Giant Valley-Zeeman Splitting from Spin-Singlet and Spin-Triplet Interlayer Excitons in WSe2/MoSe2 Heterostructure

Tailoring Valley Polarization of Interlayer Excitons in van der Waals Heterostructure toward Optical Communication

Controlling the valley polarization of interlayer excitons in van der Waals heterostructures is essential for developing valleytronic devices. Here, we demonstrate the manipulation of valley polarization of interlayer excitons in a monolayer WSe2/WS2 heterostructure using a dual-handedness metasurface. This metasurface, composed of left- and right-handed gold nanoantenna arrays, exhibits distinct chiral optical responses. Introducing the metasurface into heterostructures significantly enhances the degree of interlayer exciton valley polarization, which quantitatively corresponds to the circular dichroism (CD) of interlayer excitons, via chiral Purcell effects. A negative CD of -16% is yielded via the left-handed metasurface, and a positive CD of +25% is harvested via the right-handed metasurface under σ+ excitation of 532 nm at 77 K. Moreover, the CD is tunable with excitation wavelength, reaching a maximum of 38% at 620 nm under σ- excitation, the highest value from interlayer excitons reported so far without applying external fields. Further, we demonstrate that this platform enables direct and byte-invert arithmetic operations for information transmission. This capability highlights its potential for error detection in valleytronics-based optical communication systems.

Magneto-Polarization Controlled by Intervalley Scattering of Interlayer Excitons and Carriers in WS2/WSe2 Heterostructure

The photoluminescence polarization of interlayer excitons (IXs) offers a powerful tool for exploring moiré physics of transition metal dichalcogenide (TMD) heterostructures. However, in WS2/WSe2 heterostructures, this polarization is often weak and the underlying mechanism of intervalley scattering remains unclear. Notably, the closeness of IX lifetime and carrier valley lifetime complicates the investigation of the scattering process. Here, we demonstrate that magnetic fields can sensitively tune the polarization and valley dynamics of both IX and carriers in WS2/WSe2 heterostructures. We find that small magnetic fields can suppress IX intervalley scattering, significantly enhancing valley polarization, whereas at higher magnetic fields, IX emission is largely controlled by the intervalley scattering of electrons, leading to excitation-dependent polarization and saturation effects. Our results highlight the interplay between carrier dynamics and exciton valley behaviors in tailoring IX photoluminescence and offering potential pathways for the design of valleytronic devices leveraging TMD heterostructures.

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

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

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

Abstract

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

Graphical abstract

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.

Quantum Beats between Spin-Singlet and Spin-Triplet Interlayer Exciton Transitions in WSe2-MoSe2 Heterobilayers

The long-lived interlayer excitons (IXs) of semiconducting transition metal dichalcogenide heterobilayers are prime candidates for developing various optoelectronic and valleytronic devices. Their photophysical properties, including fine structure, have been the focus of recent studies, and the presence of two spin states, namely, spin-singlet and spin-triplet, has been experimentally confirmed. However, the existence of the interaction between these states and their nature remains unknown to date. Here, we demonstrate the presence of coherent coupling between the spin-singlet and spin-triplet IXs of a WSe2-MoSe2 heterobilayer utilizing quantum beat spectroscopy via a home-built Michelson interferometer. As a clear signature of coherent coupling, the quantum beat signal has been observed for the first time between closely spaced transitions of IXs. The observed strong damping of the quantum beat signals with fast dephasing times of 270-400 fs indicates that fluctuations giving rise to inhomogeneous broadening in the photoluminescence emission of these states are uncorrelated.

Room-Temperature Magnetic-Induced Circularly Polarized Photoluminescence in Two-Dimensional Er2O2S

Two-dimensional (2D) materials with spin polarization have great potential for achieving next-generation spintronic applications. However, spin polarization of 2D materials is usually produced at a cryogenic temperature because of thermal fluctuations, which severely hinder their further applications. Here, we report room-temperature intrinsic magnetic-induced circularly polarized photoluminescence (PL) in 2D Er2O2S flakes. The geff factor of 2D Er2O2S stays at around -6.3 from the liquid He temperature limit to room temperature, which is independent of temperature. This anomalous phenomenon in Er2O2S is totally different from previous materials, which all have a decreasing Zeeman splitting with increasing temperature resulting from thermal fluctuations. The anomalous temperature-dependent magnetic-induced circularly polarized PL originates from the weak electron-phonon coupling in 2D Er2O2S, which has been proven by both the temperature-dependent Raman and theoretical calculations. This work sheds light on the understanding and manipulation of 2D materials for practical spintronic applications.

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.

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.

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.

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

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

Observation of quadrupolar and dipolar excitons in a semiconductor heterotrilayer

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

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

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

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.

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

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

Lattice Reconstruction in MoSe2-WSe2 Heterobilayers Synthesized by Chemical Vapor Deposition

Vertical van der Waals heterostructures of semiconducting transition metal dichalcogenides realize moiré systems with rich correlated electron phases and moiré exciton phenomena. For material combinations with small lattice mismatch and twist angles as in MoSe₂-WSe₂, however, lattice reconstruction eliminates the canonical moiré pattern and instead gives rise to arrays of periodically reconstructed nanoscale domains and mesoscopically extended areas of one atomic registry. Here, we elucidate the role of atomic reconstruction in MoSe₂-WSe₂ heterostructures synthesized by chemical vapor deposition. With complementary imaging down to the atomic scale, simulations, and optical spectroscopy methods, we identify the coexistence of moiré-type cores and extended moiré-free regions in heterostacks with parallel and antiparallel alignment. Our work highlights the potential of chemical vapor deposition for applications requiring laterally extended heterosystems of one atomic registry or exciton-confining heterostack arrays.

The Interaction of 2D Materials With Circularly Polarized Light

2D materials (2DMs), due to spin-valley locking degree of freedom, exhibit strongly bound exciton and chiral optical selection rules and become promising material candidates for optoelectronic and spin/valleytronic devices. Over the last decade, the manifesting of 2D materials by circularly polarized lights expedites tremendous fascinating phenomena, such as valley/exciton Hall effect, Moiré exciton, optical Stark effect, circular dichroism, circularly polarized photoluminescence, and spintronic property. In this review, recent advance in the interaction of circularly polarized light with 2D materials covering from graphene, black phosphorous, transition metal dichalcogenides, van der Waals heterostructures as well as small proportion of quasi-2D perovskites and topological materials, is overviewed. The confronted challenges and theoretical and experimental opportunities are also discussed, attempting to accelerate the prosperity of chiral light-2DMs interactions.

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.

Structure modulation of two-dimensional transition metal chalcogenides: recent advances in methodology, mechanism and applications

Together with the development of two-dimensional (2D) materials, transition metal dichalcogenides (TMDs) have become one of the most popular series of model materials for fundamental sciences and practical applications. Due to the ever-growing requirements of customization and multi-function, dozens of modulated structures have been introduced in TMDs. In this review, we present a systematic and comprehensive overview of the structure modulation of TMDs, including point, linear and out-of-plane structures, following and updating the conventional classification for silicon and related bulk semiconductors. In particular, we focus on the structural characteristics of modulated TMD structures and analyse the corresponding root causes. We also summarize the recent progress in modulating methods, mechanisms, properties and applications based on modulated TMD structures. Finally, we demonstrate challenges and prospects in the structure modulation of TMDs and forecast potential directions about what and how breakthroughs can be achieved.

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.

Strain-Induced Exciton Hybridization in WS_{2} Monolayers Unveiled by Zeeman-Splitting Measurements

Mechanical deformations and ensuing strain are routinely exploited to tune the band gap energy and to enhance the functionalities of two-dimensional crystals. In this Letter, we show that strain leads also to a strong modification of the exciton magnetic moment in WS_{2} monolayers. Zeeman-splitting measurements under magnetic fields up to 28.5 T were performed on single, one-layer-thick WS_{2} microbubbles. The strain of the bubbles causes a hybridization of k-space direct and indirect excitons resulting in a sizable decrease in the modulus of the g factor of the ground-state exciton. These findings indicate that strain may have major effects on the way the valley number of excitons can be used to process binary information in two-dimensional crystals.

Two-dimensional transition metal dichalcogenides as an emerging platform for singlet fission solar cells

Singlet fission, a rapid exciton doubling process via inverse Auger recombination, is recognized as one of the most practical and feasible means for overcoming the Shockley-Queisser limit. Singlet fission solar cells are generally developed by integrating photon downconversion organic semiconductors into conventional photovoltaic devices to break the maximum photovoltaic response of the host semiconductors by virtue of extra triplet excitons. In this regard, proper matching of two different semiconductors and heterointerface engineering are both crucial for highly efficient singlet fission solar cells. Therefore, the aim of this study is to review the prerequisite conditions for efficient triplet transfer at the heterointerfaces and thus highlight the robust spin and valley degrees of freedom of transition metal dichalcogenides with the ultimate goal of stimulating research into next-generation singlet fission solar cells.

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.

Dipole moment and pressure dependent interlayer excitons in MoSSe/WSSe heterostructures

The broken mirror symmetry of two-dimensional (2D) Janus materials brings novel quantum properties and various application prospects. Particularly, when stacking into heterostructures, their intrinsic dipole moments and large band offsets are very favorable to the photoexcited properties concerning electron-hole pairs, i.e., excitons. However, the effect of the intrinsic dipole moments on the interlayer excitons in the heterostructures composed of 2D Janus materials is still unclear. Here we use the GW/BSE methods to explore the effect of the intrinsic dipole moments on the interlayer excitons via varying the stacking configuration of MoSSe/WSSe heterostructures. Surprisingly, our results reveal that the parallel-arranged intrinsic dipole moments enhance the interlayer coupling in the heterostructures, and hence make the lowest interlayer exciton have an intensity comparable to the bright excitons while accompanied by a large binding energy and a radiative lifetime as long as 10^-7 s at 300 K, though it is almost a spin-forbidden process, and with the out-of-plane light polarization, long lifetime interlayer excitons are observed under the effect of selection rules. More intriguingly, we found that the photoexcited properties of the interlayer excitons considering the momentum in the stacking configuration with parallel-arranged intrinsic dipole moments are greatly tunable through hydrostatic pressure. These explorations provide a basic perspective for optoelectronic applications by means of engineering the intrinsic dipole moments in Janus heterostructures.

Enhanced Valley Polarization in WS2 /LaMnO3 Heterostructure

Monolayer transition metal dichalcogenides have attracted great attention for potential applications in valleytronics. However, the valley polarization degree is usually not high because of the intervalley scattering. Here, a largely enhanced valley polarization up to 80% in monolayer WS₂ under nonresonant excitation at 4.2 K is demonstrated using WS₂ /LaMnO₃ thin film heterostructure, which is much higher than that for monolayer WS₂ on SiO₂ /Si substrate with a valley polarization of 15%. Furthermore, the greatly enhanced valley polarization can be maintained to a high temperature of about 160 K with a valley polarization of 53%. The temperature dependence of valley polarization is strongly correlated with the thermomagnetic curve of LaMnO₃ , indicating an exciton-magnon coupling between WS₂ and LaMnO₃ . A simple model is introduced to illustrate the underlying mechanisms. The coupling of WS₂ and LaMnO₃ is further confirmed with an observation of two interlayer excitons with opposite valley polarizations in the heterostructure, resulting from the spin-orbit coupling induced splitting of the conduction bands in monolayer transition metal dichalcogenides. The results provide a pathway to control the valleytronic properties of transition metal dichalcogenides by means of ferromagnetic van der Waals engineering, paving a way to practical valleytronic applications.

Excitons in semiconductor moiré superlattices

Semiconductor moiré superlattices represent a rapidly developing area of engineered photonic materials and a new platform to explore correlated electron states and quantum simulation. In this Review, we briefly introduce early experiments that identified new exciton resonances in transition metal dichalcogenide heterobilayers and discuss several topics including two types of transition metal dichalcogenide moiré superlattice, new optical selection rules, early evidence of moiré excitons, and how the resonant energy, dynamics and diffusion properties of moiré excitons can be controlled via the twist angle. To interpret optical spectra, it is important to measure the energy modulation within a moiré supercell. In this context, we describe a few scanning tunnelling microscopy experiments that measure the moiré potential landscape directly. Finally, we review a few recent experiments that applied excitonic optical spectroscopy to probe correlated electron phenomena in transition metal dichalcogenide moiré superlattices.

Moiré trions in MoSe2/WSe2 heterobilayers

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

Control of Giant Topological Magnetic Moment and Valley Splitting in Trilayer Graphene

Bloch states of electrons in honeycomb two-dimensional crystals with multivalley band structure and broken inversion symmetry have orbital magnetic moments of a topological nature. In crystals with two degenerate valleys, a perpendicular magnetic field lifts the valley degeneracy via a Zeeman effect due to these magnetic moments, leading to magnetoelectric effects which can be leveraged for creating valleytronic devices. In this work, we demonstrate that trilayer graphene with Bernal stacking (ABA TLG), hosts topological magnetic moments with a large and widely tunable valley g factor (g_{ν}), reaching a value g_{ν}∼1050 at the extreme of the studied parametric range. The reported experiment consists in sublattice-resolved scanning tunneling spectroscopy under perpendicular electric and magnetic fields that control the TLG bands. The tunneling spectra agree very well with the results of theoretical modeling that includes the full details of the TLG tight-binding model and accounts for a quantum-dot-like potential profile formed electrostatically under the scanning tunneling microscope tip.

Anapole enhanced on-chip routing of spin-valley photons in 2D materials for silicon integrated optical communication

Controlling the propagation direction of polarized light is crucial for optical communications and functional optical components. However, all-dielectric on-chip technology exploiting valley photon emission in transition metal dichalcogenides with enhanced emission has yet to be fully explored. Here, we report a design for enhancing valley emission and manipulating valley photon propagation based on degenerate non-radiating anapole states. By placing circularly polarized dipoles on top of a C₄ symmetric cross-slotted silicon disk, the rotating anapole state is excited with a Purcell factor up to two orders. In addition, the photon coupled to the preferred direction of the waveguide are about 2 times larger than that to the opposite direction. Our design could pave the way for realizing on-chip valley-dependent optical communication.

Strong interaction between interlayer excitons and correlated electrons in WSe2/WS2 moiré superlattice

Heterobilayers of transition metal dichalcogenides (TMDCs) can form a moiré superlattice with flat minibands, which enables strong electron interaction and leads to various fascinating correlated states. These heterobilayers also host interlayer excitons in a type-II band alignment, in which optically excited electrons and holes reside on different layers but remain bound by the Coulomb interaction. Here we explore the unique setting of interlayer excitons interacting with strongly correlated electrons, and we show that the photoluminescence (PL) of interlayer excitons sensitively signals the onset of various correlated insulating states as the band filling is varied. When the system is in one of such states, the PL of interlayer excitons is relatively amplified at increased optical excitation power due to reduced mobility, and the valley polarization of interlayer excitons is enhanced. The moiré superlattice of the TMDC heterobilayer presents an exciting platform to engineer interlayer excitons through the periodic correlated electron states.

Signatures of moiré trions in WSe2/MoSe2 heterobilayers

Moiré superlattices formed by van der Waals materials can support a wide range of electronic phases, including Mott insulators^1-4, superconductors^5-10 and generalized Wigner crystals². When excitons are confined by a moiré superlattice, a new class of exciton emerges, which holds promise for realizing artificial excitonic crystals and quantum optical effects^11-16. When such moiré excitons are coupled to charge carriers, correlated states may arise. However, no experimental evidence exists for charge-coupled moiré exciton states, nor have their properties been predicted by theory. Here we report the optical signatures of trions coupled to the moiré potential in tungsten diselenide/molybdenum diselenide heterobilayers. The moiré trions show multiple sharp emission lines with a complex charge-density dependence, in stark contrast to the behaviour of conventional trions. We infer distinct contributions to the trion emission from radiative decay in which the remaining carrier resides in different moiré minibands. Variation of the trion features is observed in different devices and sample areas, indicating high sensitivity to sample inhomogeneity and variability. The observation of these trion features motivates further theoretical and experimental studies of higher-order electron correlation effects in moiré superlattices.

Interlayer exciton formation, relaxation, and transport in TMD van der Waals heterostructures

Van der Waals (vdW) heterostructures based on transition metal dichalcogenides (TMDs) generally possess a type-II band alignment that facilitates the formation of interlayer excitons between constituent monolayers. Manipulation of the interlayer excitons in TMD vdW heterostructures holds great promise for the development of excitonic integrated circuits that serve as the counterpart of electronic integrated circuits, which allows the photons and excitons to transform into each other and thus bridges optical communication and signal processing at the integrated circuit. As a consequence, numerous studies have been carried out to obtain deep insight into the physical properties of interlayer excitons, including revealing their ultrafast formation, long population recombination lifetimes, and intriguing spin-valley dynamics. These outstanding properties ensure interlayer excitons with good transport characteristics, and may pave the way for their potential applications in efficient excitonic devices based on TMD vdW heterostructures. At present, a systematic and comprehensive overview of interlayer exciton formation, relaxation, transport, and potential applications is still lacking. In this review, we give a comprehensive description and discussion of these frontier topics for interlayer excitons in TMD vdW heterostructures to provide valuable guidance for researchers in this field.

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.

Optical control of the valley Zeeman effect through many-exciton interactions

Charge carriers in two-dimensional transition metal dichalcogenides (TMDs), such as WSe₂, have their spin and valley-pseudospin locked into an optically addressable index that is proposed as a basis for future information processing^1,2. The manipulation of this spin-valley index, which carries a magnetic moment³, requires tuning its energy. This is typically achieved through an external magnetic field (B), which is practically cumbersome. However, the valley-contrasting optical Stark effect achieves valley control without B, but requires large incident powers^4,5. Thus, other efficient routes to control the spin-valley index are desirable. Here we show that many-body interactions among interlayer excitons (IXs) in a WSe₂/MoSe₂ heterobilayer (HBL) induce a steady-state valley Zeeman splitting that corresponds to B ≈ 6 T. This anomalous splitting, present at incident powers as low as microwatts, increases with power and is able to enhance, suppress or even flip the sign of a B-induced splitting. Moreover, the g-factor of valley Zeeman splitting can be tuned by ~30% with incident power. In addition to valleytronics, our results could prove helpful to achieve optical non-reciprocity using two-dimensional materials.

Interlayer Exciton Transport in MoSe2/WSe2 Heterostructures

A moiré superlattice formed by stacking two lattice mismatched transition metal dichalcogenide monolayers, functions as a diffusion barrier that affects the energy transport and dynamics of interlayer excitons (electron and hole spatially concentrated in different monolayers). In this work, we experimentally quantify the diffusion barrier experienced by interlayer excitons in hexagonal boron nitride-encapsulated molybdenum diselenide/tungsten diselenide (MoSe₂/WSe₂) heterostructures with different twist angles. We observe the localization of interlayer excitons at low temperature and the temperature-activated diffusivity as a function of twist angle and hence attribute it to the deep periodic potentials arising from the moiré superlattice. We further support the observations with theoretical calculations, Monte Carlo simulations, and a three-level model that represents the exciton dynamics at various temperatures.

Routing valley exciton emission of a WS2 monolayer via delocalized Bloch modes of in-plane inversion-symmetry-broken photonic crystal slabs

The valleys of two-dimensional transition metal dichalcogenides (TMDCs) offer a new degree of freedom for information processing. To take advantage of this valley degree of freedom, on the one hand, it is feasible to control valleys by utilizing different external stimuli, such as optical and electric fields. On the other hand, nanostructures are also used to separate the valleys by near-field coupling. However, for both of the above methods, either the required low-temperature environment or low degree of coherence properties limit their further applications. Here, we demonstrate that all-dielectric photonic crystal (PhC) slabs without in-plane inversion symmetry (C2 symmetry) can separate and route valley exciton emission of a WS2 monolayer at room temperature. Coupling with circularly polarized photonic Bloch modes of such PhC slabs, valley photons emitted by a WS2 monolayer are routed directionally and are efficiently separated in the far field. In addition, far-field emissions are directionally enhanced and have long-distance spatial coherence properties.

Selective Chemical Modulation of Interlayer Excitons in Atomically Thin Heterostructures

Strongly bound interlayer excitons (X_Is) in atomically thin transition metal dichalcogenide (TMDC) heterostructures such as MoS₂/WSe₂ show promising optoelectronic properties for spin-valleytronics and excitonic devices. The ability to probe and control X_Is is critical for the development of such applications. This Letter introduces a versatile chemical method for selectively tailoring interlayer excitons in TMDC heterostructures. We show that two organic layers form uniform layers on a WSe₂/MoS₂ heterostructure and that the X_I photoluminescence may be either preserved or quenched. The interlayer emission can also be modulated differently by the formation of the organic layer on either side of the TMDC/TMDC heterostructure. We find that the resulting interlayer emission is dominated by selective photoinduced charge transfer over dark-state p-doping effects. These results shed critical insights on interlayer excitons at the TMDC/TMDC heterointerfaces and provide a versatile approach for selectively tailoring them for optoelectronic applications.