Twist Angle-Dependent Interlayer Exciton Lifetimes in van der Waals Heterostructures

Enhancement of Interlayer Exciton Emission in a TMDC Heterostructure via a Multi-Resonant Chirped Microresonator Upto Room Temperature

We report on multi-resonance chirped distributed Bragg reflector (DBR) microcavities. These systems are employed to investigate the light-mater interaction with both intra- and inter-layer excitons of transition metal dichalcogenide (TMDC) bilayer heterostructures. The chirped DBRs consisting of SiO2 and Si3N4 layers of gradually varying thickness exhibit a broad stopband with a width exceeding 600 nm. Importantly, the structures provide multiple resonances across a broad spectral range, which can be matched to resonances of the embedded TMDC heterostructures. Studying cavity-coupled emission of both intra- and inter-layer excitons from an integrated WSe2/MoSe2 heterostructure in a chirped microcavity system, an enhanced interlayer exciton emission with a Purcell factor of 6.67 ± 1.02 at 4 K is observed. The cavity-enhanced emission of the interlayer exciton is used to investigate its temperature-dependent luminescence lifetime of 60 ps at room temperature. The cavity system modestly suppresses intralayer exciton emission by intentional detuning, thereby promoting a higher IX population and enhancing cavity-coupled interlayer exciton emission. This approach provides an intriguing platform for future studies of energetically distant and confined excitons in different semiconducting materials, which paves the way for various applications such as microlasers and single-photon sources by enabling precise emission control and utilizing multimode resonance light-matter interaction.

Spatial Filtering of Interlayer Exciton Ground State in WSe2/MoS2 Heterobilayer

Long-life interlayer excitons (IXs) in transition metal dichalcogenide (TMD) heterostructure are promising for realizing excitonic condensates at high temperatures. Critical to this objective is to separate the IX ground state (the lowest energy of IX state) emission from other states' emissions. Filtering the IX ground state is also essential in uncovering the dynamics of correlated excitonic states, such as the excitonic Mott insulator. Here, we show that the IX ground state in the WSe2/MoS2 heterobilayer can be separated from other states by its spatial profile. The emissions from different moiré IX modes are identified by their different energies and spatial distributions, which fits well with the rate-diffusion model for cascading emission. Our results show spatial filtering of the ground state mode and enrich the toolbox to realize correlated states at elevated temperatures.

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.

Revealing the Optical Transition Properties of Interlayer Excitons in Defective WS2/WSe2 Heterobilayers

Manipulation of physical properties in multidimensional tunable moiré superlattice systems is a key focus in nanophotonics, especially for interlayer excitons (IXs) in two-dimensional materials. However, the impact of defects on IXs remains unclear. Here, we thoroughly study the optical properties of WS2/WSe2 heterobilayers with varying defect densities. Low-temperature photoluminescence (PL) characterizations reveal that the low-energy IXs are more susceptible to defects compared to the high-energy IXs. The low-energy IXs also show much faster PL quenching rate with temperature, faster peak width broadening rate with laser power, shorter lifetime, and lower circular polarization compared to the low-energy IXs in the region with fewer defects. These effects are attributed to the combined effects of increased electron scattering, exciton-phonon interactions, and nonradiative channels introduced by the defects. Our findings aid in optimizing moiré superlattice structures.

Anomalous Interlayer Exciton Diffusion in WS2/WSe2 Moiré Heterostructure

Stacking van der Waals crystals allows for the on-demand creation of a periodic potential landscape to tailor the transport of quasiparticle excitations. We investigate the diffusion of photoexcited electron-hole pairs, or excitons, at the interface of WS2/WSe2 van der Waals heterostructure over a wide range of temperatures. We observe the appearance of distinct interlayer excitons for parallel and antiparallel stacking and track their diffusion through spatially and temporally resolved photoluminescence spectroscopy from 30 to 250 K. While the measured exciton diffusivity decreases with temperature, it surprisingly plateaus below 90 K. Our observations cannot be explained by classical models like hopping in the moiré potential. A combination of ab initio theory and molecular dynamics simulations suggests that low-energy phonons arising from the mismatched lattices of moiré heterostructures, also known as phasons, play a key role in describing and understanding this anomalous behavior of exciton diffusion. Our observations indicate that the moiré potential landscape is dynamic down to very low temperatures and that the phason modes can enable efficient transport of energy in the form of excitons.

Twist angle-dependent valley polarization switching in heterostructures

The twist engineering of moiré superlattice in van der Waals heterostructures of transition metal dichalcogenides can manipulate valley physics of interlayer excitons (IXs), paving the way for next-generation valleytronic devices. However, the twist angle-dependent control of excitonic potential on valley polarization is not investigated so far in electrically controlled heterostructures and the physical mechanism underneath needs to be explored. Here, we demonstrate the dependence of both polarization switching and degree of valley polarization on the moiré period. We also find the mechanisms to reveal the modulation of twist angle on the exciton potential and the electron-hole exchange interaction, which elucidate the experimentally observed twist angle-dependent valley polarization of IXs. Furthermore, we realize the valley-addressable devices based on polarization switch. Our work demonstrates the manipulation of the valley polarization of IXs by tunning twist angle in electrically controlled heterostructures, which opens an avenue for electrically controlling the valley degrees of freedom in twistronic devices.

Excitonic Thermalization Bottleneck in Twisted TMD Heterostructures

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

Localisation-to-delocalisation transition of moiré excitons in WSe2/MoSe2 heterostructures

Moiré excitons (MXs) are electron-hole pairs localised by the periodic (moiré) potential forming in two-dimensional heterostructures (HSs). MXs can be exploited, e.g., for creating nanoscale-ordered quantum emitters and achieving or probing strongly correlated electronic phases at relatively high temperatures. Here, we studied the exciton properties of WSe2/MoSe2 HSs from T = 6 K to room temperature using time-resolved and continuous-wave micro-photoluminescence also under a magnetic field. The exciton dynamics and emission lineshape evolution with temperature show clear signatures that MXs de-trap from the moiré potential and turn into free interlayer excitons (IXs) for temperatures above 100 K. The MX-to-IX transition is also apparent from the exciton magnetic moment reversing its sign when the moiré potential is not capable of localising excitons at elevated temperatures. Concomitantly, the exciton formation and decay times reduce drastically. Thus, our findings establish the conditions for a truly confined nature of the exciton states in a moiré superlattice with increasing temperature and photo-generated carrier density.

Low-Frequency Raman Study of Large-Area Twisted Bilayers of WS2 Stacked by an Etchant-Free Transfer Method

Monolayer transition metal dichalcogenides have strong intracovalent bonding. When stacked in multilayers, however, weak van der Waals interactions dominate interlayer mechanical coupling and, thus, influence their lattice vibrations. This study presents the frequency evolution of interlayer phonons in twisted WS2 bilayers, highly subject to the twist angle. The twist angle between the layers is controlled to modulate the spacing between the layers, which, in turn, affects the interlayer coupling that is probed by Raman spectroscopy. The shifts of high-frequency E2g1 (Γ) and A1g (Γ) phonon modes and their frequency separations are dependent on the twist angle, reflecting the correlation between the interlayer mechanical coupling and twist angle. In this work, we fabricated large-area, twisted bilayer WS2 with a clean interface with controlled twist angles. Polarized Raman spectroscopy identified new interlayer modes, which were not previously reported, depending on the twist angle. The appearance of breathing modes in Raman phonon spectra provides evidence of strong interlayer coupling in bilayer structures. We confirm that the twist angle can alter the exciton and trion dynamics of bilayers as indicated by the photoluminescence peak shift. These large-area controlled twist angle samples have practical applications in optoelectronic device fabrication and twistronics.

Lasing of moiré trapped MoSe2/WSe2 interlayer excitons coupled to a nanocavity

We report lasing of moiré trapped interlayer excitons (IXs) by integrating a pristine hBN-encapsulated MoSe2/WSe2 heterobilayer into a high-Q (>104) nanophotonic cavity. We control the cavity-IX detuning using a magnetic field and measure their dipolar coupling strength to be 78 ± 4 micro-electron volts, fully consistent with the 82 micro-electron volts predicted by theory. The emission from the cavity mode shows clear threshold-like behavior as the transition is tuned into resonance with the cavity. We observe a superlinear power dependence accompanied by a narrowing of the linewidth as the distinct features of lasing. The onset and prominence of these threshold-like behaviors are pronounced at resonance while weak off-resonance. Our results show that a lasing transition can be induced in interacting moiré IXs with macroscopic coherence extending over the length scale of the cavity mode. Such systems raise interesting perspectives for low-power switching and synaptic nanophotonic devices using two-dimensional materials.

Synergetic Enhancement of Quantum Yield and Exciton Lifetime of Monolayer WS2 by Proximal Metal Plate and Negative Electric Bias

The efficiency of light emission is a critical performance factor for monolayer transition metal dichalcogenides (1L-TMDs) for photonic applications. While various methods have been studied to compensate for lattice defects to improve the quantum yield (QY) of 1L-TMDs, exciton-exciton annihilation (EEA) is still a major nonradiative decay channel for excitons at high exciton densities. Here, we demonstrate that the combined use of a proximal Au plate and a negative electric gate bias (NEGB) for 1L-WS2 provides a dramatic enhancement of the exciton lifetime at high exciton densities with the corresponding QY enhanced by 30 times and the EEA rate constant decreased by 80 times. The suppression of EEA by NEGB is attributed to the reduction of the defect-assisted EEA process, which we also explain with our theoretical model. Our results provide a synergetic solution to cope with EEA to realize high-intensity 2D light emitters using TMDs.

Coherent acoustic phonons in a coupled hexagonal boron nitride-graphite heterostructure

Femtosecond optically excited coherent acoustic phonon modes (CAPs) are investigated in a free-standing van der Waals heterostructure composed of a 20-nm transparent hexagonal boron nitride (hBN) and a 42-nm opaque graphite layer. Employing ultrafast electron diffraction, which allows for the independent evaluation of strain dynamics in the constituent material layers, three different CAP modes are identified within the bilayer stack after the optical excitation of the graphite layer. An analytical model is used to discuss the creation of individual CAP modes. Furthermore, their excitation mechanisms in the heterostructure are inferred from the relative phases of these modes by comparison with a numerical linear-chain model. The results support an ultrafast heat transfer mechanism from graphite to the hBN lattice system, which is important to consider when using this material combination in devices.

Electrostatic moiré potential from twisted hexagonal boron nitride layers

Moiré superlattices host a rich variety of correlated electronic phases. However, the moiré potential is fixed by interlayer coupling, and it is dependent on the nature of carriers and valleys. In contrast, it has been predicted that twisted hexagonal boron nitride (hBN) layers can impose a periodic electrostatic potential capable of engineering the properties of adjacent functional layers. Here, we show that this potential is described by a theory of electric polarization originating from the interfacial charge redistribution, validated by its dependence on supercell sizes and distance from the twisted interfaces. This enables controllability of the potential depth and profile by controlling the twist angles between the two interfaces. Employing this approach, we further demonstrate how the electrostatic potential from a twisted hBN substrate impedes exciton diffusion in semiconductor monolayers, suggesting opportunities for engineering the properties of adjacent functional layers using the surface potential of a twisted hBN substrate.

Probing the interlayer excitation dynamics in WS2/WSe2 heterostructures with broadly tunable pump and probe energies

van der Waals heterostructures based on transition metal dichalcogenides (TMDs) provide a fascinating platform for exploring new physical phenomena and novel optoelectronic functionalities. Revealing the energy-dependence of photocarrier population dynamics in heterostructures is key for developing optoelectronic or valleytronic devices. Here, the broadband transient dynamics of interlayer excitation of a nearly-aligned WS2/WSe2 heterostructure is investigated by using energy-dependent pump-probe spectroscopy at cryogenic temperatures. Interestingly, WS2/WSe2 interlayer excitation, herein comprising a mixture of intra- and inter-layer excitons, exhibits largely constant lifetimes of a few hundred picoseconds across a broad energy range, in stark contrast to the salient energy-dependent dynamics of intralayer excitons in monolayer WSe2. While the PL emission of the WS2/WSe2 heterostructure is found to be strongly affected by electrostatic doping, the lifetimes of interlayer excitation show negligible changes. Our work elaborates the signatures of ultrafast dynamics introduced by intra- and interlayer co-existing excitonic species and enriches the understanding of interlayer couplings in van der Waals heterostructures.

Substrate Ferroelectric Proximity Effects Have a Strong Influence on Charge Carrier Lifetime in Black Phosphorus

By stacking monolayer black phosphorus (MBP) with nonpolarized and ferroelectric polarized bilayer hexagonal boron nitride (h-BN), we demonstrate that ferroelectric proximity effects have a strong influence on the charge carrier lifetime of MBP using nonadiabatic (NA) molecular dynamics simulations. Through enhancing the motion of phosphorus atoms, ferroelectric polarization enhances the overlap of electron-hole wave functions that improves NA coupling and decreases the bandgap, resulting in a rapid electron-hole recombination completing within a quarter of nanoseconds, which is two times shorter than that in nonpolarized stackings. In addition to the dominant in-plane Ag2 mode in free-standing MBP, the out-of-plane high-frequency Ag1 and low-frequency interlayer breathing modes presented in the heterojunctions drive the recombination. Notably, the resonance between the breathing mode within bilayer h-BN and the B1u mode of MBP provides an additional nonradiative channel in ferroelectric stackings, further accelerating charge recombination. These findings are crucial for charge dynamics manipulation in two-dimensional materials via substrate ferroelectric proximity effects.

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.

Localization and interaction of interlayer excitons in MoSe2/WSe2 heterobilayers

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

Interlayer donor-acceptor pair excitons in MoSe2/WSe2 moiré heterobilayer

Localized interlayer excitons (LIXs) in two-dimensional moiré superlattices exhibit sharp and dense emission peaks, making them promising as highly tunable single-photon sources. However, the fundamental nature of these LIXs is still elusive. Here, we show the donor-acceptor pair (DAP) mechanism as one of the origins of these excitonic peaks. Numerical simulation results of the DAP model agree with the experimental photoluminescence spectra of LIX in the moiré MoSe2/WSe2 heterobilayer. In particular, we find that the emission energy-lifetime correlation and the nonmonotonic power dependence of the lifetime agree well with the DAP IX model. Our results provide insight into the physical mechanism of LIX formation in moiré heterostructures and pave new directions for engineering interlayer exciton properties in moiré superlattices.

Harmonic to anharmonic tuning of moiré potential leading to unconventional Stark effect and giant dipolar repulsion in WS2/WSe2 heterobilayer

Excitonic states trapped in harmonic moiré wells of twisted heterobilayers is an intriguing testbed for exploring many-body physics. However, the moiré potential is primarily governed by the twist angle, and its dynamic tuning remains a challenge. Here we demonstrate anharmonic tuning of moiré potential in a WS2/WSe2 heterobilayer through gate voltage and optical power. A gate voltage can result in a local in-plane perturbing field with odd parity around the high-symmetry points. This allows us to simultaneously observe the first (linear) and second (parabolic) order Stark shift for the ground state and first excited state, respectively, of the moiré trapped exciton - an effect opposite to conventional quantum-confined Stark shift. Depending on the degree of confinement, these excitons exhibit up to twenty-fold gate-tunability in the lifetime (100 to 5 ns). Also, exciton localization dependent dipolar repulsion leads to an optical power-induced blueshift of ~ 1 meV/μW - a five-fold enhancement over previous reports.

Dynamics of Moiré Trion and Its Valley Polarization in a Microfabricated WSe2/MoSe2 Heterobilayer

The moiré potential, induced by stacking two monolayer semiconductors with slightly different lattice mismatches, acts as periodic quantum confinement for optically generated excitons, resulting in spatially ordered zero-dimensional quantum systems. However, there are limitations to exploring intrinsic optical properties of moiré excitons due to ensemble emissions and broadened emissions from many peaks caused by the inhomogeneity of the moiré potential. In this study, we proposed a microfabrication technique based on focused Ga⁺ ion beams, which enables us to control the number of peaks originating from the moiré potential and thus explore unknown moiré optical characteristics of WSe₂/MoSe₂ heterobilayer. By taking advantage of this approach, we reveal emissions from a single moiré exciton and charged moiré exciton (trion) under electrostatic doping conditions. We show the momentum dark moiré trion state above the bright trion state with a splitting energy of approximately 4 meV and clarify that the dynamics are determined by the initial trion population in the bright state. Furthermore, the degree of negative circularly polarized emissions and their valley dynamics of moiré trions are dominated by a very long valley relaxation process lasting ∼700 ns. Our findings on microfabricated heterobilayer could be viewed as an extension of our groundbreaking efforts in the field of quantum optics application using moiré superlattices.

Fermi Pressure and Coulomb Repulsion Driven Rapid Hot Plasma Expansion in a van der Waals Heterostructure

Transition metal dichalcogenide heterostructures provide a versatile platform to explore electronic and excitonic phases. As the excitation density exceeds the critical Mott density, interlayer excitons are ionized into an electron-hole plasma phase. The transport of the highly non-equilibrium plasma is relevant for high-power optoelectronic devices but has not been carefully investigated previously. Here, we employ spatially resolved pump-probe microscopy to investigate the spatial-temporal dynamics of interlayer excitons and hot-plasma phase in a MoSe₂/WSe₂ twisted bilayer. At the excitation density of ∼10¹⁴ cm^-2, well exceeding the Mott density, we find a surprisingly rapid initial expansion of hot plasma to a few microns away from the excitation source within ∼0.2 ps. Microscopic theory reveals that this rapid expansion is mainly driven by Fermi pressure and Coulomb repulsion, while the hot carrier effect has only a minor effect in the plasma phase.

Layer-dependent correlated phases in WSe2/MoS2 moiré superlattice

Electron correlation plays an essential role in the macroscopic quantum phenomena in the moiré heterostructure, such as antiferromagnetism and correlated insulating phases. Unlike the phenomena where the interaction involves only electrons in one layer, the interaction of distinct phases in two or more layers represents a new horizon forward, such as the one in the Kondo lattice model. Here, using interlayer excitons as a probe, we show that the interlayer interactions in heterobilayers of tungsten diselenide and molybdenum disulfide (WSe₂/MoS₂) can be electrically switched on and off, resulting in a layer-dependent correlated phase diagram, including single-layer, layer-selective, excitonic-insulator and layer-hybridized regions. We demonstrate that these correlated phases affect the interlayer exciton non-radiative decay pathways. These results reveal the role of strong correlation on interlayer exciton dynamics and pave the way for studying the layer-resolved strong correlation behaviour in moiré heterostructures.

Complex Strain Scapes in Reconstructed Transition-Metal Dichalcogenide Moiré Superlattices

We investigate the intrinsic strain associated with the coupling of twisted MoS₂/MoSe₂ heterobilayers by combining experiments and molecular dynamics simulations. Our study reveals that small twist angles (between 0 and 2°) give rise to considerable atomic reconstructions, large moiré periodicities, and high levels of local strain (with an average value of ∼1%). Moreover, the formation of moiré superlattices is assisted by specific reconstructions of stacking domains. This process leads to a complex strain distribution characterized by a combined deformation state of uniaxial, biaxial, and shear components. Lattice reconstruction is hindered with larger twist angles (>10°) that produce moiré patterns of small periodicity and negligible strains. Polarization-dependent Raman experiments also evidence the presence of an intricate strain distribution in heterobilayers with near-0° twist angles through the splitting of the E_2g¹ mode of the top (MoS₂) layer due to atomic reconstruction. Detailed analyses of moiré patterns measured by AFM unveil varying degrees of anisotropy in the moiré superlattices due to the heterostrain induced during the stacking of monolayers.

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.

Preparation, properties and applications of two-dimensional superlattices

As a combination concept of a 2D material and a superlattice, two-dimensional superlattices (2DSs) have attracted increasing attention recently. The natural advantages of 2D materials in their properties, dimension, diversity and compatibility, and their gradually improved technologies for preparation and device fabrication serve as solid foundations for the development of 2DSs. Compared with the existing 2D materials and even their heterostructures, 2DSs relate to more materials and elaborate architectures, leading to novel systems with more degrees of freedom to modulate material properties at the nanoscale. Here, three typical types of 2DSs, including the component, strain-induced and moiré superlattices, are reviewed. The preparation methods, properties and state-of-the-art applications of each type are summarized. An outlook of the challenges and future developments is also presented. We hope that this work can provide a reference for the development of 2DS-related research.

Twist-Dependent Intra- and Interlayer Excitons in Moiré MoSe_{2} Homobilayers

Optoelectronic properties of van der Waals homostructures can be selectively engineered by the relative twist angle between layers. Here, we study the twist-dependent moiré coupling in MoSe_{2} homobilayers. For small angles, we find a pronounced redshift of the K-K and Γ-K excitons accompanied by a transition from K-K to Γ-K emission. Both effects can be traced back to the underlying moiré pattern in the MoSe_{2} homobilayers, as confirmed by our low-energy continuum model for different moiré excitons. We identify two distinct intralayer moiré excitons for R stacking, while H stacking yields two degenerate intralayer excitons due to inversion symmetry. In both cases, bright interlayer excitons are found at higher energies. The performed calculations are in excellent agreement with experiment and allow us to characterize the observed exciton resonances, providing insight about the layer composition and relevant stacking configuration of different moiré exciton species.

Charge Transfer Dynamics in MoSe2/hBN/WSe2 Heterostructures

Ultrafast charge transfer processes provide a facile way to create interlayer excitons in directly contacted transition metal dichalcogenide (TMD) layers. More sophisticated heterostructures composed of TMD/hBN/TMD enable new ways to control interlayer exciton properties and achieve novel exciton phenomena, such as exciton insulators and condensates, where longer lifetimes are desired. In this work, we experimentally study the charge transfer dynamics in a heterostructure composed of a 1 nm thick hBN spacer between MoSe₂ and WSe₂ monolayers. We observe the hole transfer from MoSe₂ to WSe₂ through the hBN barrier with a time constant of 500 ps, which is over 3 orders of magnitude slower than that between TMD layers without a spacer. Furthermore, we observe strong competition between the interlayer charge transfer and intralayer exciton-exciton annihilation processes at high excitation densities. Our work opens possibilities to understand charge transfer pathways in TMD/hBN/TMD heterostructures for the efficient generation and control of interlayer excitons.

Recent progress of two-dimensional heterostructures for thermoelectric applications

The rapid development of synthesis and fabrication techniques has opened up a research upsurge in two-dimensional (2D) material heterostructures, which have received extensive attention due to their superior physical and chemical properties. Currently, thermoelectric energy conversion is an effective means to deal with the energy crisis and increasingly serious environmental pollution. Therefore, an in-depth understanding of thermoelectric transport properties in 2D heterostructures is crucial for the development of micro-nano energy devices. In this review, the recent progress of 2D heterostructures for thermoelectric applications is summarized in detail. Firstly, we systematically introduce diverse theoretical simulations and experimental measurements of the thermoelectric properties of 2D heterostructures. Then, the thermoelectric applications and performance regulation of several common 2D materials, as well as in-plane heterostructures and van der Waals heterostructures, are also discussed. Finally, the challenges of improving the thermoelectric performance of 2D heterostructures materials are summarized, and related prospects are described.

Signature of Cascade Transitions between Interlayer Excitons in a Moiré Superlattice

A moiré superlattice in transition metal dichalcogenides heterostructure provides an exciting platform for studying strongly correlated electronics and excitonic physics, such as multiple interlayer exciton (IX) energy bands. However, the correlations between these IXs remain elusive. Here, we demonstrate the cascade transitions between IXs in a moiré superlattice by performing energy- and time-resolved photoluminescence measurements in the MoS_{2}/WSe_{2} heterostructure. Furthermore, we show that the lower-energy IX can be excited to higher-energy ones, facilitating IX population inversion. Our finding of cascade transitions between IXs contributes to the fundamental understanding of the IX dynamics in moiré superlattices and may have important applications, such as in exciton condensate, quantum information protocols, and quantum cascade lasers.

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.

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.

Intrinsic type-II van der Waals heterostructures based on graphdiyne and XSSe (X = Mo, W): a first-principles study

Typical transition-metal dichalcogenides (TMDs) and graphdiyne (GDY) often form type-I heterojunctions, which will limit their applications in optoelectronic devices. Here, type-II heterojunctions based on GDY and TMDs are constructed by introducing Janus structures. An intrinsic type-II heterojunction is presented when the GDY is in contact with a Se-terminated layer, but a type-I heterojunction would appear when it is in contact with the S-terminated surface. Such a difference in band alignment can be attributed to the interaction between the dipole moment formed by the Janus structure and the graphdiyne layer. Furthermore, for heterojunctions in contact with the S-terminated layer, they can be converted into type-II heterojunctions by a small external electric field (for WSSe, only 0.05 V A^-1 is required). This approach can suggest a convenient design strategy for the application of graphdiyne in a wider range of applications.

Constructing van der Waals heterostructures by dry-transfer assembly for novel optoelectronic device

Since the first successful exfoliation of graphene, the superior physical and chemical properties of two-dimensional (2D) materials, such as atomic thickness, strong in-plane bonding energy and weak inter-layer van der Waals (vdW) force have attracted wide attention. Meanwhile, there is a surge of interest in novel physics which is absent in bulk materials. Thus, vertical stacking of 2D materials could be critical to discover such physics and develop novel optoelectronic applications. Although vdW heterostructures have been grown by chemical vapor deposition, the available choices of materials for stacking is limited and the device yield is yet to be improved. Another approach to build vdW heterostructure relies on wet/dry transfer techniques like stacking Lego bricks. Although previous reviews have surveyed various wet transfer techniques, novel dry transfer techniques have been recently been demonstrated, featuring clean and sharp interfaces, which also gets rid of contamination, wrinkles, bubbles formed during wet transfer. This review summarizes the optimized dry transfer methods, which paves the way towards high-quality 2D material heterostructures with optimized interfaces. Such transfer techniques also lead to new physical phenomena while enable novel optoelectronic applications on artificial vdW heterostructures, which are discussed in the last part of this review.

Exchange between Interlayer and Intralayer Exciton in WSe2/WS2 Heterostructure by Interlayer Coupling Engineering

Because of type-II band alignment, interlayer exciton (IX) is found in a van der Waals (vdW) heterostructure (HS) formed by two monolayers of transition-metal dichalcogenides. Manipulation of IXs is of great importance for excitonic integrated devices. Here, we demonstrate that high pressure and tensile strain can be applied to enhance and reduce interlayer coupling of WSe₂/WS₂ HS, respectively. High pressure induces the transform of intralayer excitons to IX, while tensile strain leads to the transform of IXs to intralayer excitons. In addition, there is a direct-to-indirect band gap transition of WSe₂/WS₂ HS. The interlayer distance of WSe₂/WS₂ HS is reduced under high pressure, but it increased under uniaxial tensile strain from first-principles calculations. The calculated band structures explain well the transformation between interlayer and intralayer excitons of WSe₂/WS₂ HS. This work demonstrates the exchange of interlayer and intralayer excitons and paves the way to manipulate excitons of HS for excitonic applications.

Imaging dynamic exciton interactions and coupling in transition metal dichalcogenides

Transition metal dichalcogenides (TMDs) are regarded as a possible material platform for quantum information science and related device applications. In TMD monolayers, the dephasing time and inhomogeneity are crucial parameters for any quantum information application. In TMD heterostructures, coupling strength and interlayer exciton lifetimes are also parameters of interest. However, many demonstrations in TMDs can only be realized at specific spots on the sample, presenting a challenge to the scalability of these applications. Here, using multi-dimensional coherent imaging spectroscopy, we shed light on the underlying physics—including dephasing, inhomogeneity, and strain—for a MoSe2 monolayer and identify both promising and unfavorable areas for quantum information applications. We, furthermore, apply the same technique to a MoSe2/WSe2 heterostructure. Despite the notable presence of strain and dielectric environment changes, coherent and incoherent coupling and interlayer exciton lifetimes are mostly robust across the sample. This uniformity is despite a significantly inhomogeneous interlayer exciton photoluminescence distribution that suggests a bad sample for device applications. This robustness strengthens the case for TMDs as a next-generation material platform in quantum information science and beyond.

Twist Angle-Dependent Interlayer Exciton in MoS2 Bilayers Revealed by Room-Temperature Reflectance

In 2H stacking bilayer MoS2, the exciton with an interlayer nature has been evidenced due to the hybridization of hole states among both layers. The transition energy of this interlayer exciton is located between the A and B excitons. In this work, we investigate the evolution of optical properties in stacking MoS2 bilayers with the twisted angles ranging from 0° to 60°, especially focusing on the interlayer exciton. The clear modulations of the exciton responses are observed by the room-temperature reflectance. The interlayer exciton transition is observed in the artificial stacking bilayer MoS2 with the twisted angle around 60°. We found that the interlayer exciton is very sensitive to the twisted angle. Once the stacking angle deviates the 2H stacking by a few degrees, the interlayer transition is quenched. This is due to the bilayer symmetry and interlayer coupling of this unique system.

Theory of Excitons in Atomically Thin Semiconductors: Tight-Binding Approach

Atomically thin semiconductors from the transition metal dichalcogenide family are materials in which the optical response is dominated by strongly bound excitonic complexes. Here, we present a theory of excitons in two-dimensional semiconductors using a tight-binding model of the electronic structure. In the first part, we review extensive literature on 2D van der Waals materials, with particular focus on their optical response from both experimental and theoretical points of view. In the second part, we discuss our ab initio calculations of the electronic structure of MoS2, representative of a wide class of materials, and review our minimal tight-binding model, which reproduces low-energy physics around the Fermi level and, at the same time, allows for the understanding of their electronic structure. Next, we describe how electron-hole pair excitations from the mean-field-level ground state are constructed. The electron-electron interactions mix the electron-hole pair excitations, resulting in excitonic wave functions and energies obtained by solving the Bethe-Salpeter equation. This is enabled by the efficient computation of the Coulomb matrix elements optimized for two-dimensional crystals. Next, we discuss non-local screening in various geometries usually used in experiments. We conclude with a discussion of the fine structure and excited excitonic spectra. In particular, we discuss the effect of band nesting on the exciton fine structure; Coulomb interactions; and the topology of the wave functions, screening and dielectric environment. Finally, we follow by adding another layer and discuss excitons in heterostructures built from two-dimensional semiconductors.

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.

Transition Metal Dichalcogenides (TMDCs) Heterostructures: Synthesis, Excitons and Photoelectric Properties

Transition metal dichalcogenides (TMDCs) have good flexibility, light absorption, and carrier mobility, and can be used to fabricate wearable devices and photodetectors. In addition, the band gaps of these materials are adjustable, which are related to the number of stacking layers. The the material properties can be changed by vertically stacking TMDCs to form van der Waals (vdW) heterostructures. Compared with single-layer TMDC, the vdW heterostructure has better light response and more efficient photoelectric conversion. Interlayer excitons formed in vdW heterostructure have a longer exciton lifetime and unique valley selectivity compared with intralayer excitons, which promotes the research on TMDCs materials in photoelectric field, valley electronics, carrier dynamics, etc. In this paper, the methods of synthesizing heterostructures are introduced. Photoelectric properties, valley dynamics, electronic properties and related applications of TMDCs vdW heterostructures are also discussed. Heterostructures stacked with different materials, stacking modes, and twist angles all can affect the properties. Hence, it brings more creativity and research direction to the material field.

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.

Moiré excitons in MoSe2-WSe2 heterobilayers and heterotrilayers

Layered two-dimensional materials exhibit rich transport and optical phenomena in twisted or lattice-incommensurate heterostructures with spatial variations of interlayer hybridization arising from moiré interference effects. Here, we report experimental and theoretical studies of excitons in twisted heterobilayers and heterotrilayers of transition metal dichalcogenides. Using MoSe₂-WSe₂ stacks as representative realizations of twisted van der Waals bilayer and trilayer heterostructures, we observe contrasting optical signatures and interpret them in the theoretical framework of interlayer moiré excitons in different spin and valley configurations. We conclude that the photoluminescence of MoSe₂-WSe₂ heterobilayer is consistent with joint contributions from radiatively decaying valley-direct interlayer excitons and phonon-assisted emission from momentum-indirect reservoirs that reside in spatially distinct regions of moiré supercells, whereas the heterotrilayer emission is entirely due to momentum-dark interlayer excitons of hybrid-layer valleys. Our results highlight the profound role of interlayer hybridization for transition metal dichalcogenide heterostacks and other realizations of multi-layered semiconductor van der Waals heterostructures.