the doped carriers; so far the exciton-electron dynamic interactions were presumed to be site-dependent. Thus, the transient emergence of nonequilibrium correlations are open questions, but existing studies are limited to steady-state optical measurements. Here we report experimental fingerprints of site-dependent exciton correlations under continuous-wave as well as ultrashort optical excitations. In near-zero angle-aligned WSe2/WS2 heterobilayers, we observe intriguing polarization switching and strongly enhanced Pauli blocking near the Mott insulating state, dictating the dominant correlation-driven effects. When the twist angle is near 60°, no such correlations are observed, suggesting the strong dependence of atomic registry in moiré supercell configuration. Our studies open the door to largely unexplored nonequilibrium correlations of excitons in moiré superlattices.

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.

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.

Biexcitons-plasmon coupling of Ag@Au hollow nanocube/MoS2 heterostructures based on scattering spectra

The strong interaction between light and matter is one of the current research hotspots in the field of nanophotonics, and provides a suitable platform for fundamental physics research such as on nanolasers, high-precision sensing in biology, quantum communication and quantum computing. In this study, double Rabi splitting was achieved in a composite structure monolayer MoS2 and a single Ag@Au hollow nanocube (HNC) in room temperature mainly due to the two excitons in monolayer MoS2. Moreover, the tuning of the plasmon resonance peak was realized in the scattering spectrum by adjusting the thickness of the shell to ensure it matches the energy of the two excitons. Two distinct anticrossings are observed at both excitons resonances, and large double Rabi splittings (90 meV and 120 meV) are obtained successfully. The finite-difference time domain (FDTD) method was also used to simulate the scattering spectra of the nanostructures, and the simulation results were in good agreement with the experimental results. Additionally, the local electromagnetic field ability of the Ag@Au hollow HNC was proved to be stronger by calculating and comparing the mode volume of different nanoparticles. Our findings provides a good platform for the realization of strong multi-mode coupling and open up a new way to construct nanoscale photonic devices.

Mixed Stochastic-Deterministic Approach for Many-Body Perturbation Theory Calculations

We present an approach for GW calculations of quasiparticle energies with quasiquadratic scaling by approximating high-energy contributions to the Green's function in its Lehmann representation with effective stochastic vectors. The method is easy to implement without altering the GW code, converges rapidly with stochastic parameters, and treats systems of various dimensionality and screening response. Our calculations on a 5.75° twisted MoS_{2} bilayer show how large-scale GW methods include geometry relaxations and electronic correlations on an equal basis in structurally nontrivial materials.

Field-Induced Hybridization of Moiré Excitons in MoSe_{2}/WS_{2} Heterobilayers

We study experimentally and theoretically the hybridization among intralayer and interlayer moiré excitons in a MoSe_{2}/WS_{2} heterostructure with antiparallel alignment. Using a dual-gate device and cryogenic white light reflectance and narrow-band laser modulation spectroscopy, we subject the moiré excitons in the MoSe_{2}/WS_{2} heterostack to a perpendicular electric field, monitor the field-induced dispersion and hybridization of intralayer and interlayer moiré exciton states, and induce a crossover from type I to type II band alignment. Moreover, we employ perpendicular magnetic fields to map out the dependence of the corresponding exciton Landé g factors on the electric field. Finally, we develop an effective theoretical model combining resonant and nonresonant contributions to moiré potentials to explain the observed phenomenology, and highlight the relevance of interlayer coupling for structures with close energetic band alignment as in MoSe_{2}/WS_{2}.

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.

Bright and Dark Quadrupolar Excitons in the WSe_{2}/MoSe_{2}/WSe_{2} Heterotrilayer

Transition metal dichalcogenide heterostructures have been extensively studied as a platform for investigating exciton physics. While heterobilayers such as WSe_{2}/MoSe_{2} have received significant attention, there has been comparatively less research on heterotrilayers, which may offer new excitonic species and phases, as well as unique physical properties. In this Letter, we present theoretical and experimental investigations on the emission properties of quadrupolar excitons (QXs), a newly predicted type of exciton, in a WSe_{2}/MoSe_{2}/WSe_{2} heterotrilayer device. Our findings reveal that the optical brightness or darkness of QXs is determined by horizontal mirror symmetry and valley and spin selection rules. Additionally, the emission intensity and energy of both bright and dark QXs can be adjusted by applying an out-of-plane electric field, due to changes in hole distribution and the Stark effect. These results not only provide experimental evidence for the existence of QXs in heterotrilayers but also uncover their novel properties, which have the potential to drive the development of new exciton-based 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.

Thermally induced atomic reconstruction into fully commensurate structures of transition metal dichalcogenide layers

Twist angle between two-dimensional layers is a critical parameter that determines their interfacial properties, such as moiré excitons and interfacial ferro-electricity. To achieve better control over these properties for fundamental studies and various applications, considerable efforts have been made to manipulate twist angle. However, due to mechanical limitations and the inevitable formation of incommensurate regions, there remains a challenge in attaining perfect alignment of crystalline orientation. Here we report a thermally induced atomic reconstruction of randomly stacked transition metal dichalcogenide multilayers into fully commensurate heterostructures with zero twist angle by encapsulation annealing, regardless of twist angles of as-stacked samples and lattice mismatches. We also demonstrate the selective formation of R- and H-type fully commensurate phases with a seamless lateral junction using chemical vapour-deposited transition metal dichalcogenides. The resulting fully commensurate phases exhibit strong photoluminescence enhancement of the interlayer excitons, even at room temperature, due to their commensurate structure with aligned momentum coordinates. Our work not only demonstrates a way to fabricate zero-twisted, two-dimensional bilayers with R- and H-type configurations, but also provides a platform for studying their unexplored properties.

Pressure-Induced Dynamic Tuning of Interlayer Coupling in Twisted WSe2/WSe2 Homobilayers

Moiré superlattices induced by twisted van der Waals (vdW) heterostructures or homostructures have recently gained significant attention due to their potential to generate exotic strong-correlation electronic and phonon phenomena. However, the lack of dynamic tuning for interlayer coupling of moiré superlattices hinders a thorough understanding and development of the moiré correlation state. Here, we present a dynamic tuning method for twisted WSe2/WSe2 homobilayers using a diamond anvil cell (DAC). We demonstrate the powerful tuning of interlayer coupling and observe an enhanced response to pressure for interlayer breathing modes and the rapid descent of indirect excitons in twisted WSe2/WSe2 homobilayers. Our findings indicate that the introduction of a moiré superlattice for WSe2 bilayers gives rise to hybridized excitons, which lead to the different pressure-evolution exciton behaviors compared to natural WSe2 bilayers. Our results provide a novel understanding of moiré physics and offer an effective method to tune interlayer coupling of moiré superlattices.

D-Band Center Optimization of Edge-Rich Ultrathin RuZn Nanosheets With Moiré Superlattices for pH-Universal Hydrogen Evolution Reaction

Electrocatalytic hydrogen evolution reaction (HER) is a promising way to produce pure and clean hydrogen. However, the preparation of efficient and economical catalysts for pH-universal HER remains a challenging but rewarding task. Herein, ultrathin RuZn nanosheets (NSs) with moiré superlattices and abundant edges are synthesized. The RuZn NSs with unique structure exhibit superb HER performance with overpotentials of 11, 13, and 29 mV to achieve 10 mA cm-2 in 1 M KOH, 1 M PBS, and 0.5 M H2 SO4 , respectively, which is substantially lower than those of Ru NSs and RuZn NSs without moiré superlattices. Density functional theory investigations reveal that the charge transfer from Zn to Ru will lead the appropriate downshift of the d-band center of surface Ru atoms, thus accelerating hydrogen desorption from the Ru sites, lowering the dissociation energy barrier of water and greatly improving the HER performance. This work provides an effective design scheme for high-performance HER electrocatalysts over a wide pH range, and propose a general route to prepare Ru-based bimetallic nanosheets with moiré superlattices.

Tunable phononic coupling in excitonic quantum emitters

Engineering the coupling between fundamental quantum excitations is at the heart of quantum science and technologies. An outstanding case is the creation of quantum light sources in which coupling between single photons and phonons can be controlled and harnessed to enable quantum information transduction. Here we report the deterministic creation of quantum emitters featuring highly tunable coupling between excitons and phonons. The quantum emitters are formed in strain-induced quantum dots created in homobilayer WSe2. The colocalization of quantum-confined interlayer excitons and terahertz interlayer breathing-mode phonons, which directly modulates the exciton energy, leads to a uniquely strong phonon coupling to single-photon emission, with a Huang-Rhys factor reaching up to 6.3. The single-photon spectrum of interlayer exciton emission features a single-photon purity >83% and multiple phonon replicas, each heralding the creation of a phonon Fock state in the quantum emitter. Due to the vertical dipole moment of the interlayer exciton, the phonon-photon interaction is electrically tunable to be higher than the exciton and phonon decoherence rate, and hence promises to reach the strong-coupling regime. Our result demonstrates a solid-state quantum excitonic-optomechanical system at the atomic interface of the WSe2 bilayer that emits flying photonic qubits coupled with stationary phonons, which could be exploited for quantum transduction and interconnection.

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.

Electrical control of hybrid exciton transport in a van der Waals heterostructure

Interactions between out-of-plane dipoles in bosonic gases enable the long-range propagation of excitons. The lack of direct control over collective dipolar properties has so far limited the degrees of tunability and the microscopic understanding of exciton transport. In this work we modulate the layer hybridization and interplay between many-body interactions of excitons in a van der Waals heterostructure with an applied vertical electric field. By performing spatiotemporally resolved measurements supported by microscopic theory, we uncover the dipole-dependent properties and transport of excitons with different degrees of hybridization. Moreover, we find constant emission quantum yields of the transporting species as a function of excitation power with radiative decay mechanisms dominating over nonradiative ones, a fundamental requirement for efficient excitonic devices. Our findings provide a complete picture of the many-body effects in the transport of dilute exciton gases, and have crucial implications for studying emerging states of matter such as Bose-Einstein condensation and optoelectronic applications based on exciton propagation.

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.

Distinctive g-Factor of Moiré-Confined Excitons in van der Waals Heterostructures

We investigated the valley Zeeman splitting of excitonic peaks in the microphotoluminescence (μPL) spectra of high-quality hBN/WS₂/MoSe₂/hBN heterostructures under perpendicular magnetic fields up to 20 T. We identify two neutral exciton peaks in the μPL spectra; the lower-energy peak exhibits a reduced g-factor relative to that of the higher energy peak and much lower than the recently reported values for interlayer excitons in other van der Waals (vdW) heterostructures. We provide evidence that such a discernible g-factor stems from the spatial confinement of the exciton in the potential landscape created by the moiré pattern due to lattice mismatch or interlayer twist in heterobilayers. This renders magneto-μPL an important tool to reach a deeper understanding of the effect of moiré patterns on excitonic confinement in vdW heterostructures.

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.

A tunable bilayer Hubbard model in twisted WSe2

Moiré materials with flat electronic bands provide a highly controllable quantum system for studies of strong-correlation physics and topology. In particular, angle-aligned heterobilayers of semiconducting transition metal dichalcogenides with large band offset realize the single-band Hubbard model. Introduction of a new layer degree of freedom is expected to foster richer interactions, enabling Hund's physics, interlayer exciton condensation and new superconducting pairing mechanisms to name a few. Here we report competing electronic states in twisted AB-homobilayer WSe₂, which realizes a bilayer Hubbard model in the weak interlayer hopping limit for holes. By layer-polarizing holes via a perpendicular electric field, we observe a crossover from an excitonic insulator to a charge-transfer insulator at a hole density of ν = 1 (in units of moiré density), a transition from a paramagnetic to an antiferromagnetic charge-transfer insulator at ν = 2 and evidence for a layer-selective Mott insulator at 1 < ν < 2. The unique coupling of charge and spin to external electric and magnetic fields also manifests a giant magnetoelectric response. Our results establish a new solid-state simulator for the bilayer Hubbard model Hamiltonian.

Dielectric catastrophe at the Wigner-Mott transition in a moiré superlattice

The bandwidth-tuned Wigner-Mott transition is an interaction-driven phase transition from a generalized Wigner crystal to a Fermi liquid. Because the transition is generally accompanied by both magnetic and charge-order instabilities, it remains unclear if a continuous Wigner-Mott transition exists. Here, we demonstrate bandwidth-tuned metal-insulator transitions at fixed fractional fillings of a MoSe2/WS2 moiré superlattice. The bandwidth is controlled by an out-of-plane electric field. The dielectric response is probed optically with the 2s exciton in a remote WSe2 sensor layer. The exciton spectral weight is negligible for the metallic state with a large negative dielectric constant. It continuously vanishes when the transition is approached from the insulating side, corresponding to a diverging dielectric constant or a 'dielectric catastrophe' driven by the critical charge dynamics near the transition. Our results support the scenario of continuous Wigner-Mott transitions in two-dimensional triangular lattices and stimulate future explorations of exotic quantum phases in their vicinities.

Anomalous Magneto-Optical Response and Chiral Interface of Dipolar Excitons at Twisted Valleys

An anomalous magneto-optical spectrum is discovered for dipolar valley excitons in twisted double-layer transition metal dichalcogenides, where the in-plane magnetic field induces a sizable multiplet splitting of exciton states inside the light cone. Chiral dispersions of the split branches make possible an efficient optical injection of the unidirectional exciton current. We also find an analog effect with a modest heterostrain replacing the magnetic field for introducing large splitting and chiral dispersions in the light cone. Angular orientation of the photoinjected exciton flow can be controlled by strain, with left-right unidirectionality selected by circular polarization.

Semiconductor moiré materials

Moiré materials have emerged as a platform for exploring the physics of strong electronic correlations and non-trivial band topology. Here we review the recent progress in semiconductor moiré materials, with a particular focus on transition metal dichalcogenides. Following a brief overview of the general features in this class of materials, we discuss recent theoretical and experimental studies on Hubbard physics, Kane-Mele-Hubbard physics and equilibrium moiré excitons. We also comment on the future opportunities and challenges in the studies of transition metal dichalcogenide and other semiconductor moiré materials.

Moiré-Induced Optical Nonlinearities: Single- and Multiphoton Resonances

Moiré excitons promise a new platform with which to generate and manipulate hybrid quantum phases of light and matter in unprecedented regimes of interaction strength. We explore the properties in this regime, through studies of a Bose-Hubbard model of excitons coupled to cavity photons. We show that the steady states exhibit a rich phase diagram with pronounced bistabilities governed by multiphoton resonances reflecting the strong interexciton interactions. In the presence of an incoherent pumping of excitons we find that the system can realize single- and multiphoton lasers.

Scalable Moiré Lattice with Oriented TMD Monolayers

Moiré lattice in artificially stacked monolayers of two-dimensional (2D) materials effectively modulates the electronic structures of materials, which is widely highlighted. Formation of the electronic Moiré superlattice promises the prospect of uniformity among different moiré cells across the lattice, enabling a new platform for novel properties, such as unconventional superconductivity, and scalable quantum emitters. Recently, epitaxial growth of the monolayer transition metal dichalcogenide (TMD) is achieved on the sapphire substrate by chemical vapor deposition (CVD) to realize scalable growth of highly-oriented monolayers. However, fabrication of the scalable Moiré lattice remains challenging due to the lack of essential manipulation of the well-aligned monolayers for clean interface quality and precise twisting angle control. Here, scalable and highly-oriented monolayers of TMD are realized on the sapphire substrates by using the customized CVD process. Controlled growth of the epitaxial monolayers is achieved by promoting the rotation of the nuclei-like domains in the initial growth stage, enabling aligned domains for further grain growth in the steady-state stage. A full coverage and distribution of the highly-oriented domains are verified by second-harmonic generation (SHG) microscopy. By developing the method for clean monolayer manipulation, hetero-stacked bilayer (epi-WS₂/epi-MoS₂) is fabricated with the specific angular alignment of the two major oriented monolayers at the edge direction of 0°/ ± 60°. On account of the optimization for scalable Moiré lattice with a high-quality interface, the observation of interlayer exciton at low temperature illustrates the feasibility of scalable Moiré superlattice based on the oriented monolayers.

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.

Interlayer electronic coupling on demand in a 2D magnetic semiconductor

When monolayers of two-dimensional (2D) materials are stacked into van der Waals structures, interlayer electronic coupling can introduce entirely new properties, as exemplified by recent discoveries of moiré bands that host highly correlated electronic states and quantum dot-like interlayer exciton lattices. Here we show the magnetic control of interlayer electronic coupling, as manifested in tunable excitonic transitions, in an A-type antiferromagnetic 2D semiconductor CrSBr. Excitonic transitions in bilayers and above can be drastically changed when the magnetic order is switched from the layered antiferromagnetic ground state to a field-induced ferromagnetic state, an effect attributed to the spin-allowed interlayer hybridization of electron and hole orbitals in the latter, as revealed by Green's function-Bethe-Salpeter equation (GW-BSE) calculations. Our work uncovers a magnetic approach to engineer electronic and excitonic effects in layered magnetic semiconductors.

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.

Steering Room-Temperature Plexcitonic Strong Coupling: A Diexcitonic Perspective

Plexcitonic strong coupling between a plasmon-polariton and a quantum emitter empowers ultrafast quantum manipulations in the nanoscale under ambient conditions. The main body of previous studies deals with homogeneous quantum emitters. To enable multiqubit states for future quantum computing and network, the strong coupling involving two excitons of the same material but different resonant energies has been investigated and observed primarily at very low temperature. Here, we report a room-temperature diexcitonic strong coupling (DiSC) nanosystem in which the excitons of a transition metal dichalcogenide monolayer and dye molecules are both strongly coupled to a single Au nanocube. Coherent information exchange in this DiSC nanosystem could be observed even when exciton energy detuning is about five times larger than the respective line widths. The strong coupling behaviors in such a DiSC nanosystem can be manipulated by tuning the plasmon resonant energies and the coupling strengths, opening up a paradigm of controlling plasmon-assisted coherent energy transfer.

Moiré trions in MoSe2/WSe2 heterobilayers

Transition metal dichalcogenide moiré bilayers with spatially periodic potentials have emerged as a highly tunable platform for studying both electronic^1-6 and excitonic^4,7-13 phenomena. The power of these systems lies in the combination of strong Coulomb interactions with the capability of controlling the charge number in a moiré potential trap. Electronically, exotic charge orders at both integer and fractional fillings have been discovered^2,5. However, the impact of charging effects on excitons trapped in moiré potentials is poorly understood. Here, we report the observation of moiré trions and their doping-dependent photoluminescence polarization in H-stacked MoSe₂/WSe₂ heterobilayers. We find that as moiré traps are filled with either electrons or holes, new sets of interlayer exciton photoluminescence peaks with narrow linewidths emerge about 7 meV below the energy of the neutral moiré excitons. Circularly polarized photoluminescence reveals switching from co-circular to cross-circular polarizations as moiré excitons go from being negatively charged and neutral to positively charged. This switching results from the competition between valley-flip and spin-flip energy relaxation pathways of photo-excited electrons during interlayer trion formation. Our results offer a starting point for engineering both bosonic and fermionic many-body effects based on moiré excitons¹⁴.

WS2 moiré superlattices derived from mechanical flexibility for hydrogen evolution reaction

The discovery of moiré superlattices (MSLs) opened an era in the research of ‘twistronics’. Engineering MSLs and realizing unique emergent properties are key challenges. Herein, we demonstrate an effective synthetic strategy to fabricate MSLs based on mechanical flexibility of WS₂ nanobelts by a facile one-step hydrothermal method. Unlike previous MSLs typically created through stacking monolayers together with complicated method, WS₂ MSLs reported here could be obtained directly during synthesis of nanobelts driven by the mechanical instability. Emergent properties are found including superior conductivity, special superaerophobicity and superhydrophilicity, and strongly enhanced electro-catalytic activity when we apply ‘twistronics’ to the field of catalytic hydrogen production. Theoretical calculations show that such excellent catalytic performance could be attributed to a closer to thermoneutral hydrogen adsorption free energy value of twisted bilayers active sites. Our findings provide an exciting opportunity to design advanced WS₂ catalysts through moiré superlattice engineering based on mechanical flexibility.

Expanding the available materials with moiré superlattices is interesting but also challenging. Here the authors use a one-step hydrothermal approach to synthesis WS₂ moiré superlattices with high catalytic activity for hydrogen evolution reaction

Excitonic and Valley-Polarization Signatures of Fractional Correlated Electronic Phases in a WSe_{2}/WS_{2} Moiré Superlattice

We have measured the reflectance contrast, photoluminescence, and valley polarization of a WSe_{2}/WS_{2} heterobilayer moiré superlattice at gate-tunable charge density. We observe absorption modulation of three intralayer moiré excitons at filling factors ν=1/3 and 2/3. We also observe luminescence modulation of interlayer trions at around a dozen fractional filling factors, including ν=-3/2, 1/4, 1/3, 2/5, 2/3, 6/7, 5/3. Remarkably, the valley polarization of interlayer trions is suppressed at some fractional fillings. These results demonstrate that electron crystallization can modulate the absorption, emission, and valley dynamics of the excitonic states in a moiré superlattice.

A High-Efficiency Wavelength-Tunable Monolayer LED with Hybrid Continuous-Pulsed Injection

High-efficiency and wavelength-tunable light-emitting diode (LED) devices will play an important role in future advanced optoelectronic systems. Traditional semiconductor LED devices typically have a fixed emission wavelength that is determined by the energy of the emission states. Here, a novel high-efficiency and wavelength-tunable monolayer WS₂ LED device, which operates in the hybrid mode of continuous-pulsed injection, is developed. This hybrid injection enables highly enhanced emission efficiency (>20 times) and effective size of emission area (>5 times) at room temperature. The emission wavelength of the WS₂ monolayer LED device can be tuned over more than 40 nm by driving AC voltages, from exciton emission to trion emission, and further to defect emission. The quantum efficiency of defect electroluminescence (EL) emission is measured to be more than 24.5 times larger than that from free exciton and trion EL emission. The separate carrier injection in the LED also demonstrates advantages in allowing defect species to be visualized and distinguished in real space. Those defects are assigned to be negatively charged defects. The results open a new route to develop high-performance and wavelength-tunable LED devices for future advanced optoelectronic applications.

Van der Waals heterostructure polaritons with moiré-induced nonlinearity

Controlling matter-light interactions with cavities is of fundamental importance in modern science and technology¹. This is exemplified in the strong-coupling regime, where matter-light hybrid modes form, with properties that are controllable by optical-wavelength photons^2,3. By contrast, matter excitations on the nanometre scale are harder to access. In two-dimensional van der Waals heterostructures, a tunable moiré lattice potential for electronic excitations may form⁴, enabling the generation of correlated electron gases in the lattice potentials^5-9. Excitons confined in moiré lattices have also been reported^10,11, but no cooperative effects have been observed and interactions with light have remained perturbative^12-15. Here, by integrating MoSe₂-WS₂ heterobilayers in a microcavity, we establish cooperative coupling between moiré-lattice excitons and microcavity photons up to the temperature of liquid nitrogen, thereby integrating versatile control of both matter and light into one platform. The density dependence of the moiré polaritons reveals strong nonlinearity due to exciton blockade, suppressed exciton energy shift and suppressed excitation-induced dephasing, all of which are consistent with the quantum confined nature of the moiré excitons. Such a moiré polariton system combines strong nonlinearity and microscopic-scale tuning of matter excitations using cavity engineering and long-range light coherence, providing a platform with which to study collective phenomena from tunable arrays of quantum emitters.