Emergent Multifunctional Magnetic Proximity in van der Waals Layered Heterostructures

Proximity effect, which is the coupling between distinct order parameters across interfaces of heterostructures, has attracted immense interest owing to the customizable multifunctionalities of diverse 3D materials. This facilitates various physical phenomena, such as spin order, charge transfer, spin torque, spin density wave, spin current, skyrmions, and Majorana fermions. These exotic physics play important roles for future spintronic applications. Nevertheless, several fundamental challenges remain for effective applications: unavoidable disorder and lattice mismatch limits in the growth process, short characteristic length of proximity, magnetic fluctuation in ultrathin films, and relatively weak spin-orbit coupling (SOC). Meanwhile, the extensive library of atomically thin, 2D van der Waals (vdW) layered materials, with unique characteristics such as strong SOC, magnetic anisotropy, and ultraclean surfaces, offers many opportunities to tailor versatile and more effective functionalities through proximity effects. Here, this paper focuses on magnetic proximity, i.e., proximitized magnetism and reviews the engineering of magnetism-related functionalities in 2D vdW layered heterostructures for next-generation electronic and spintronic devices. The essential factors of magnetism and interfacial engineering induced by magnetic layers are studied. The current limitations and future challenges associated with magnetic proximity-related physics phenomena in 2D heterostructures are further discussed.

Spin-Valley Depolarization in van der Waals Heterostructures

The appearance of van der Waals heterostructures offers a new solution to valleytronics. Here, we observe the spin-valley depolarization process of electrons and holes in type-II MoS₂-WSe₂ heterostructures simultaneously for the first time by valley-resolved broad-band femtosecond pump-probe experiments. The different depolarization paths between electrons and holes make them have different spin-valley polarization lifetimes. The spin-valley depolarization pathway of holes is mainly dominated by a phonon-assisted intervalley scattering process, while intra- and intervalley coupling can trigger additional depolarization pathways for electrons. The hole polarization lifetime can be further prolonged to more than three times in trilayer heterostructure 2MoS₂-WSe₂. For MoS₂-WS₂ that has strong orbital hybridization of Mo and W atoms, both electrons and holes lose the spin-valley polarization extremely soon after charge separation, behaving similarly to intraexcitons in a monolayer. Our work advances the basic understanding of spin-valley depolarization of van der Waals heterostructures and facilitates the effort toward longer lifetime valleytronic devices for information transfer and storage applications.

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.

Directional Exciton-Energy Transport in a Lateral Heteromonolayer of WSe2-MoSe2

Controlling the direction of exciton-energy flow in two-dimensional (2D) semiconductors is crucial for developing future high-speed optoelectronic devices using excitons as the information carriers. However, intrinsic exciton diffusion in conventional 2D semiconductors is omnidirectional, and efficient exciton-energy transport in a specific direction is difficult to achieve. Here we demonstrate directional exciton-energy transport across the interface in tungsten diselenide (WSe₂)-molybdenum diselenide (MoSe₂) lateral heterostructures. Unidirectional transport is spontaneously driven by the built-in asymmetry of the exciton-energy landscape with respect to the heterojunction interface. At excitation positions close to the interface, the exciton photoluminescence (PL) intensity was substantially decreased in the WSe₂ region and enhanced in the MoSe₂ region. In PL excitation spectroscopy, it was confirmed that the observed phenomenon arises from lateral exciton-energy transport from WSe₂ to MoSe₂. This directional exciton-energy flow in lateral 2D heterostructures can be exploited in future optoelectronic devices.

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.

Magnon-Coupled Intralayer Moiré Trion in Monolayer Semiconductor-Antiferromagnet Heterostructures

Moiré fringe patterns created by stacking different 2D layered materials as artificial van der Waals (vdW) heterostructures have become a novel platform to study and engineer optically generated excitonic properties. The moiré patterns contribute to the formation of spatially ordered excitonic states (excitons and trions), which can be used in the quantum simulation of many-body systems and ensembles of coherent quantum light emitters. The intriguing moiré excitonic properties are affected by and controlled via the interaction with magnetic elements. Here, a moiré excitonic system interacting with the magnetic elementary excitation of antiferromagnetic orders in MoSe₂ /MnPS₃ vdW heterostructures is reported. The low-temperature photoluminescence spectra with additional fine spectral structures on the low-energy side, which are coupled magnon-trion peaks below the Néel temperature of MnPS₃ , are carefully investigated. The fine spectral structures with long lifetime and coherence time are assigned to intralayer trion-magnon complexes trapped in the moiré potentials (moiré trion-magnon complexes). These findings highlight the emergence of moiré trion-magnon complexes and provide a new way to explore novel quantum phenomena in moiré excitonic systems with magnetic functionalities.

Self-Trapped Interlayer Excitons in van der Waals Heterostructures

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

Quantum transport on honeycomb networks

We study the transport properties on honeycomb networks motivated by graphene structures by using the continuous-time quantum walk (CTQW) model. For various relevant topologies we consider the average return probability and its long-time average as measures for the transport efficiency. These quantities are fully determined by the eigenvalues and the eigenvectors of the connectivity matrix of the network. For all networks derived from graphene structures we notice a nontrivial interplay between good spreading and localization effects. Flat graphene with similar number of hexagons along both directions shows a decrease in transport efficiency compared to more one-dimensional structures. This loss can be overcome by increasing the number of layers, thus creating a graphite network, but it gets less efficient when rolling up the sheets so that a nanotube structure is considered. We found peculiar results for honeycomb networks constructed from square graphene, i.e. the same number of hexagons along both directions of the graphene sheet. For these kind of networks we encounter significant differences between networks with an even or odd number of hexagons along one of the axes.

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.

Strain modulation of the exciton anisotropy and carrier lifetime in black phosphorene

Manipulating excitons is of great significance to explore the optical properties of 2D materials. In this work, we investigate the excitonic properties and carrier dynamics of bilayer black phosphorene by imposing in-plane biaxial strain. The results show that the strain can modulate not only the contribution of the excitons to optical absorption but also the anisotropic shape of the first exciton. This can be ascribed to the strain effect on the band realignment as well as to changes of the parity and the electron effective mass at the CBM. At the temperature of 300 K, a 3% strain reduces the non-adiabatic coupling between the VBM and CBM and then increases the carrier lifetime by a factor of 13, and the results can be used to estimate the strain effect on the excitonic lifetime. Our results demonstrate that manipulation of the biaxial strain is a promising strategy to modulate the exciton properties of black phosphorene.

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

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

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.

Laser-Patterned Submicrometer Bi2Se3-WS2 Pixels with Tunable Circular Polarization at Room Temperature

Characterizing and manipulating the circular polarization of light is central to numerous emerging technologies, including spintronics and quantum computing. Separately, monolayer tungsten disulfide (WS₂) is a versatile material that has demonstrated promise in a variety of applications, including single photon emitters and valleytronics. Here, we demonstrate a method to tune the photoluminescence (PL) intensity (factor of ×161), peak position (38.4 meV range), circular polarization (39.4% range), and valley polarization of a Bi₂Se₃-WS₂ 2D heterostructure using a low-power laser (0.762 μW) in ambient conditions. Changes are spatially confined to the laser spot, enabling submicrometer (814 nm) features, and are long-term stable (>334 days). PL and valley polarization changes can be controllably reversed through laser exposure in a vacuum, allowing the material to be erased and reused. Atmospheric experiments and first-principles calculations indicate oxygen diffusion modulates the exciton radiative vs nonradiative recombination pathways, where oxygen absorption leads to brightening and desorption to darkening.

Monolayer Graphitic Carbon Nitride as Metal-Free Catalyst with Enhanced Performance in Photo- and Electro-Catalysis

The g-C₃N₄ monolayer in the perfect 2D limit was successfully realized, for the first time, by the well-defined chemical strategy based on the bottom-up process. The most striking evidence was made from Cs-high resolution transmission electron microscopy measurements by observing directly the atomic structure of g-C₃N₄ unit cell, which was again supported by the corresponding high resolution transmission electron microscopy image simulation results. We demonstrated that the newly prepared g-C₃N₄ monolayer showed outstanding photocatalytic activity for H₂O₂ generation as well as excellent electrocatalytic activity for oxygen reduction reaction. The exfoliation of bulk graphitic carbon nitride (g-C₃N₄) into monolayer has been intensively studied to induce maximum surface area for fundamental studies, but ended in failure to realize chemically and physically well-defined monolayer of g-C₃N₄ mostly due to the difficulty in reducing the layer thickness down to an atomic level. It has, therefore, remained as a challenging issue in two-dimensional (2D) chemistry and physics communities. In this study, an "atomic monolayer of g-C₃N₄ with perfect two-dimensional limit" was successfully prepared by the chemically well-defined two-step routes. The atomically resolved monolayer of g-C₃N₄ was also confirmed by spectroscopic and microscopic analyses. In addition, the experimental Cs-HRTEM image was collected, for the first time, which was in excellent agreement with the theoretically simulated; the evidence of monolayer of g-C₃N₄ in the perfect 2D limit becomes now clear from the HRTEM image of orderly hexagonal symmetry with a cavity formed by encirclement of three adjacent heptazine units. Compared to bulk g-C₃N₄, the present g-C₃N₄ monolayer showed significantly higher photocatalytic generation of H₂O₂ and H₂, and electrocatalytic oxygen reduction reaction. In addition, its photocatalytic efficiency for H₂O₂ production was found to be the best for any known g-C₃N₄ nanomaterials, underscoring the remarkable advantage of monolayer formation in optimizing the catalyst performance of g-C₃N₄.

Nonvolatile electrical switching of optical and valleytronic properties of interlayer excitons

Long-lived interlayer excitons (IXs) in van der Waals heterostructures (HSs) stacked by monolayer transition metal dichalcogenides (TMDs) carry valley-polarized information and thus could find promising applications in valleytronic devices. Current manipulation approaches for valley polarization of IXs are mainly limited in electrical field/doping, magnetic field or twist-angle engineering. Here, we demonstrate an electrochemical-doping method, which is efficient, in-situ and nonvolatile. We find the emission characteristics of IXs in WS2/WSe2 HSs exhibit a large excitonic/valley-polarized hysteresis upon cyclic-voltage sweeping, which is ascribed to the chemical-doping of O2/H2O redox couple trapped between WSe2 and substrate. Taking advantage of the large hysteresis, a nonvolatile valley-addressable memory is successfully demonstrated. The valley-polarized information can be non-volatilely switched by electrical gating with retention time exceeding 60 min. These findings open up an avenue for nonvolatile valley-addressable memory and could stimulate more investigations on valleytronic devices.

Excitonic transport driven by repulsive dipolar interaction in a van der Waals heterostructure

Dipolar bosonic gases are currently the focus of intensive research due to their interesting many-body physics in the quantum regime. Their experimental embodiments range from Rydberg atoms to GaAs double quantum wells and van der Waals heterostructures built from transition metal dichalcogenides. Although quantum gases are very dilute, mutual interactions between particles could lead to exotic many-body phenomena such as Bose-Einstein condensation and high-temperature superfluidity. Here, we report the effect of repulsive dipolar interactions on the dynamics of interlayer excitons in the dilute regime. By using spatial and time-resolved photoluminescence imaging, we observe the dynamics of exciton transport, enabling a direct estimation of the exciton mobility. The presence of interactions significantly modifies the diffusive transport of excitons, effectively acting as a source of drift force and enhancing the diffusion coefficient by one order of magnitude. The repulsive dipolar interactions combined with the electrical control of interlayer excitons opens up appealing new perspectives for excitonic devices.

Developing Graphene-Based Moiré Heterostructures for Twistronics

Graphene-based moiré heterostructures are strongly correlated materials, and they are considered to be an effective platform to investigate the challenges of condensed matter physics. This is due to the distinct electronic properties that are unique to moiré superlattices and peculiar band structures. The increasing research on strongly correlated physics via graphene-based moiré heterostructures, especially unconventional superconductors, greatly promotes the development of condensed matter physics. Herein, the preparation methods of graphene-based moiré heterostructures on both in situ growth and assembling monolayer 2D materials are discussed. Methods to improve the quality of graphene and optimize the transfer process are presented to mitigate the limitations of low-quality graphene and damage caused by the transfer process during the fabrication of graphene-based moiré heterostructures. Then, the topological properties in various graphene-based moiré heterostructures are reviewed. Furthermore, recent advances regarding the factors that influence physical performances via a changing twist angle, the exertion of strain, and regulation of the dielectric environment are presented. Moreover, various unique physical properties in graphene-based moiré heterostructures are demonstrated. Finally, the challenges faced during the preparation and characterization of graphene-based moiré heterostructures are discussed. An outlook for the further development of moiré heterostructures is also presented.

Negative valley polarization in doped monolayer MoSe2

Monolayer molybdenum di-selenide (1L-MoSe₂) stands out in the transition metal dichalcogenide family of materials as an outlier where optical generation of valley polarization is inefficient. Here we show that using charge doping in conjunction with an external magnetic field, the valley polarization of 1L-MoSe₂ can be controlled effectively. Most remarkably, the valley polarization can be tuned to negative values, where the higher energy Zeeman mode emission is more intense than the lower energy one. Our experimental observations are interpreted with valley-selective exciton-charge dressing that manifests when gate induced doping populates predominantly one valley in the presence of Zeeman splitting.

Atomic-Level Structure Determines Electron-Phonon Scattering Rates in 2-D Polar Metal Heterostructures

The electron dynamics of atomically thin 2-D polar metal heterostructures, which consisted of a few crystalline metal atomic layers intercalated between hexagonal silicon carbide and graphene grown from the silicon carbide, were studied using nearly degenerate transient absorption spectroscopy. Optical pumping created charge carriers in both the 2-D metals and graphene components. Wavelength-dependent probing suggests that graphene-to-metal carrier transfer occurred on a sub-picosecond time scale. Following rapid (<300 fs) carrier-carrier scattering, charge carriers monitored through the metal interband transition relaxed through several consecutive cooling mechanisms that included sub-picosecond carrier-phonon scattering and dissipation to the silicon carbide substrate over tens of picoseconds. By studying 2-D In, 2-D Ga, and a Ga/In alloy, we resolved accelerated electron-phonon scattering rates upon alloy formation as well as structural influences on the excitation of in-plane phonon shear modes. More rapid cooling in alloys is attributed to increased lattice disorder, which was observed through correlative polarization-resolved second harmonic generation and electron microscopy. This connection between the electronic relaxation rates, far-field optical responses, and metal lattice disorder is made possible by the intimate relation between nonlinear optical properties and atomic-level structure in these materials. These studies provided insights into electronic carrier dynamics in 2-D crystalline elemental metals, including resolving contributions from specific components of a 2-D metal-containing heterojunction. The correlative ultrafast spectroscopy and nonlinear microscopy results suggest that the energy dissipation rates can be tuned through atomic-level structures.

Excitons and emergent quantum phenomena in stacked 2D semiconductors

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

Enhanced Emission from Interlayer Excitons Coupled to Plasmonic Gap Cavities

The emergence of interlayer excitons (IEs) from atomic layered transition metal dichalcogenides (TMDCs) heterostructures has drawn tremendous attention due to their unique and exotic optoelectronic properties. Coupling the IEs into optical cavities provides distinctive electromagnetic environments which plays an important role in controlling multiple optical processes such as optical nonlinear generation or photoluminescence enhancement. Here, the integration of IEs in TMDCs into plasmonic nanocavities based on a nanocube on a metallic mirror is reported. Spectroscopic studies reveal an order of magnitude enhancement of the IE at room temperature and a 5-time enhancement in fluorescence at cryogenic temperatures. Cavity modeling reveals that the enhancement of the emission is attributed to both increased excitation efficiency and Purcell effect from the cavity. The results show a novel method to control the excitonic processes in TMDC heterostructures to build high performance photonics and optoelectronics devices.

Anomalously polarised emission from a MoS2/WS2 heterostructure

We report circularly polarised emission, with helicity opposite to the optical excitation, from a van der Waals heterostructure (HS) consisting of a monolayer MoS₂ and three-layer WS₂. Selective excitation of the MoS₂ layer confirms that this cross-polarized emission is due to the charge transfer from the WS₂ layers to the MoS₂ layer. We propose that the high levels of n-doping in the constituent layers due to sulphur vacancies and defects give rise to an enhanced transition rate of electrons from the k valley of WS₂ to the k' valley of MoS₂, which leads to the emission, counter polarized to the excitation. Simulations based on the rate equation model support this conclusion.

Spin/valley pumping of resident electrons in WSe2 and WS2 monolayers

Monolayers of transition metal dichalcogenides are ideal materials to control both spin and valley degrees of freedom either electrically or optically. Nevertheless, optical excitation mostly generates excitons species with inherently short lifetime and spin/valley relaxation time. Here we demonstrate a very efficient spin/valley optical pumping of resident electrons in n-doped WSe2 and WS2 monolayers. We observe that, using a continuous wave laser and appropriate doping and excitation densities, negative trion doublet lines exhibit circular polarization of opposite sign and the photoluminescence intensity of the triplet trion is more than four times larger with circular excitation than with linear excitation. We interpret our results as a consequence of a large dynamic polarization of resident electrons using circular light.

Spin/Valley Coupled Dynamics of Electrons and Holes at the MoS2-MoSe2 Interface

The coupled spin and valley degrees of freedom in transition metal dichalcogenides (TMDs) are considered a promising platform for information processing. Here, we use a TMD heterostructure MoS₂-MoSe₂ to study optical pumping of spin/valley polarized carriers across the interface and to elucidate the mechanisms governing their subsequent relaxation. By applying time-resolved Kerr and reflectivity spectroscopies, we find that the photoexcited carriers conserve their spin for both tunneling directions across the interface. Following this, we measure dramatically different spin/valley depolarization rates for electrons and holes, ∼30 and <1 ns^-1, respectively, and show that this difference relates to the disparity in the spin-orbit splitting in conduction and valence bands of TMDs. Our work provides insights into the spin/valley dynamics of photoexcited carriers unaffected by complex excitonic processes and establishes TMD heterostructures as generators of spin currents in spin/valleytronic devices.

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.

Nonclassical Exciton Diffusion in Monolayer WSe_{2}

We experimentally demonstrate time-resolved exciton propagation in a monolayer semiconductor at cryogenic temperatures. Monitoring phonon-assisted recombination of dark states, we find a highly unusual case of exciton diffusion. While at 5 K the diffusivity is intrinsically limited by acoustic phonon scattering, we observe a pronounced decrease of the diffusion coefficient with increasing temperature, far below the activation threshold of higher-energy phonon modes. This behavior corresponds neither to well-known regimes of semiclassical free-particle transport nor to the thermally activated hopping in systems with strong localization. Its origin is discussed in the framework of both microscopic numerical and semiphenomenological analytical models illustrating the observed characteristics of nonclassical propagation. Challenging the established description of mobile excitons in monolayer semiconductors, these results open up avenues to study quantum transport phenomena for excitonic quasiparticles in atomically thin van der Waals materials and their heterostructures.

Direct formation of interlayer exciton in two-dimensional van der Waals heterostructures

In atomically thin two-dimensional van der Waals (2D vdW) heterostructures, spatially separated interlayer excitons play an important role in the optoelectronic performance and show great potential for the exploration of many-body quantum phenomena. A commonly accepted formation mode for interlayer excitons is via a two-step intralayer exciton transfer mechanism, namely, photo-excited intralayer excitons are initially generated in individual sublayers, and photogenerated electrons and holes are then separated into opposite sublayers based on the type-II band alignment. Herein, we expand the concept of interlayer exciton formation and reveal that bright interlayer excitons can be generated in one step by direct interlayer photoexcitation in 2D vdW heterostructures that have strong interlayer coupling and a short photoexcitation channel. First-principles and many-body perturbation theory calculations demonstrate that indium selenide/antimonene and indium selenide/black phosphorus heterostructures are two promising systems that show an exceptionally large interlayer transition probability (>500 Debye²). This study enriches the understanding of interlayer exciton formation and provides a new avenue to acquiring strong interlayer excitons in artificial 2D vdW heterostructures.

Electrical tuning of optically active interlayer excitons in bilayer MoS2

Interlayer (IL) excitons, comprising electrons and holes residing in different layers of van der Waals bonded two-dimensional semiconductors, have opened new opportunities for room-temperature excitonic devices. So far, two-dimensional IL excitons have been realized in heterobilayers with type-II band alignment. However, the small oscillator strength of the resulting IL excitons and difficulties with producing heterostructures with definite crystal orientation over large areas have challenged the practical applicability of this design. Here, following the theoretical prediction and recent experimental confirmation of the existence of IL excitons in bilayer MoS₂, we demonstrate the electrical control of such excitons up to room temperature. We find that the IL excitonic states preserve their large oscillator strength as their energies are manipulated by the electric field. We attribute this effect to the mixing of the pure IL excitons with intralayer excitons localized in a single layer. By applying an electric field perpendicular to the bilayer MoS₂ crystal plane, excitons with IL character split into two peaks with an X-shaped field dependence as a clear fingerprint of the shift of the monolayer bands with respect to each other. Finally, we demonstrate the full control of the energies of IL excitons distributed homogeneously over a large area of our device.

Deciphering asymmetric charge transfer at transition metal dichalcogenide-graphene interface by helicity-resolved ultrafast spectroscopy

Transition metal dichalcogenide (TMD)/graphene (Gr) heterostructures constitute a key component for two-dimensional devices. The operation of TMD/Gr devices relies on interfacial charge/energy transfer processes, which remains unclear and challenging to unravel. Fortunately, the coupled spin and valley index in TMDs adds a new degree of freedom to the charges and, thus, another dimension to spectroscopy. Here, by helicity-resolved ultrafast spectroscopy, we find that photoexcitation in TMDs transfers to graphene by asynchronous charge transfer, with one type of charge transferring in the order of femtoseconds and the other in picoseconds. The rate correlates well with energy offset between TMD and graphene, regardless of compositions and charge species. Spin-polarized hole injection or long-lived polarized hole can be achieved with deliberately designed heterostructures. This study shows helicity-resolved ultrafast spectroscopy as a powerful and facile approach to reveal the fundamental and complex charge/spin dynamics in TMD-based heterostructures, paving the way toward valleytronic and optoelectronic applications.

Identification of twist-angle-dependent excitons in WS2/WSe2 heterobilayers

Stacking atomically thin films enables artificial construction of van der Waals heterostructures with exotic functionalities such as superconductivity, the quantum Hall effect, and engineered light-matter interactions. In particular, heterobilayers composed of monolayer transition metal dichalcogenides have attracted significant interest due to their controllable interlayer coupling and trapped valley excitons in moiré superlattices. However, the identification of twist-angle-modulated optical transitions in heterobilayers is sometimes controversial since both momentum-direct (K-K) and -indirect excitons reside on the low energy side of the bright exciton in the monolayer constituents. Here, we attribute the optical transition at approximately 1.35 eV in the WS2/WSe2 heterobilayer to an indirect Γ-K transition based on a systematic analysis and comparison of experimental PL spectra with theoretical calculations. The exciton wavefunction obtained by the state-of-the-art GW-Bethe-Salpeter equation (GW-BSE) approach indicates that both the electron and hole of the exciton are contributed by the WS2 layer. Polarization-resolved k-space imaging further confirms that the transition dipole moment of this optical transition is dominantly in-plane and is independent of the twist angle. The calculated absorption spectrum predicts that the usually called interlayer exciton peak coming from the K-K transition is located at 1.06 eV, but with a much weaker amplitude. Our work provides new insights into understanding the steady-state and dynamic properties of twist-angle-dependent excitons in van der Waals heterostructures.

Ultrafast Insights into High Energy (C and D) Excitons in Few Layer WS2

High energy (C and D) excitons possess extraordinary influence over the optical properties of atomically thin transition metal dichalcogenides (TMDCs), and the comprehensive understanding of these would play a pivotal role in advancing research on 2D optoelectronics. Herein, we employed transient absorption spectroscopy to monitor the underlying photophysical processes involved with different excitonic features in few layer WS₂, modeled as a TMDC representative. We observed a strong intervalley coupling across the momentum space and proposed the most plausible relaxation pathway for different excitons in few layer scenario. C and D exciton dynamics were significantly slower as compared to canonical A and B excitons, as a consequence of the indirect Λ-Γ relaxation in C and D and direct K-K combination in A and B. Most importantly, all four excitons emerge in the system and influence each other irrespective of the incident photon energy, which would be extremely impactful in fabricating wide range photonic devices.

Nanoscale Trapping of Interlayer Excitons in a 2D Semiconductor Heterostructure

For quantum technologies based on single excitons and spins, the deterministic placement and control of a single exciton is a longstanding goal. MoSe₂-WSe₂ heterostructures host spatially indirect interlayer excitons (IXs) that exhibit highly tunable energies and unique spin-valley physics, making them promising candidates for quantum information processing. Previous IX trapping approaches involving moiré superlattices and nanopillars do not meet the quantum technology requirements of deterministic placement and energy tunability. Here, we use a nanopatterned graphene gate to create a sharply varying electric field in close proximity to a MoSe₂-WSe₂ heterostructure. The dipole interaction between the IX and the electric field creates an ∼20 nm trap. The trapped IXs show the predicted electric-field-dependent energy, saturation at low excitation power, and increased lifetime, all signatures of strong spatial confinement. The demonstrated architecture is a crucial step toward the deterministic trapping of single IXs, which has broad applications to scalable quantum technologies.

Layer-engineered interlayer excitons

Photoluminescence (PL) from excitons serves as a powerful tool to characterize the optoelectronic property and band structure of semiconductors, especially for atomically thin two-dimensional transition metal dichalcogenide (TMD) materials. However, PL quenches quickly when the thickness of TMD materials increases from monolayer to a few layers, due to the change from direct to indirect band transition. Here, we show that PL can be recovered by engineering multilayer heterostructures, with the band transition reserved to be a direct type. We report emission from layer-engineered interlayer excitons from these multilayer heterostructures. Moreover, as desired for valleytronics devices, the lifetime, valley polarization, and valley lifetime of the generated interlayer excitons can all be substantially improved as compared with that in the monolayer-monolayer heterostructure. Our results pave the way for controlling the properties of interlayer excitons by layer engineering.

Sub-10 fs Intervalley Exciton Coupling in Monolayer MoS2 Revealed by Helicity-Resolved Two-Dimensional Electronic Spectroscopy

The valley pseudospin at the K and K' high-symmetry points in monolayer transition metal dichalcogenides (TMDs) has potential as an optically addressable degree of freedom in next-generation optoelectronics. However, intervalley scattering and relaxation of charge carriers leads to valley depolarization and limits practical applications. In addition, enhanced Coulomb interactions lead to pronounced excitonic effects that dominate the optical response and initial valley depolarization dynamics but complicate the interpretation of ultrafast spectroscopic experiments at short time delays. Employing broadband helicity-resolved two-dimensional electronic spectroscopy (2DES), we observe ultrafast (∼10 fs) intervalley coupling between all A and B valley exciton states that results in a complete breakdown of the valley index in large-area monolayer MoS₂ films. These couplings and subsequent dynamics exhibit minimal excitation fluence or temperature dependence and are robust toward changes in sample grain size and inherent strain. Our observations strongly suggest that this direct intervalley coupling on the time scale of optical excitation is an inherent property of large-area MoS₂ distinct from dynamic carrier or exciton scattering, phonon-driven processes, and multiexciton effects. This ultrafast intervalley coupling poses a fundamental challenge for exciton-based valleytronics in monolayer TMDs and must be overcome to fully realize large-area valleytronic devices.

Moiré superlattices and related moiré excitons in twisted van der Waals heterostructures

Recent advances in moiré superlattices and moiré excitons, such as quantum emission arrays, low-energy flat bands, and Mott insulators, have rapidly attracted attention in the fields of optoelectronics, materials, and energy research. The interlayer twist turns into a degree of freedom that alters the properties of the systems of materials, and the realization of moiré excitons also offers the feasibility of making artificial exciton crystals. Moreover, moiré excitons exhibit many exciting properties under the regulation of various external conditions, including spatial polarisation, alternating dipolar to alternating dipolar moments and gate-dependence to gate voltage dependence; all are pertinent to their applications in nano-photonics and quantum information. But the lag in theoretical development and the low-efficiency of processing technologies significantly limit the potential of moiré superlattice applications. In this review, we systematically summarise and discuss the recent progress in moiré superlattices and moiré excitons, and analyze the current challenges, and put forward relevant recommendations. There is no doubt that further research will lead to breakthroughs in their application and promote reforms and innovations in traditional solid-state physics and materials science.

Theory and Ab Initio Calculation of Optically Excited States-Recent Advances in 2D Materials

Recent studies of the optical properties of 2D materials have reported unique phenomena and features that are absent in conventional bulk semiconductors. Many of these interesting properties, such as enhanced light-matter coupling, gate-tunable photoluminescence, and unusual excitonic optical selection rules arise from the nature of the two- and multi-particle excited states such as strongly bound Wannier excitons and charged excitons. The theory, modeling, and ab initio calculations of these optically excited states in 2D materials are reviewed. Several analytical and ab initio approaches are introduced. These methods are compared with each other, revealing their relative strength and limitations. Recent works that apply these methods to a variety of 2D materials and material-defect systems are then highlighted. Understanding of the optically excited states in these systems is relevant not only for fundamental scientific research of electronic excitations and correlations, but also plays an important role in the future development of quantum information science and nano-photonics.

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.

Spatially-resolved measurements of spin valley polarization in MOCVD-grown monolayer WSe2

Time-resolved Kerr rotation microscopy is used to generate and measure spin valley polarization in MOCVD-grown monolayer tungsten diselenide (WSe₂). The Kerr signal reveals bi-exponential decay with time constants of 100 ps and 3 ns. Measurements are performed on several triangular flakes from the same growth cycle and reveal larger spin valley polarization near the edges of the flakes. This spatial dependence is observed across multiple WSe₂ flakes in the Kerr rotation measurements but not in the spatially resolved reflectivity or microphotoluminescence data. Time-resolved pump-probe overlap measurements further reveal that the Kerr signal's spatial dependence is not due to spin diffusion on the nanosecond timescale.

MoS2 and Janus (MoSSe) based 2D van der Waals heterostructures: emerging direct Z-scheme photocatalysts

Two-dimensional (2D) materials, viz. transition metal dichalcogenides (TMD) and transition metal oxides (TMO), offer a platform that allows the creation of heterostructures with a variety of properties. The optoelectronic industry has observed an upheaval in the research arena of MoS₂ based van der Waals (vdW) heterostructures (HTSs) and Janus structures. Therefore, interest towards these structures is backed by the ability to select their electronic and optical properties. The present study investigates the photocatalytic abilites of bilayer, MoS₂ and Janus (MoSSe) based vdW HTSs, viz. MoS₂/TMO, MoS₂/TMD, MoSSe/TMO and MoSSe/TMD, by a first-principles based approach under the framework of (hybrid) density functional theory (DFT) and many body perturbation theory (GW approximation). We have considered HfS₂, ZrS₂, TiS₂ and WS₂, and HfO₂, T-SnO₂ and T-PtO₂ from the families of TMDs and TMOs, respectively. The photocatalytic properties of these vdW HTSs are thoroughly investigated and compared with their respective individual monolayers by visualizing their band edge alignments, electron-hole recombination and optical properties. Strikingly, we observe that, despite most of the individual monolayers not performing optimally as photocatalysts, type II band edge alignment is noticed in vdW HTSs and they appear to be efficient photocatalysts via the Z-scheme. Moreover, these vdW HTSs have also shown promising optical responses in the visible region. Finally, electron-hole recombination, H₂O adsorption and hydrogen evolution reaction (HER) results establish that MoSSe/HfS₂, MoSSe/TiS₂, MoS₂/T-SnO₂ and MoSSe/ZrS₂ are probable highly efficient Z-scheme photocatalysts.

Ultrafast Electron Transfer with Long-Lived Charge Separation and Spin Polarization in WSe2/C60 Heterojunction

The strong excitonic effect in monolayer transition-metal dichalcogenides (TMDs) endows them with intriguing optoelectronic properties but also short-lived population and valley polarization. Exciton dissociation by interfacial charge transfer has been shown as an effective approach to prolonging excited-state lifetimes. Herein, by ultrafast spectroscopy and building-block molecule C₆₀, we investigated exciton and valley polarization dynamics in the prototypical WSe₂/C₆₀ inorganic-organic hybrid. We show that excitons in WSe₂ can be dissociated through ultrafast (∼1 ps) electron transfer to C₆₀, with nanosecond charge separation due to thermally activated electron diffusion in C₆₀ film. Because of suppressed electron-hole exchange interaction after electron transfer, hole in WSe₂ exhibits a spin/valley polarization lifetime of ∼60 ps at room temperature, more than 2 orders of magnitude longer than that in WSe₂ monolayer. This study suggests exciton dissociation as a general approach to suppress electron-hole interaction and prolong the charge/spin/valley lifetime in TMDs.

Control of light-valley interactions in 2D transition metal dichalcogenides with nanophotonic structures

Electronic valley in two-dimensional transition-metal dichalcogenides (2D TMDCs) offers a new degree of freedom for information storage and processing. The valley pseudospin can be optically encoded by photons with specific helicity, enabling the construction of electronic information devices with both high performance and low power consumption. Robust detection, manipulation and transport of the valley pseudospins at room temperature are still challenging because of the short lifetime of valley-polarized carriers and excitons. Integrating 2D TMDCs with nanophotonic objects such as plasmonic nanostructures provides a competitive solution to address the challenge. The research in this field is of practical interest and can also present rich physics of light-matter interactions. In this minireview, recent progress on using nanophotonic strategies to enhance the valley polarization degree, especially at room temperature, is highlighted. Open questions, major challenges, and interesting future developments in manipulating the valley information in 2D semiconductors with the help of nanophotonic structures will also be discussed.

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.

Predictions of moiré excitons in twisted two-dimensional organic-inorganic halide perovskites

Recent breakthrough in synthesizing arbitrary vertical heterostructures of Ruddlesden–Popper (RP) perovskites opens doors to myriad quantum optoelectronic applications. However, it is not clear whether moiré excitons and flat bands can be formed in such heterostructures. Here, we predict from first principles that twisted homobilayers of RP perovskite, MA₂PbI₄, can host moiré excitons and yield flat energy bands. The moiré excitons exhibit unique and hybridized characteristics with electrons confined in a single layer of a striped distribution while holes localized in both layers. Nearly flat valence bands can be formed in the bilayers with relatively large twist angles, thanks to the presence of hydrogen bonds that strengthen the interlayer coupling. External pressures can further increase the interlayer coupling, yielding more localized moiré excitons and flatter valence bands. Finally, electrostatic gating is predicted to tune the degree of hybridization, energy, position and localization of moiré excitons in twisted MA₂PbI₄ bilayers.

Excitonic states in twisted MA₂PbI₄ bilayers were calculated by first-principles calculations.

Diffusivity Reveals Three Distinct Phases of Interlayer Excitons in MoSe_{2}/WSe_{2} Heterobilayers

Charge separated interlayer excitons in transition metal dichalcogenide heterobilayers are being explored for moiré exciton lattices and exciton condensates. The presence of permanent dipole moments and the poorly screened Coulomb interaction make many-body interactions particularly strong for interlayer excitons. Here we reveal two distinct phase transitions for interlayer excitons in the MoSe_{2}/WSe_{2} heterobilayer using time and spatially resolved photoluminescence imaging: from trapped excitons in the moiré potential to the modestly mobile exciton gas as exciton density increases to n_{ex}∼10^{11}  cm^{-2} and from the exciton gas to the highly mobile charge separated electron-hole plasma for n_{ex}>10^{12}  cm^{-2}. The latter is the Mott transition and is confirmed in photoconductivity measurements. These findings set fundamental limits for achieving quantum states of interlayer excitons.

Electronic Properties of Monolayer and van der Waals Bilayer of Janus TiClI

In this work, the novel electronic properties of the Janus TiClI monolayer (ML) and van der Waals (vdW) bilayers (BLs) have been demonstrated. As a result of the strong spin-orbit coupling (SOC) together with the inversion symmetry breaking, the TiClI ML shows valley spin splitting of 62.67 meV at the K/K' point. In magnetic V- and Cr-doped TiClI MLs, sizable valley polarization of 36.70 and 45.35 meV occurs, respectively. TiClI vdW BLs indicate typical type-II band alignment with a quite large band offset (>500 meV), and interestingly, the interlayer-polarization P_H is almost 100% for all considered stacking orders. In addition, the interlayer-polarization is insensitive to the interlayer distance. In this situation, the interlayer exciton and valley polarization lifetimes could be prolonged, and thus, TiClI vdW BLs provide new opportunities for light-energy conversion and valleytronics. As the interlayer distance decreases, the TiClI BLs of AB' and AB stacking indicate a semiconductor-to-metal transition and are characterized by hole-doping, and the doping concentration can be further tuned by changing the interlayer distance.

High-order superlattices by rolling up van der Waals heterostructures

Two-dimensional (2D) materials^1,2 and the associated van der Waals (vdW) heterostructures^3-7 have provided great flexibility for integrating distinct atomic layers beyond the traditional limits of lattice-matching requirements, through layer-by-layer mechanical restacking or sequential synthesis. However, the 2D vdW heterostructures explored so far have been usually limited to relatively simple heterostructures with a small number of blocks^8-18. The preparation of high-order vdW superlattices with larger number of alternating units is exponentially more difficult, owing to the limited yield and material damage associated with each sequential restacking or synthesis step^8-29. Here we report a straightforward approach to realizing high-order vdW superlattices by rolling up vdW heterostructures. We show that a capillary-force-driven rolling-up process can be used to delaminate synthetic SnS₂/WSe₂ vdW heterostructures from the growth substrate and produce SnS₂/WSe₂ roll-ups with alternating monolayers of WSe₂ and SnS₂, thus forming high-order SnS₂/WSe₂ vdW superlattices. The formation of these superlattices modulates the electronic band structure and the dimensionality, resulting in a transition of the transport characteristics from semiconducting to metallic, from 2D to one-dimensional (1D), with an angle-dependent linear magnetoresistance. This strategy can be extended to create diverse 2D/2D vdW superlattices, more complex 2D/2D/2D vdW superlattices, and beyond-2D materials, including three-dimensional (3D) thin-film materials and 1D nanowires, to generate mixed-dimensional vdW superlattices, such as 3D/2D, 3D/2D/2D, 1D/2D and 1D/3D/2D vdW superlattices. This study demonstrates a general approach to producing high-order vdW superlattices with widely variable material compositions, dimensions, chirality and topology, and defines a rich material platform for both fundamental studies and technological applications.