Twist-angle dependence of moiré excitons in WS2/MoSe2 heterobilayers

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

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

Nonlinear physics of moiré superlattices

Nonlinear physics is one of the most important research fields in modern physics and materials science. It offers an unprecedented paradigm for exploring many fascinating physical phenomena and realizing diverse cutting-edge applications inconceivable in the framework of linear processes. Here we review the recent theoretical and experimental progress concerning the nonlinear physics of synthetic quantum moiré superlattices. We focus on the emerging nonlinear electronic, optical and optoelectronic properties of moiré superlattices, including but not limited to the nonlinear anomalous Hall effect, dynamically twistable harmonic generation, nonlinear optical chirality, ultralow-power-threshold optical solitons and spontaneous photogalvanic effect. We also present our perspectives on the future opportunities and challenges in this rapidly progressing field, and highlight the implications for advances in both fundamental physics and technological innovations.

Homo-Site Nucleation Growth of Twisted Bilayer MoS2 with Commensurate Angles

Moiré superlattices, composed of two layers of transition metal dichalcogenides with a relative twist angle, provide a novel platform for exploring the correlated electronic phases and excitonic physics. Here, a gas-flow perturbation chemical vapor deposition (CVD) approach is demonstrated to directly grow MoS2 bilayer with versatile twist angles. It is found that the formation of twisted bilayer MoS2 homostructures sensitively depends on the gas-flow perturbation modes, correspondingly featuring the nucleation sites of the second layer at the same (homo-site) as or at the different (hetero-site) from that of the first layer. The commensurate twist angle of ≈22° in homo-site nucleation strategy accounts for ≈16% among the broad range of twist angles due to its low formation energy, which is in consistence with the theoretical calculation. More importantly, moiré interlayer excitons with the enhanced photoluminescence (PL) intensity and the prolonged lifetime are evidenced in the twisted bilayer MoS2 with a commensurate angle of 22°, which is owing to the reason that the strong moiré potential facilitates the interlayer excitons to be trapped in the moiré superlattices. The work provides a feasible route to controllably built twisted MoS2 homostructures with strong moiré potential to investigate the correlated physics in twistronics systems.

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.

A Deterministic Method to Construct a Common Supercell Between Two Similar Crystalline Surfaces

Here, a deterministic algorithm is proposed, that is capable of constructing a common supercell between two similar crystalline surfaces without scanning all possible cases. Using the complex plane, the 2D lattice is defined as the 2D complex vector. Then, the relationship between two surfaces becomes the eigenvector-eigenvalue relation where an operator corresponds to a transformation matrix. It is shown that this transformation matrix can be directly determined from the lattice parameters and rotation angle of the two given crystalline surfaces with O(log Nmax) time complexity, where Nmax is the maximum index of repetition matrix elements. This process is much faster than the conventional brute force approach (O ( N max 4 ) $O(N_{\mathrm{max}}^4)$ ). By implementing the method in Python code, experimental 2D heterostructures and their moiré patterns and additionally find new moiré patterns that have not yet been reported are successfully generated. According to the density functional theory (DFT) calculations, some of the new moiré patterns are expected to be as stable as experimentally-observed moiré patterns. Taken together, it is believed that the method can be widely applied as a useful tool for designing new heterostructures with interesting properties.

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.

High Efficiency of Exciton-Polariton Lasing in a 2D Multilayer Structure

We have placed a van der Waals homostructure, formed by stacking three two-dimensional layers of WS2 separated by insulating hBN, similar to a multiple-quantum well structure, inside a microcavity, which facilitates the formation of quasiparticles known as exciton-polaritons. The polaritons are a combination of light and matter, allowing laser emission to be enhanced by nonlinear scattering, as seen in prior polariton lasers. In the experiments reported here, we have observed laser emission with an ultralow threshold. The threshold was approximately 59 nW/μm2, with a lasing efficiency of 3.82%. These findings suggest a potential for efficient laser operations using such homostructures.

Emergence of Optical Anisotropy in Moiré Superlattice via Heterointerface Engineering

The interaction between light and moiré superlattices presents a platform for exploring unique light-matter phenomena. Tailoring these optical properties holds immense potential for advancing the utilization of moiré superlattices in photonics, optoelectronics, and valleytronics. However, the control of the optical polarization state in moiré superlattices, particularly in the presence of moiré effects, remains elusive. Here, we unveil the emergence of optical anisotropy in moiré superlattices by constructing twisted WSe2/WSe2/SiP heterostructures. We report a linear polarization degree of ∼70% for moiré excitons, attributed to the spatially nonuniform charge distribution, corroborated by first-principles calculations. Furthermore, we demonstrate the modulation of this linear polarization state via the application of a magnetic field, resulting in polarization angle rotation and a magnetic-field-dependent linear polarization degree, influenced by valley coherence and moiré potential effects. Our findings demonstrate an efficient strategy for tuning the optical polarization state of moiré superlattices using heterointerface engineering.

Chirality-Dependent Valley Polarization in Magnetic van der Waals Heterostructures via Spin-Selective Charge Transfer

Magnetic proximity interaction provides a promising route to manipulate the spin and valley degrees of freedom in van der Waals heterostructures. Here, we report a control of valley pseudospin in the WS2/MoSe2 heterostructure by utilizing the magnetic proximity effect of few-layered CrBr3 and, for the first time, observe a substantial difference in valley polarization of intra/interlayer excitons under different circularly polarized laser excitations, referred to as chirality-dependent valley polarization. Theoretical and experimental results reveal that the spin-selective charge transfer between MoSe2 and CrBr3, as well as between MoSe2 and WS2, is mostly responsible for the chiral feature of valley polarization in comparison with the proximity exchange field. This means that a long-distance manipulation of exciton behaviors in multilayer heterostructures can be achieved through spin-selective charge transfer. This work marks a significant advancement in the control of spin and valley pseudospin in multilayer structures.

Exciton Localization Modulated by Ultradeep Moiré Potential in Twisted Bilayer γ-Graphdiyne

Twisted moiré superlattice is featured with its moiré potential energy, the depth of which renders an effective approach to strengthening the exciton-exciton interaction and exciton localization toward high-performance quantum photonic devices. However, it remains as a long-standing challenge to further push the limit of moiré potential depth. Herein, owing to the pz orbital induced band edge states enabled by the unique sp-C in bilayer γ-graphdiyne (GDY), an ultradeep moiré potential of ∼289 meV is yielded. After being twisted into the hole-to-hole layer stacking configuration, the interlayer coupling is substantially intensified to augment the lattice potential of bilayer GDY up to 475%. The presence of lateral constrained moiré potential shifts the spatial distribution of electrons and holes in excitons from the regular alternating mode to their respective separated and localized mode. According to the well-established wave function distribution of electrons contained in excitons, the AA-stacked site is identified to serve for exciton localization. This work extends the materials systems available for moiré superlattice design further to serial carbon allotropes featured with benzene ring-alkyne chain coupling, unlocking tremendous potential for twistronic-based quantum device applications.

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.

Twisted van der Waals Quantum Materials: Fundamentals, Tunability, and Applications

Twisted van der Waals (vdW) quantum materials have emerged as a rapidly developing field of two-dimensional (2D) semiconductors. These materials establish a new central research area and provide a promising platform for studying quantum phenomena and investigating the engineering of novel optoelectronic properties such as single photon emission, nonlinear optical response, magnon physics, and topological superconductivity. These captivating electronic and optical properties result from, and can be tailored by, the interlayer coupling using moiré patterns formed by vertically stacking atomic layers with controlled angle misorientation or lattice mismatch. Their outstanding properties and the high degree of tunability position them as compelling building blocks for both compact quantum-enabled devices and classical optoelectronics. This paper offers a comprehensive review of recent advancements in the understanding and manipulation of twisted van der Waals structures and presents a survey of the state-of-the-art research on moiré superlattices, encompassing interdisciplinary interests. It delves into fundamental theories, synthesis and fabrication, and visualization techniques, and the wide range of novel physical phenomena exhibited by these structures, with a focus on their potential for practical device integration in applications ranging from quantum information to biosensors, and including classical optoelectronics such as modulators, light emitting diodes, lasers, and photodetectors. It highlights the unique ability of moiré superlattices to connect multiple disciplines, covering chemistry, electronics, optics, photonics, magnetism, topological and quantum physics. This comprehensive review provides a valuable resource for researchers interested in moiré superlattices, shedding light on their fundamental characteristics and their potential for transformative applications in various fields.

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}.

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

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

Properties of Layered TMDC Superlattices for Electrodes in Li-Ion and Mg-Ion Batteries

In this work, we present a first-principles investigation of the properties of superlattices made from transition metal dichalcogenides for use as electrodes in lithium-ion and magnesium-ion batteries. From a study of 50 pairings, we show that, in general, the volumetric expansion, intercalation voltages, and thermodynamic stability of vdW superlattice structures can be well approximated with the average value of the equivalent property for the component layers. We also found that the band gap can be reduced, improving the conductivity. Thus, we conclude that superlattice construction can be used to improve material properties through the tuning of intercalation voltages toward specific values and by increasing the stability of conversion-susceptible materials. For example, we demonstrate how pairing SnS2 with systems such as MoS2 can change it from a conversion to an intercalation material, thus opening it up for use in intercalation electrodes.

Tuning commensurability in twisted van der Waals bilayers

Moiré superlattices based on van der Waals bilayers1-4 created at small twist angles lead to a long wavelength pattern with approximate translational symmetry. At large twist angles (θt), moiré patterns are, in general, incommensurate except for a few discrete angles. Here we show that large-angle twisted bilayers offer distinctly different platforms. More specifically, by using twisted tungsten diselenide bilayers, we create the incommensurate dodecagon quasicrystals at θt = 30° and the commensurate moiré crystals at θt = 21.8° and 38.2°. Valley-resolved scanning tunnelling spectroscopy shows disparate behaviours between moiré crystals (with translational symmetry) and quasicrystals (with broken translational symmetry). In particular, the K valley shows rich electronic structures exemplified by the formation of mini-gaps near the valence band maximum. These discoveries demonstrate that bilayers with large twist angles offer a design platform to explore moiré physics beyond those formed with small twist angles.

Strongly Localized Moiré Exciton in Twisted Homobilayers

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

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.

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.

Remarkably Deep Moiré Potential for Intralayer Excitons in MoSe2/MoS2 Twisted Heterobilayers

A moiré superlattice formed in twisted van der Waals bilayers has emerged as a new tuning knob for creating new electronic states in two-dimensional materials. Excitonic properties can also be altered drastically due to the presence of moiré potential. However, quantifying the moiré potential for excitons is nontrivial. By creating a large ensemble of MoSe₂/MoS₂ heterobilayers with a systematic variation of twist angles, we map out the minibands of interlayer and intralayer excitons as a function of twist angles, from which we determine the moiré potential for excitons. Surprisingly, the moiré potential depth for intralayer excitons is up to ∼130 meV, comparable to that for interlayer excitons. This result is markedly different from theoretical calculations based on density functional theory, which show an order of magnitude smaller moiré potential for intralayer excitons. The remarkably deep intralayer moiré potential is understood within the framework of structural reconstruction within the moiré unit cell.

Electric Field and Strain Tuning of 2D Semiconductor van der Waals Heterostructures for Tunnel Field-Effect Transistors

Heterostacks consisting of low-dimensional materials are attractive candidates for future electronic nanodevices in the post-silicon era. In this paper, using first-principles calculations based on density functional theory (DFT), we explore the structural and electronic properties of MoTe₂/ZrS₂ heterostructures with various stacking patterns and thicknesses. Our simulations show that the valence band (VB) edge of MoTe₂ is almost aligned with the conduction band (CB) edge of ZrS₂, and (MoTe₂)_m/(ZrS₂)_m (m = 1, 2) heterostructures exhibit the long-sought broken gap band alignment, which is pivotal for realizing tunneling transistors. Electrons are found to spontaneously flow from MoTe₂ to ZrS₂, and the system resembles an ultrascaled parallel plate capacitor with an intrinsic electric field pointed from MoTe₂ to ZrS₂. The effects of strain and external electric fields on the electronic properties are also investigated. For vertical compressive strains, the charge transfer increases due to the decreased coupling between the layers, whereas tensile strains lead to the opposite behavior. For negative electric fields a transition from the type-III to the type-II band alignment is induced. In contrast, by increasing the positive electric fields, a larger overlap between the valence and conduction bands is observed, leading to a larger band-to-band tunneling (BTBT) current. Low-strained heterostructures with various rotation angles between the constituent layers are also considered. We find only small variations in the energies of the VB and CB edges with respect to the Fermi level, for different rotation angles up to 30°. Overall, our simulations offer insights into the fundamental properties of low-dimensional heterostructures and pave the way for their future application in energy-efficient electronic nanodevices.

PVD growth of spiral pyramid-shaped WS2 on SiO2/Si driven by screw dislocations

Atomically thin layered transition metal dichalcogenides (TMDs), such as MoS₂ and WS₂, have been getting much attention recently due to their interesting electronic and optoelectronic properties. Especially, spiral TMDs provide a variety of candidates for examining the light-matter interaction resulting from the broken inversion symmetry, as well as the potential new utilization in functional optoelectronic, electromagnetic and nanoelectronics devices. To realize their potential device applications, it is desirable to achieve controlled growth of these layered nanomaterials with a tunable stacking. Here, we demonstrate the Physical Vapor Deposition (PVD) growth of spiral pyramid-shaped WS₂ with ∼200  μ m in size and the interesting optical properties via AFM and Raman spectroscopy. By controlling the precursors concentration and changing the initial nucleation rates in PVD growth, WS₂ in different nanoarchitectures can be obtained. We discuss the growth mechanism for these spiral-patterned WS₂ nanostructures based on the screw dislocations. This study provides a simple, scalable approach of screw dislocation-driven (SDD) growth of distinct TMD nanostructures with varying morphologies, and stacking.

Torsional periodic lattice distortions and diffraction of twisted 2D materials

Twisted 2D materials form complex moiré structures that spontaneously reduce symmetry through picoscale deformation within a mesoscale lattice. We show twisted 2D materials contain a torsional displacement field comprised of three transverse periodic lattice distortions (PLD). The torsional PLD amplitude provides a single order parameter that concisely describes the structural complexity of twisted bilayer moirés. Moreover, the structure and amplitude of a torsional periodic lattice distortion is quantifiable using rudimentary electron diffraction methods sensitive to reciprocal space. In twisted bilayer graphene, the torsional PLD begins to form at angles below 3.89° and the amplitude reaches 8 pm around the magic angle of 1. 1°. At extremely low twist angles (e.g. below 0.25°) the amplitude increases and additional PLD harmonics arise to expand Bernal stacked domains separated by well defined solitonic boundaries. The torsional distortion field in twisted bilayer graphene is analytically described and has an upper bound of 22.6 pm. Similar torsional distortions are observed in twisted WS₂, CrI₃, and WSe₂/MoSe₂.

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.

One-Step Exfoliation Method for Plasmonic Activation of Large-Area 2D Crystals

Advanced exfoliation techniques are crucial for exploring the intrinsic properties and applications of 2D materials. Though the recently discovered Au-enhanced exfoliation technique provides an effective strategy for the preparation of large-scale 2D crystals, the high cost of gold hinders this method from being widely adopted in industrial applications. In addition, direct Au contact could significantly quench photoluminescence (PL) emission in 2D semiconductors. It is therefore crucial to find alternative metals that can replace gold to achieve efficient exfoliation of 2D materials. Here, the authors present a one-step Ag-assisted method that can efficiently exfoliate many large-area 2D monolayers, where the yield ratio is comparable to Au-enhanced exfoliation method. Differing from Au film, however, the surface roughness of as-prepared Ag films on SiO₂ /Si substrate is much higher, which facilitates the generation of surface plasmons resulting from the nanostructures formed on the rough Ag surface. More interestingly, the strong coupling between 2D semiconductor crystals (e.g., MoS₂ , MoSe₂ ) and Ag film leads to a unique PL enhancement that has not been observed in other mechanical exfoliation techniques, which can be mainly attributed to enhanced light-matter interaction as a result of extended propagation of surface plasmonic polariton (SPP). This work provides a lower-cost and universal Ag-assisted exfoliation method, while at the same time offering enhanced SPP-matter interactions.

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.

Valley Relaxation of the Moiré Excitons in a WSe2/MoSe2 Heterobilayer

The moiré superlattice consisting of lattice- or angular-mismatched van der Waals heterostructures drastically changes the physical properties of constituent atomically thin materials by confinement of the exciton by the moiré potential, which is promising for next-generation quantum optics. The moiré superlattice also affects the valley degrees of freedom of the monolayer transition-metal dichalcogenides (TMDs) and the valley-dependent optical selection rule, which results in the characteristic circular polarized light emission of the moiré exciton. However, the valley relaxation process of excitons in the moiré superlattice remains to be understood. Here, we studied valley relaxation of moiré excitons in a twisted WSe₂/MoSe₂ heterobilayer by circularly polarized photoluminescence and photoluminescence excitation (PLE) spectroscopy. The experimentally observed circularly polarized emission strongly depends on the excitation power density, which contrasts with the case of two-dimensional monolayer TMDs. The excitation power-dependent circularly polarized emission suggests the characteristic valley relaxation of the moiré exciton with a small density of states in zero-dimensional systems. In addition, the resonant PLE measurement reveals the intravalley relaxation process from the triplet to singlet state of the moiré exciton via Γ₅ phonon emission. Our findings clarified the valley relaxation of the moiré excitons, which would lead to the application of the circularly polarized quantum light emitter in twisted semiconducting heterobilayers.

Observation of moiré excitons in the twisted WS2/WS2 homostructure

Moiré superlattices offer a fascinating platform for designing the properties of optical excitons. The moiré pattern can generate an ordered exciton array in space, making it possible for topological excitons and quantum emitters. Recently, evidence of moiré excitons in the twisted heterostructures of TMDs has been widely reported. However, to date, the capture and investigation of moiré excitons in the twisted homostructure (T-HS) remain elusive. Here, we report the observation of moiré excitons in the WS₂/WS₂ T-HS with a twist angle of about 1.5°. The PL spectrum of the T-HS region shows many small peaks with nearly constant peak spacing, which is attributed to the reconstructed moiré potential generated by the reconstructed moiré pattern to confine the intralayer excitons, thereby forming an ordered moiré exciton array. Furthermore, we have studied the influence of temperature and laser power on the moiré excitons as well as the valley polarization of the moiré excitons. Our results provide a promising prospect for further exploration of artificial excitonic crystals and quantum emitters of TMD moiré patterns.

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.

Tunable Feshbach Resonances and Their Spectral Signatures in Bilayer Semiconductors

Feshbach resonances provide an invaluable tool in atomic physics, enabling precise control of interactions and the preparation of complex quantum phases of matter. Here, we theoretically analyze a solid-state analog of a Feshbach resonance in two dimensional semiconductor heterostructures. In the presence of interlayer electron tunneling, the scattering of excitons and electrons occupying different layers can be resonantly enhanced by tuning an applied electric field. The emergence of an interlayer Feshbach molecule modifies the optical excitation spectrum, and can be understood in terms of Fermi polaron formation. We discuss potential implications for the realization of correlated Bose-Fermi mixtures in bilayer semiconductors.

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.

Twist Angle Tuning of Moiré Exciton Polaritons in van der Waals Heterostructures

Twisted atomically thin semiconductors are characterized by moiré excitons. Their optical signatures and selection rules are well understood. However, their hybridization with photons in the strong coupling regime for heterostructures integrated in an optical cavity has not been the focus of research yet. Here, we combine an excitonic density matrix formalism with a Hopfield approach to provide microscopic insights into moiré exciton polaritons. In particular, we show that exciton-light coupling, polariton energy, and even the number of polariton branches can be controlled via the twist angle. We find that these new hybrid light-exciton states become delocalized relative to the constituent excitons due to the mixing with light and higher-energy excitons. The system can be interpreted as a natural quantum metamaterial with a periodicity that can be engineered via the twist angle. Our study presents a significant advance in microscopic understanding and control of moiré exciton polaritons in twisted atomically thin semiconductors.

Tunable Green Light-Emitting CsPbBr3 Based Perovskite-Nanocrystals-in-Glass Flexible Film Enables Production of Stable Backlight Display

Despite recent advances in producing perovskite-nanocrystals-in-glass (PNG) for display application, it remains challenging to achieve ultrapure and large-area CsPbBr₃ PNG-based flexible films with tunable green emission. Herein, we report a facile strategy to produce flexible film containing CsPbBr₃ PNG. Specifically, the achievement of CsPbBr₃ PNG with tunable green emissions (517-528 nm) is realized by elaborate regulation of the glass precursor concentration and thermal treatment temperature by an in situ growth method. With the integration of red-light-emitting CsPbBr_xI_3-x PNG powder, the color gamut of as-prepared white-light-emitting sources can cover up to 126.27% of the NTSC 1953 standard and 93.9% of the Rec. 2020 standard. Notably, flexible and large-area white-light-emitting films can be readily obtained by sandwiching and gluing mixed PNG powders between two layers of hydrophobic and transparent PET films. Intriguingly, as-prepared PNG films exhibit excellent hydrothermal, photostability, and long-term operation stability, making them promising for practical ultrahigh-definition displays.

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.

Enhanced light-matter interaction in two-dimensional transition metal dichalcogenides

Two-dimensional (2D) transition metal dichalcogenide (TMDC) materials, such as MoS₂, WS₂, MoSe₂, and WSe₂, have received extensive attention in the past decade due to their extraordinary electronic, optical and thermal properties. They evolve from indirect bandgap semiconductors to direct bandgap semiconductors while their layer number is reduced from a few layers to a monolayer limit. Consequently, there is strong photoluminescence in a monolayer (1L) TMDC due to the large quantum yield. Moreover, such monolayer semiconductors have two other exciting properties: large binding energy of excitons and valley polarization. These properties make them become ideal materials for various electronic, photonic and optoelectronic devices. However, their performance is limited by the relatively weak light-matter interactions due to their atomically thin form factor. Resonant nanophotonic structures provide a viable way to address this issue and enhance light-matter interactions in 2D TMDCs. Here, we provide an overview of this research area, showcasing relevant applications, including exotic light emission, absorption and scattering features. We start by overviewing the concept of excitons in 1L-TMDC and the fundamental theory of cavity-enhanced emission, followed by a discussion on the recent progress of enhanced light emission, strong coupling and valleytronics. The atomically thin nature of 1L-TMDC enables a broad range of ways to tune its electric and optical properties. Thus, we continue by reviewing advances in TMDC-based tunable photonic devices. Next, we survey the recent progress in enhanced light absorption over narrow and broad bandwidths using 1L or few-layer TMDCs, and their applications for photovoltaics and photodetectors. We also review recent efforts of engineering light scattering, e.g., inducing Fano resonances, wavefront engineering in 1L or few-layer TMDCs by either integrating resonant structures, such as plasmonic/Mie resonant metasurfaces, or directly patterning monolayer/few layers TMDCs. We then overview the intriguing physical properties of different van der Waals heterostructures, and their applications in optoelectronic and photonic devices. Finally, we draw our opinion on potential opportunities and challenges in this rapidly developing field of research.

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.

Nonreciprocal Transport in a Bilayer of MnBi2Te4 and Pt

MnBi₂Te₄ (MBT) is the first intrinsic magnetic topological insulator with the interaction of spin-momentum locked surface electrons and intrinsic magnetism, and it exhibits novel magnetic and topological phenomena. Recent studies suggested that the interaction of electrons and magnetism can be affected by the Mn-doped Bi₂Te₃ phase at the surface due to inevitable structural defects. Here, we report an observation of nonreciprocal transport, that is, current-direction-dependent resistance, in a bilayer composed of antiferromagnetic MBT and nonmagnetic Pt. The emergence of the nonreciprocal response below the Néel temperature confirms a correlation between nonreciprocity and intrinsic magnetism in the surface state of MBT. The angular dependence of the nonreciprocal transport indicates that nonreciprocal response originates from the asymmetry scattering of electrons at the surface of MBT mediated by magnon. Our work provides an insight into nonreciprocity arising from the correlation between magnetism and Dirac surface electrons in intrinsic magnetic topological insulators.

Dirac Magic and Lifshitz Transitions in AA-Stacked Twisted Multilayer Graphene

We uncover a new type of magic-angle phenomena when an AA-stacked graphene bilayer is twisted relative to another graphene system with band touching. In the simplest case this constitutes a trilayer system formed by an AA-stacked bilayer twisted relative to a single layer of graphene. We find multiple anisotropic Dirac cones coexisting in such twisted multilayer structures at certain angles, which we call "Dirac magic." We trace the origin of Dirac magic angles to the geometric structure of the twisted AA-bilayer Dirac cones relative to the other band-touching spectrum in the moiré reciprocal lattice. The anisotropy of the Dirac cones and a concomitant cascade of saddle points induce a series of topological Lifshitz transitions that can be tuned by the twist angle and perpendicular electric field. We discuss the possibility of direct observation of Dirac magic as well as its consequences for the correlated states of electrons in this moiré system.

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.

Excitons and emergent quantum phenomena in stacked 2D semiconductors

The design and control of material interfaces is a foundational approach to realize technologically useful effects and engineer material properties. This is especially true for two-dimensional (2D) materials, where van der Waals stacking allows disparate materials to be freely stacked together to form highly customizable interfaces. This has underpinned a recent wave of discoveries based on excitons in stacked double layers of transition metal dichalcogenides (TMDs), the archetypal family of 2D semiconductors. In such double-layer structures, the elegant interplay of charge, spin and moiré superlattice structure with many-body effects gives rise to diverse excitonic phenomena and correlated physics. Here we review some of the recent discoveries that highlight the versatility of TMD double layers to explore quantum optics and many-body effects. We identify outstanding challenges in the field and present a roadmap for unlocking the full potential of excitonic physics in TMD double layers and beyond, such as incorporating newly discovered ferroelectric and magnetic materials to engineer symmetries and add a new level of control to these remarkable engineered materials.

Dynamic Tuning of Moiré Excitons in a WSe2/WS2 Heterostructure via Mechanical Deformation

Moiré superlattices in van der Waals (vdW) heterostructures form by stacking atomically thin layers on top of one another with a twist angle or lattice mismatch. The resulting moiré potential leads to a strong modification of the band structure, which can give rise to exotic quantum phenomena ranging from correlated insulators and superconductors to moiré excitons and Wigner crystals. Here, we demonstrate the dynamic tuning of moiré potential in a WSe₂/WS₂ heterostructure at cryogenic temperature. We utilize the optical fiber tip of a cryogenic scanning near-field optical microscope (SNOM) to locally deform the heterostructure and measure its near-field optical response simultaneously. The deformation of the heterostructure increases the moiré potential, which leads to a red shift of the moiré exciton resonances. We observe the interlayer exciton resonance shifts up to 20 meV, while the intralayer exciton resonances shift up to 17 meV.

Zitterbewegung of Moiré Excitons in Twisted MoS_{2}/WSe_{2} Heterobilayers

The moiré pattern observed in stacked noncommensurate crystal lattices, such as heterobilayers of transition metal dichalcogenides, produces a periodic modulation of their band gap. Excitons subjected to this potential landscape exhibit a band structure that gives rise to a quasiparticle dubbed the moiré exciton. In the case of MoS_{2}/WSe_{2} heterobilayers, the moiré trapping potential has honeycomb symmetry and, consequently, the moiré exciton band structure is the same as that of a Dirac-Weyl fermion, whose mass can be further tuned down to zero with a perpendicularly applied field. Here we show that, analogously to other Dirac-like particles, the moiré exciton exhibits a trembling motion, also known as Zitterbewegung, whose long timescales are compatible with current experimental techniques for exciton dynamics. This promotes the study of the dynamics of moiré excitons in van der Waals heterostructures as an advantageous solid-state platform to probe Zitterbewegung, broadly tunable by gating and interlayer twist angle.

Twisting of 2D Kagomé Sheets in Layered Intermetallics

Chemical bonding in 2D layered materials and van der Waals solids is central to understanding and harnessing their unique electronic, magnetic, optical, thermal, and superconducting properties. Here, we report the discovery of spontaneous, bidirectional, bilayer twisting (twist angle ∼4.5°) in the metallic kagomé MgCo₆Ge₆ at T = 100(2) K via X-ray diffraction measurements, enabled by the preparation of single crystals by the Laser Bridgman method. Despite the appearance of static twisting on cooling from T ∼300 to 100 K, no evidence for a phase transition was found in physical property measurements. Combined with the presence of an Einstein phonon mode contribution in the specific heat, this implies that the twisting exists at all temperatures but is thermally fluctuating at room temperature. Crystal Orbital Hamilton Population analysis demonstrates that the cooperative twisting between layers stabilizes the Co-kagomé network when coupled to strongly bonded and rigid (Ge₂) dimers that connect adjacent layers. Further modeling of the displacive disorder in the crystal structure shows the presence of a second, Mg-deficient, stacking sequence. This alternative stacking sequence also exhibits interlayer twisting, but with a different pattern, consistent with the change in electron count due to the removal of Mg. Magnetization, resistivity, and low-temperature specific heat measurements are all consistent with a Pauli paramagnetic, strongly correlated metal. Our results provide crucial insight into how chemical concepts lead to interesting electronic structures and behaviors in layered materials.

Resonant Coupling of a Moiré Exciton to a Phonon in a WSe2/MoSe2 Heterobilayer

Moiré patterns with an angular mismatch in van der Waals heterostructures are a fascinating platform to engineer optically generated excitonic properties. The moiré pattern can give rise to spatially ordered exciton ensembles, which offer the possibility for coherent quantum emitters and quantum simulation of many-body physics. The intriguing moiré exciton properties are affected by their dynamics and exciton-phonon interaction. Here, we report the moiré exciton and phonon interaction in a twisted WSe₂/MoSe₂ heterobilayer. By tuning the excitation energy, we realized the selective excitation of the moiré exciton at phonon resonances and the otherwise negligible small absorption. Furthermore, we revealed the relaxation of moiré exciton ensembles between different potential minima via the resonant phonon scattering process. Our findings highlight resonant coupling of a moiré exciton to a phonon and could pave a new way for the exploration of novel quantum phenomena of the moiré exciton.

Observation of Strong Valley Magnetic Response in Monolayer Transition Metal Dichalcogenide Alloys of Mo0.5W0.5Se2 and Mo0.5W0.5Se2/WS2 Heterostructures

Monolayer transition metal dichalcogenide (TMD) alloys have emerged as a unique material system for promising applications in electronics, optoelectronics, and spintronics due to their tunable electronic structures, effective masses of carriers, and valley polarization with various alloy compositions. Although spin-orbit engineering has been extensively studied in monolayer TMD alloys, the valley Zeeman effect in these alloys still remains largely unexplored. Here we demonstrate the enhanced valley magnetic response in Mo_0.5W_0.5Se₂ alloy monolayers and Mo_0.5W_0.5Se₂/WS₂ heterostructures probed by magneto-photoluminescence spectroscopy. The large g factors of negatively charged excitons (trions) of Mo_0.5W_0.5Se₂ have been extracted for both pure Mo_0.5W_0.5Se₂ monolayers and Mo_0.5W_0.5Se₂/WS₂ heterostructures, which are attributed to the significant impact of doping-induced strong many-body Coulomb interactions on trion emissions under an out-of-plane magnetic field. Moreover, compared with the monolayer Mo_0.5W_0.5Se₂, the slightly reduced valley Zeeman splitting in Mo_0.5W_0.5Se₂/WS₂ is a consequence of the weakened exchange interaction arising from p-doping in Mo_0.5W_0.5Se₂ via interlayer charge transfer between Mo_0.5W_0.5Se₂ and WS₂. Such interlayer charge transfer further evidences the formation of type-II band alignment, in agreement with the density functional theory calculations. Our findings give insights into the spin-valley and interlayer coupling effects in monolayer TMD alloys and their heterostructures, which are essential to develop valleytronic applications based on the emerging family of TMD alloys.

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.