Atomic reconstruction in twisted bilayers of transition metal dichalcogenides

Twist Angle-Dependent Phonon Hybridization in WSe2/WSe2 Homobilayer

The emerging moiré superstructure of twisted transition metal dichalcogenides (TMDs) leads to various correlated electronic and optical properties compared to those of twisted bilayer graphene. In such a versatile architecture, phonons can also be renormalized and evolve due to atomic reconstruction, which, in turn, depends on the twist angle. However, observing this reconstruction and its relationship to phonon behavior with conventional, cost-effective imaging methods remains challenging. Here, we used noninvasive Raman spectroscopy on twisted WSe2/WSe2 (t-WSe2) homobilayers to examine the evolution of phonon modes due to interlayer coupling and atomic reconstruction. Unlike in the natural bilayer (NB), ∼0° as well as ∼60° t-WSe2 samples, the nearly degenerate A1g/E2g mode in the twisted samples (1-7°) split into a doublet in addition to the nondegenerate B2g mode, and the maximum splitting is observed around 2-3°. Our detailed theoretical calculations qualitatively capture the splitting and its dependence as a function of the twist angle and highlight the role of the moiré potential in phonon hybridization. Additionally, we found that around the 2° twist angle, the anharmonic phonon-phonon interaction is higher than the natural bilayer and decreases for larger twist angles. Interestingly, we observed anomalous Raman frequency softening and line-width increase with the decreasing temperature below 50 K, pointing to the combined effect of enhanced electron-phonon coupling and cubic anharmonic interactions in moiré superlattice.

Constructing Slip Stacking Diversity in Van der Waals Homobilayers

The van der Waals (vdW) interface provides two important degrees of freedom-twist and slip-to tune interlayer structures and inspire unique physics. However, constructing diversified high-quality slip stackings (i.e., lattice orientations between layers are parallel with only interlayer sliding) is more challenging than twisted stackings due to angstrom-scale structural discrepancies between different slip stackings, sparsity of thermodynamically stable candidates and insufficient mechanism understanding. Here, using transition metal dichalcogenide (TMD) homobilayers as a model system, this work theoretically elucidates that vdW materials with low lattice symmetry and weak interlayer coupling allow the creation of multifarious thermodynamically advantageous slip stackings, and experimentally achieves 13 and 9 slip stackings in 1T″-ReS2 and 1T″-ReSe2 bilayers via direct growth, which are systematically revealed by atomic-resolution scanning transmission electron microscopy (STEM), angle-resolved polarization Raman spectroscopy, and second harmonic generation (SHG) measurements. This work also develops modulation strategies to switch the stacking via grain boundaries (GBs) and to expand the slip stacking library from thermodynamic to kinetically favored structures via in situ thermal treatment. Finally, density functional theory (DFT) calculations suggest a prominent dependence of the pressure-induced electronic band structure transition on stacking configurations. These studies unveil a unique vdW epitaxy and offer a viable means for manipulating interlayer atomic registries.

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

Crossover between rigid and reconstructed moiré lattice in h-BN-encapsulated twisted bilayer WSe2 with different twist angles

A moiré lattice in a twisted-bilayer transition metal dichalcogenide (tBL-TMD) exhibits a complex atomic reconstruction effect when its twist angle is less than a few degrees. The influence of the atomic reconstruction on material properties of the tBL-TMD has been of particular interest. In this study, we performed scanning transmission electron microscopy (STEM) imaging of a moiré lattice in h-BN-encapsulated twisted bilayer WSe2 with various twist angles. Atomic-resolution imaging of the moiré lattice revealed a reconstructed moiré lattice below a crossover twist angle of ∼4° and a rigid moiré lattice above this angle. Our findings indicate that h-BN encapsulation has a considerable influence on lattice reconstruction, as the crossover twist angle was larger in h-BN-encapsulated devices compared to non-encapsulated devices. We believe that this difference is due to the improved flatness and uniformity of the twisted bilayers with h-BN encapsulation. Our results provide a foundation for a deeper understanding of the lattice reconstruction in twisted TMD materials with h-BN encapsulation.

Electrically tunable layer-hybridized trions in doped WSe2 bilayers

Doped van der Waals heterostructures host layer-hybridized trions, i.e. charged excitons with layer-delocalized constituents holding promise for highly controllable optoelectronics. Combining a microscopic theory with photoluminescence (PL) experiments, we demonstrate the electrical tunability of the trion energy landscape in naturally stacked WSe2 bilayers. We show that an out-of-plane electric field modifies the energetic ordering of the lowest lying trion states, which consist of layer-hybridized Λ -point electrons and layer-localized K-point holes. At small fields, intralayer-like trions yield distinct PL signatures in opposite doping regimes characterized by weak Stark shifts in both cases. Above a doping-asymmetric critical field, interlayer-like species are energetically favored and produce PL peaks with a pronounced Stark red-shift and a counter-intuitively large intensity arising from efficient phonon-assisted recombination. Our work presents an important step forward in the microscopic understanding of layer-hybridized trions in van der Waals heterostructures and paves the way towards optoelectronic applications based on electrically controllable atomically-thin semiconductors.

Sliding Memristor in Parallel-Stacked Hexagonal Boron Nitride

Sliding ferroelectricity in 2D materials, arising from interlayer sliding-induced interlayer hybridization and charge redistribution at the van der Waals interface, offers a means to manipulate spontaneous polarization at the atomic scale through various methods such as stacking order, interfacial contact, and electric field. However, the practical application of extending 2D sliding ferroelectricity remains challenging due to the contentious mechanisms and the complex device structures required for ferroelectric switching. Here, a sliding memristor based on a graphene/parallel-stacked hexagonal boron nitride/graphene tunneling device, featuring a stable memristive hysteresis induced by interfacial polarizations and barrier height modulations, is presented. As the tunneling current density increases, the memristive window broadens, achieving an on/off ratio of ≈103 and 2 order decrease of the trigger current density, attributed to the interlayer migration of positively charged boron ions and the formation of conductive filaments, as supported by the theoretical calculations. The findings open a path for exploring the sliding memristor via a tunneling device and bridge the gap between sliding ferroelectricity and memory applications.

Manipulation of Moiré Superlattice in Twisted Monolayer-multilayer Graphene by Moving Nanobubbles

In the heterostructure of two-dimensional (2D) materials, many novel physics phenomena are strongly dependent on the Moiré superlattice. How to achieve the continuous manipulation of the Moiré superlattice in the same sample is very important to study the evolution of various physical properties. Here, in minimally twisted monolayer-multilayer graphene, we found that bubble-induced strain has a huge impact on the Moiré superlattice. By employing the AFM tip to dynamically and continuously move the nanobubble, we realized the modulation of the Moiré superlattice, like the evolution of regular triangular domains into long strip domain structures with single or double domain walls. We also achieved controllable modulation of the Moiré superlattice by moving multiple nanobubbles and establishing the coupling of nanobubbles. Our work presents a flexible method for continuous and controllable manipulation of Moiré superlattices, which will be widely used to study novel physical properties in 2D heterostructures.

Moiré Engineering of Spin-Orbit Torque by Twisted WS2 Homobilayers

Artificial moiré superlattices created by stacking 2D crystals have emerged as a powerful platform with unprecedented material-engineering capabilities. While moiré superlattices are reported to host a number of novel quantum states, their potential for spintronic applications remains largely unexplored. Here, the effective manipulation of spin-orbit torque (SOT) is demonstrated using moiré superlattices in ferromagnetic devices comprised of twisted WS2/WS2 homobilayer (t-WS2) and CoFe/Pt thin films by altering twisting angle (θ) and gate voltage. Notably, a substantial enhancement of up to 44.5% is observed in SOT conductivity at θ ≈ 8.3°. Furthermore, compared to the WS2 monolayer and untwisted WS2/WS2 bilayers, the moiré superlattices in t-WS2 enable a greater gate-voltage tunability of SOT conductivity. These results are related to the generation of the interfacial moiré magnetic field by the real-space Berry phase in moiré superlattices, which modulates the absorption of the spin-Hall current arising from Pt through the magnetic proximity effect. This study highlights the moiré physics as a new building block for designing enhanced spintronic devices.

Imaging tunable Luttinger liquid systems in van der Waals heterostructures

One-dimensional (1D) interacting electrons are often described as a Luttinger liquid1-4 having properties that are intrinsically different from those of Fermi liquids in higher dimensions5,6. In materials systems, 1D electrons exhibit exotic quantum phenomena that can be tuned by both intra- and inter-1D-chain electronic interactions, but their experimental characterization can be challenging. Here we demonstrate that layer-stacking domain walls (DWs) in van der Waals heterostructures form a broadly tunable Luttinger liquid system, including both isolated and coupled arrays. We have imaged the evolution of DW Luttinger liquids under different interaction regimes tuned by electron density using scanning tunnelling microscopy. Single DWs at low carrier density are highly susceptible to Wigner crystallization consistent with a spin-incoherent Luttinger liquid, whereas at intermediate densities dimerized Wigner crystals form because of an enhanced magneto-elastic coupling. Periodic arrays of DWs exhibit an interplay between intra- and inter-chain interactions that gives rise to new quantum phases. At low electron densities, inter-chain interactions are dominant and induce a 2D electron crystal composed of phased-locked 1D Wigner crystal in a staggered configuration. Increased electron density causes intra-chain fluctuation potentials to dominate, leading to an electronic smectic liquid crystal phase in which electrons are ordered with algebraical correlation decay along the chain direction but disordered between chains. Our work shows that layer-stacking DWs in 2D heterostructures provides opportunities to explore Luttinger liquid physics.

Engineering interfacial polarization switching in van der Waals multilayers

In conventional ferroelectric materials, polarization is an intrinsic property limited by bulk crystallographic structure and symmetry. Recently, it has been demonstrated that polar order can also be accessed using inherently non-polar van der Waals materials through layer-by-layer assembly into heterostructures, wherein interfacial interactions can generate spontaneous, switchable polarization. Here we show that deliberate interlayer rotations in multilayer van der Waals heterostructures modulate both the spatial ordering and switching dynamics of polar domains. The engendered tunability is unparalleled in conventional bulk ferroelectrics or polar bilayers. By means of operando transmission electron microscopy we show how alterations of the relative rotations of three WSe2 layers produce structural polytypes with distinct arrangements of polar domains with either a global or localized switching response. Furthermore, the presence of uniaxial strain generates structural anisotropy that yields a range of switching behaviours, coercivities and even tunable biased responses. We also provide evidence of mechanical coupling between the two interfaces of the trilayer, a key consideration for the control of switching dynamics in polar multilayer structures more broadly.

Tunnel junctions based on interfacial two dimensional ferroelectrics

Van der Waals heterostructures have opened new opportunities to develop atomically thin (opto)electronic devices with a wide range of functionalities. The recent focus on manipulating the interlayer twist angle has led to the observation of out-of-plane room temperature ferroelectricity in twisted rhombohedral bilayers of transition metal dichalcogenides. Here we explore the switching behaviour of sliding ferroelectricity using scanning probe microscopy domain mapping and tunnelling transport measurements. We observe well-pronounced ambipolar switching behaviour in ferroelectric tunnelling junctions with composite ferroelectric/non-polar insulator barriers and support our experimental results with complementary theoretical modelling. Furthermore, we show that the switching behaviour is strongly influenced by the underlying domain structure, allowing the fabrication of diverse ferroelectric tunnelling junction devices with various functionalities. We show that to observe the polarisation reversal, at least one partial dislocation must be present in the device area. This behaviour is drastically different from that of conventional ferroelectric materials, and its understanding is an important milestone for the future development of optoelectronic devices based on sliding ferroelectricity.

Electrical Control and Transport of Tightly Bound Interlayer Excitons in a MoSe_{2}/hBN/MoSe_{2} Heterostructure

Controlling interlayer excitons in Van der Waals heterostructures holds promise for exploring Bose-Einstein condensates and developing novel optoelectronic applications, such as excitonic integrated circuits. Despite intensive studies, several key fundamental properties of interlayer excitons, such as their binding energies and interactions with charges, remain not well understood. Here we report the formation of momentum-direct interlayer excitons in a high-quality MoSe_{2}/hBN/MoSe_{2} heterostructure under an electric field, characterized by bright photoluminescence (PL) emission with high quantum yield and a narrow linewidth of less than 4 meV. These interlayer excitons show electrically tunable emission energy spanning ∼180  meV through the Stark effect, and exhibit a sizable binding energy of ∼81  meV in the intrinsic regime, along with trion binding energies of a few millielectronvolts. Remarkably, we demonstrate the long-range transport of interlayer excitons with a characteristic diffusion length exceeding 10  μm, which can be attributed, in part, to their dipolar repulsive interactions. Spatially and polarization-resolved spectroscopic studies reveal rich exciton physics in the system, such as valley polarization, local trapping, and the possible existence of dark interlayer excitons. The formation and transport of tightly bound interlayer excitons with narrow linewidth, coupled with the ability to electrically manipulate their properties, open exciting new avenues for exploring quantum many-body physics, including excitonic condensate and superfluidity, and for developing novel optoelectronic devices, such as exciton and photon routers.

Polarization-driven band topology evolution in twisted MoTe2 and WSe2

Motivated by recent experimental observations of opposite Chern numbers in R-type twisted MoTe2 and WSe2 homobilayers, we perform large-scale density-functional-theory calculations with machine learning force fields to investigate moiré band topology across a range of twist angles in both materials. We find that the Chern numbers of the moiré frontier bands change sign as a function of twist angle, and this change is driven by the competition between moiré ferroelectricity and piezoelectricity. Our large-scale calculations, enabled by machine learning methods, reveal crucial insights into interactions across different scales in twisted bilayer systems. The interplay between atomic-level relaxation effects and moiré-scale electrostatic potential variation opens new avenues for the design of intertwined topological and correlated states, including the possibility of mimicking higher Landau level physics in the absence of magnetic field.

Resonant Band Hybridization in Alloyed Transition Metal Dichalcogenide Heterobilayers

Bandstructure engineering using alloying is widely utilized for achieving optimized performance in modern semiconductor devices. While alloying has been studied in monolayer transition metal dichalcogenides, its application in van der Waals heterostructures built from atomically thin layers is largely unexplored. Here, heterobilayers made from monolayers of WSe2 (or MoSe2) and MoxW1 - xSe2 alloy are fabricated and nontrivial tuning of the resultant bandstructure is observed as a function of concentration x. This evolution is monitored by measuring the energy of photoluminescence (PL) of the interlayer exciton (IX) composed of an electron and hole residing in different monolayers. In MoxW1 - xSe2/WSe2, a strong IX energy shift of ≈100 meV is observed for x varied from 1 to 0.6. However, for x < 0.6 this shift saturates and the IX PL energy asymptotically approaches that of the indirect bandgap in bilayer WSe2. This observation is theoretically interpreted as the strong variation of the conduction band K valley for x > 0.6, with IX PL arising from the K - K transition, while for x < 0.6, the bandstructure hybridization becomes prevalent leading to the dominating momentum-indirect K - Q transition. This bandstructure hybridization is accompanied with strong modification of IX PL dynamics and nonlinear exciton properties. This work provides foundation for bandstructure engineering in van der Waals heterostructures highlighting the importance of hybridization effects and opening a way to devices with accurately tailored electronic properties.

Mesoscopic Stacking Reconfigurations in Stacked van der Waals Film

Mesoscopic-scale stacking reconfigurations are investigated when van der Waals (vdW) films are stacked. A method to visualize complicated stacking structures and mechanical distortions simultaneously in stacked atom-thick films using Raman spectroscopy is developed. In the rigid limit, it is found that the distortions originate from the transfer process, which can be understood through thin film mechanics with a large elastic property mismatch. In contrast, with atomic corrugations, the in-plane strain fields are more closely correlated with the stacking configuration, highlighting the impact of atomic reconstructions on the mesoscopic scale. It is discovered that the grain boundaries do not have a significant effect while the cracks are causing inhomogeneous strain in stacked polycrystalline films. This result contributes to understanding the local variation of emerging properties from moiré structures and advancing the reliability of stacked vdW material fabrication.

Excitonic Thermalization Bottleneck in Twisted TMD Heterostructures

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

Near-field coupling of interlayer excitons in MoSe2/WSe2 heterobilayers to surface plasmon polaritons

Two-dimensional (2D) transition metal dichalcogenides have emerged as promising quantum functional blocks benefitting from their unique combination of spin, valley, and layer degrees of freedom, particularly for the tremendous flexibility of moiré superlattices formed by van der Waals stacking. These degrees of freedom coupled with the enhanced Coulomb interaction in 2D structures allow excitons to serve as on-chip information carriers. However, excitons are spatially circumscribed due to their low mobility and limited lifetime. One way to overcome these limitations is through the coupling of excitons with surface plasmon polaritons (SPPs), which facilitates an interaction between remote quantum states. Here, we showcase the successful coupling of SPPs with interlayer excitons in molybdenum diselenide/tungsten diselenide heterobilayers. Our results indicate that the valley polarization can be efficiently transferred to SPPs, enabling preservation of polarization information even after propagating tens of micrometers.

Van der Waals epitaxy of tunable moirés enabled by alloying

The unique physics in moiré superlattices of twisted or lattice-mismatched atomic layers holds great promise for future quantum technologies. However, twisted configurations are thermodynamically unfavourable, making accurate twist angle control during growth implausible. While rotationally aligned, lattice-mismatched moirés such as WSe2/WS2 can be synthesized, they lack the critical moiré period tunability, and their formation mechanisms are not well understood. Here, we report the thermodynamically driven van der Waals epitaxy of moirés with a tunable period from 10 to 45 nanometres, using lattice mismatch engineering in two WSSe layers with adjustable chalcogen ratios. Contrary to conventional epitaxy, where lattice-mismatch-induced stress hinders high-quality growth, we reveal the key role of bulk stress in moiré formation and its unique interplay with edge stress in shaping the moiré growth modes. Moreover, the superlattices display tunable interlayer excitons and moiré intralayer excitons. Our studies unveil the epitaxial science of moiré synthesis and lay the foundations for moiré-based technologies.

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

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

Competition of Moiré Network Sites to Form Electronic Quantum Dots in Reconstructed MoX2/WX2 Heterostructures

Twisted bilayers of two-dimensional semiconductors offer a versatile platform for engineering quantum states for charge carriers using moiré superlattice effects. Among the systems of recent interest are twistronic MoX2/WX2 heterostructures (X = Se or S), which undergo reconstruction into preferential stacking domains and highly strained domain wall networks, determining the electron/hole localization across moiré superlattices. Here, we present a catalogue of options for the formation of self-organized quantum dots and wires in lattice-reconstructed marginally twisted MoX2/WX2 bilayers with a relative lattice mismatch δ ≪ 1 for twist angles ranging from perfect alignment to θ ∼ 1°. On the basis of multiscale modeling taking into account twirling of domain wall networks, we analyze bilayers with both parallel and antiparallel orientations of their unit cells and describe crossovers between different positioning of band edges for electrons and holes across moiré superlattices when θ < δ and θ > δ.

Engineering correlated insulators in bilayer graphene with a remote Coulomb superlattice

Electron superlattices allow the engineering of correlated and topological quantum phenomena. The recent emergence of moiré superlattices in two-dimensional heterostructures has led to exciting discoveries related to quantum phenomena. However, the requirement for the moiré pattern poses stringent limitations, and its potential cannot be switched on and off. Here, we demonstrate remote engineering and on/off switching of correlated states in bilayer graphene. Employing a remote Coulomb superlattice realized by localized electrons in twisted bilayer WS2, we impose a Coulomb superlattice in the bilayer graphene with period and strength determined by the twisted bilayer WS2. When the remote superlattice is turned off, the two-dimensional electron gas in the bilayer graphene is described by a Fermi liquid. When it is turned on, correlated insulating states at both integer and fractional filling factors emerge. This approach enables in situ control of correlated quantum phenomena in two-dimensional materials hosting a two-dimensional electron gas.

Recent Strategies for the Synthesis of Phase-Pure Ultrathin 1T/1T' Transition Metal Dichalcogenide Nanosheets

The past few decades have witnessed a notable increase in transition metal dichalcogenide (TMD) related research not only because of the large family of TMD candidates but also because of the various polytypes that arise from the monolayer configuration and layer stacking order. The peculiar physicochemical properties of TMD nanosheets enable an enormous range of applications from fundamental science to industrial technologies based on the preparation of high-quality TMDs. For polymorphic TMDs, the 1T/1T' phase is particularly intriguing because of the enriched density of states, and thus facilitates fruitful chemistry. Herein, we comprehensively discuss the most recent strategies for direct synthesis of phase-pure 1T/1T' TMD nanosheets such as mechanical exfoliation, chemical vapor deposition, wet chemical synthesis, atomic layer deposition, and more. We also review frequently adopted methods for phase engineering in TMD nanosheets ranging from chemical doping and alloying, to charge injection, and irradiation with optical or charged particle beams. Prior to the synthesis methods, we discuss the configuration of TMDs as well as the characterization tools mostly used in experiments. Finally, we discuss the current challenges and opportunities as well as emphasize the promising fields for the future development.

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

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

Nonlinear and Negative Effective Diffusivity of Interlayer Excitons in Moiré-Free Heterobilayers

Interlayer exciton diffusion is studied in atomically reconstructed MoSe_{2}/WSe_{2} heterobilayers with suppressed disorder. Local atomic registry is confirmed by characteristic optical absorption, circularly polarized photoluminescence, and g-factor measurements. Using transient microscopy we observe propagation properties of interlayer excitons that are independent from trapping at moiré- or disorder-induced local potentials. Confirmed by characteristic temperature dependence for free particles, linear diffusion coefficients of interlayer excitons at liquid helium temperature and low excitation densities are almost 1000 times higher than in previous observations. We further show that exciton-exciton repulsion and annihilation contribute nearly equally to nonlinear propagation by disentangling the two processes in the experiment and simulations. Finally, we demonstrate effective shrinking of the light emission area over time across several hundreds of picoseconds at the transition from exciton- to the plasma-dominated regimes. Supported by microscopic calculations for band gap renormalization to identify the Mott threshold, this indicates transient crossing between rapidly expanding, short-lived electron-hole plasma and slower, long-lived exciton populations.

Multiresistance states in ferro- and antiferroelectric trilayer boron nitride

Stacking two atomic layers together can induce interlayer (sliding) ferroelectricity that is absent in their naturally occurring crystal forms. With the flexibility of two-dimensional materials, more layers could be assembled to give rise to even richer polarization states. Here, we show that three-layer boron nitride can host ferro- and antiferroelectric domains in the same sample. When used as a tunneling junction, the polarization of these domains could be switched in a layer-by-layer procedure, producing multiple resistance states. Theoretical investigation reveals an important role played by the interaction between the trilayer boron nitride and graphene substrate. These findings reveal the great potential and unique properties of 2D sliding ferroelectric materials.

Tuning commensurability in twisted van der Waals bilayers

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

Influence of Atomic Relaxations on the Moiré Flat Band Wave Functions in Antiparallel Twisted Bilayer WS2

Twisting bilayers of transition metal dichalcogenides gives rise to a moiré potential resulting in flat bands with localized wave functions and enhanced correlation effects. In this work, scanning tunneling microscopy is used to image a WS2 bilayer twisted approximately 3° off the antiparallel alignment. Scanning tunneling spectroscopy reveals localized states in the vicinity of the valence band onset, which is observed to occur first in regions with S-on-S Bernal stacking. In contrast, density functional theory calculations on twisted bilayers that have been relaxed in vacuum predict the highest-lying flat valence band to be localized in regions of AA' stacking. However, agreement with experiment is recovered when the calculations are performed on bilayers in which the atomic displacements from the unrelaxed positions have been reduced, reflecting the influence of the substrate and finite temperature. This demonstrates the delicate interplay of atomic relaxations and the electronic structure of twisted bilayer materials.

Quantifying Strain in Moiré Superlattice

In twisted van der Waals (vdW) bilayers, intrinsic strain associated with the moiré superlattice and unintentionally introduced uniaxial strain may be present simultaneously. Both strains are able to lift the degeneracy of the E2g phonon modes in Raman spectra. Because of the different rotation symmetry of the two types of strain, the corresponding Raman intensity exhibits a distinct polarization dependence. We compare a 2.5° twisted MoS2 bilayer, in which the maximal intrinsic moiré strain is anticipated, and a natural MoS2 bilayer with an intentionally introduced uniaxial strain. By analyzing the frequency shift of the E2g doublet and their polarization dependence, we can not only determine the direction of unintentional uniaxial strain in the twisted bilayer but also quantify both strain components. This simple strain characterization method based on far-field Raman spectra will facilitate the studies of electronic properties of moiré superlattices under the influence of combined intrinsic and external strains.

Mechanical, electronic, optical, piezoelectric and ferroic properties of strained graphene and other strained monolayers and multilayers: an update

This is an update of a previous review (Naumiset al2017Rep. Prog. Phys.80096501). Experimental and theoretical advances for straining graphene and other metallic, insulating, ferroelectric, ferroelastic, ferromagnetic and multiferroic 2D materials were considered. We surveyed (i) methods to induce valley and sublattice polarisation (P) in graphene, (ii) time-dependent strain and its impact on graphene's electronic properties, (iii) the role of local and global strain on superconductivity and other highly correlated and/or topological phases of graphene, (iv) inducing polarisationPon hexagonal boron nitride monolayers via strain, (v) modifying the optoelectronic properties of transition metal dichalcogenide monolayers through strain, (vi) ferroic 2D materials with intrinsic elastic (σ), electric (P) and magnetic (M) polarisation under strain, as well as incipient 2D multiferroics and (vii) moiré bilayers exhibiting flat electronic bands and exotic quantum phase diagrams, and other bilayer or few-layer systems exhibiting ferroic orders tunable by rotations and shear strain. The update features the experimental realisations of a tunable two-dimensional Quantum Spin Hall effect in germanene, of elemental 2D ferroelectric bismuth, and 2D multiferroic NiI2. The document was structured for a discussion of effects taking place in monolayers first, followed by discussions concerning bilayers and few-layers, and it represents an up-to-date overview of exciting and newest developments on the fast-paced field of 2D materials.

Anisotropic Interlayer Force Field for Group-VI Transition Metal Dichalcogenides

An anisotropic interlayer force field that describes the interlayer interactions in homogeneous and heterogeneous interfaces of group-VI transition metal dichalcogenides (MX2, where M = Mo, W, and X = S, Se) is presented. The force field is benchmarked against density functional theory calculations for bilayer systems within the Heyd-Scuseria-Ernzerhof hybrid density functional approximation, augmented by a nonlocal many-body dispersion treatment of long-range correlation. The parametrization yields good agreement with the reference calculations of binding energy curves and sliding potential energy surfaces. It is found to be transferable to transition metal dichalcogenide (TMD) junctions outside of the training set that contain the same atom types. Calculated bulk moduli agree with most previous dispersion-corrected density functional theory predictions, which underestimate the available experimental values. Calculated phonon spectra of the various junctions under consideration demonstrate the importance of appropriately treating the anisotropic nature of the layered interfaces. Considering our previous parametrization for MoS2, the anisotropic interlayer potential enables accurate and efficient large-scale simulations of the dynamical, tribological, and thermal transport properties of a large set of homogeneous and heterogeneous TMD interfaces.

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

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

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

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

Twirling and Spontaneous Symmetry Breaking of Domain Wall Networks in Lattice-Reconstructed Heterostructures of Two-Dimensional Materials

Lattice relaxation in twistronic bilayers with close lattice parameters and almost perfect crystallographic alignment of the layers results in the transformation of the moiré pattern into a sequence of preferential stacking domains and domain wall networks. Here, we show that reconstructed moiré superlattices of the perfectly aligned heterobilayers of same chalcogen transition metal dichalcogenides have broken-symmetry structures featuring twisted nodes ("twirls") of domain wall networks. The analysis of twist-angle dependence of strain characteristics for the broken-symmetry structures shows that the formation of twirl reduces the amount of hydrostatic strain around the nodes, potentially weakening their influence on the band edge energies of electrons and holes.

Visualizing moiré ferroelectricity via plasmons and nano-photocurrent in graphene/twisted-WSe2 structures

Ferroelectricity, a spontaneous and reversible electric polarization, is found in certain classes of van der Waals (vdW) materials. The discovery of ferroelectricity in twisted vdW layers provides new opportunities to engineer spatially dependent electric and optical properties associated with the configuration of moiré superlattice domains and the network of domain walls. Here, we employ near-field infrared nano-imaging and nano-photocurrent measurements to study ferroelectricity in minimally twisted WSe2. The ferroelectric domains are visualized through the imaging of the plasmonic response in a graphene monolayer adjacent to the moiré WSe2 bilayers. Specifically, we find that the ferroelectric polarization in moiré domains is imprinted on the plasmonic response of the graphene. Complementary nano-photocurrent measurements demonstrate that the optoelectronic properties of graphene are also modulated by the proximal ferroelectric domains. Our approach represents an alternative strategy for studying moiré ferroelectricity at native length scales and opens promising prospects for (opto)electronic devices.

Kinetics of Nanobubbles in Tiny-Angle Twisted Bilayer Graphene

Realization of high-quality van der Waals (vdWs) heterostructures by stacking two-dimensional (2D) layers requires atomically clean interfaces. Because of strong adhesion between the constituent layers, the vdWs forces could drive trapped contaminants together into submicron-size "bubbles", which leaves large interfacial areas atomically clean. Here, we study the kinetics of nanobubbles in tiny-angle twisted bilayer graphene (TBG) and our results reveal a substantial influence of the moiré superlattice on the motion of nanoscale interfacial substances. Our experiments indicate that the bubbles will mainly move along the triangular network of domain boundaries in the tiny-angle TBG when the sizes of the bubbles are comparable to that of an AA-stacking region. When the size of the bubble is smaller than that of an AA-stacking region, the bubble becomes motionless and is fixed in the AA-stacking region, because of its large out-of-plane corrugation.

Ferroelectric Switching at Symmetry-Broken Interfaces by Local Control of Dislocations Networks

Semiconducting ferroelectric materials with low energy polarization switching offer a platform for next-generation electronics such as ferroelectric field-effect transistors. Recently discovered interfacial ferroelectricity in bilayers of transition metal dichalcogenide films provides an opportunity to combine the potential of semiconducting ferroelectrics with the design flexibility of 2D material devices. Here, local control of ferroelectric domains in a marginally twisted WS2 bilayer is demonstrated with a scanning tunneling microscope at room temperature, and their observed reversible evolution is understood using a string-like model of the domain wall network (DWN). Two characteristic regimes of DWN evolution are identified: (i) elastic bending of partial screw dislocations separating smaller domains with twin stackings due to mutual sliding of monolayers at domain boundaries and (ii) merging of primary domain walls into perfect screw dislocations, which become the seeds for the recovery of the initial domain structure upon reversing electric field. These results open the possibility to achieve full control over atomically thin semiconducting ferroelectric domains using local electric fields, which is a critical step towards their technological use.

Atomic Resolution Imaging of Highly Air-Sensitive Monolayer and Twisted-Bilayer WTe2

Bulk Td-WTe2 is a semimetal, while its monolayer counterpart is a two-dimensional (2D) topological insulator. Recently, electronic transport resembling a Luttinger liquid state was found in twisted-bilayer WTe2 (tWTe2) with a twist angle of ∼5°. Despite the strong interest in 2D WTe2 systems, little experimental information is available about their intrinsic microstructure, leaving obstacles in modeling their physical properties. The monolayer, and consequently tWTe2, are highly air-sensitive, and therefore, probing their atomic structures is difficult. In this study, we develop a robust method for atomic-resolution visualization of monolayers and tWTe2 obtained through mechanical exfoliation and fabrication. We confirm the high crystalline quality of mechanically exfoliated WTe2 samples and observe that tWTe2 with twist angles of ∼5 and ∼2° retains its pristine moiré structure without substantial deformations or reconstructions. The results provide a structural foundation for future electronic modeling of monolayer and tWTe2 moiré lattices.

Operando electron microscopy investigation of polar domain dynamics in twisted van der Waals homobilayers

Conventional antiferroelectric materials with atomic-scale anti-aligned dipoles undergo a transition to a ferroelectric (FE) phase under strong electric fields. The moiré superlattice formed in the twisted stacks of van der Waals crystals exhibits polar domains alternating in moiré length with anti-aligned dipoles. In this moiré domain antiferroelectic (MDAF) arrangement, the distribution of electric dipoles is distinguished from that of two-dimensional FEs, suggesting dissimilar domain dynamics. Here we performed an operando transmission electron microscopy investigation on twisted bilayer WSe2 to observe the polar domain dynamics in real time. We find that the topological protection, provided by the domain wall network, prevents the MDAF-to-FE transition. As one decreases the twist angle, however, this transition occurs as the domain wall network disappears. Exploiting stroboscopic operando transmission electron microscopy on the FE phase, we measure a maximum domain wall velocity of 300 μm s-1. Domain wall pinnings by various disorders limit the domain wall velocity and cause Barkhausen noises in the polarization hysteresis loop. Atomic-scale analysis of the pinning disorders provides structural insight on how to improve the switching speed of van der Waals FEs.

Modulation of Phonons and Excitons Due to Moiré Potentials in Twisted Bilayer of WSe2/MoSe2

The application of two-dimensional materials has been expanded by introducing the twisted bilayer (TBL) system. However, the landscape of the interlayer interaction in hetero-TBLs has not yet been fully understood, while that in homo-TBLs has been extensively studied, with the dependence on the twist angle between the constituent layers. Here, we present detailed analyses on the interlayer interaction that depends on the twist angle in WSe₂/MoSe₂ hetero-TBL via Raman and photoluminescence studies combined with first-principles calculation. We observe interlayer vibrational modes, moiré phonons, and the interlayer excitonic states that evolve with the twist angle and identify different regimes with distinct characteristics of such features. Moreover, the interlayer excitons that appear strong in the hetero-TBLs with twist angles near 0° or 60° have different energies and photoluminescence excitation spectra for the two cases, which results from different electronic structures and carrier relaxation dynamics. These results would enable a better understanding of the interlayer interaction in hetero-TBLs.

Excitons in mesoscopically reconstructed moiré heterostructures

Moiré effects in vertical stacks of two-dimensional crystals give rise to new quantum materials with rich transport and optical phenomena that originate from modulations of atomic registries within moiré supercells. Due to finite elasticity, however, the superlattices can transform from moiré-type to periodically reconstructed patterns. Here we expand the notion of such nanoscale lattice reconstruction to the mesoscopic scale of laterally extended samples and demonstrate rich consequences in optical studies of excitons in MoSe₂-WSe₂ heterostructures with parallel and antiparallel alignments. Our results provide a unified perspective on moiré excitons in near-commensurate semiconductor heterostructures with small twist angles by identifying domains with exciton properties of distinct effective dimensionality, and establish mesoscopic reconstruction as a compelling feature of real samples and devices with inherent finite size effects and disorder. Generalized to stacks of other two-dimensional materials, this notion of mesoscale domain formation with emergent topological defects and percolation networks will instructively expand the understanding of fundamental electronic, optical and magnetic properties of van der Waals heterostructures.

Rotational and dilational reconstruction in transition metal dichalcogenide moiré bilayers

Lattice reconstruction and corresponding strain accumulation plays a key role in defining the electronic structure of two-dimensional moiré superlattices, including those of transition metal dichalcogenides (TMDs). Imaging of TMD moirés has so far provided a qualitative understanding of this relaxation process in terms of interlayer stacking energy, while models of the underlying deformation mechanisms have relied on simulations. Here, we use interferometric four-dimensional scanning transmission electron microscopy to quantitatively map the mechanical deformations through which reconstruction occurs in small-angle twisted bilayer MoS₂ and WSe₂/MoS₂ heterobilayers. We provide direct evidence that local rotations govern relaxation for twisted homobilayers, while local dilations are prominent in heterobilayers possessing a sufficiently large lattice mismatch. Encapsulation of the moiré layers in hBN further localizes and enhances these in-plane reconstruction pathways by suppressing out-of-plane corrugation. We also find that extrinsic uniaxial heterostrain, which introduces a lattice constant difference in twisted homobilayers, leads to accumulation and redistribution of reconstruction strain, demonstrating another route to modify the moiré potential.

Single Photon Emitters with Polarization and Orbital Angular Momentum Locking in Monolayer Semiconductors

Excitons in monolayer transition metal dichalcogenide are endowed with intrinsic valley-orbit coupling between their center-of-mass motion and valley pseudospin. When trapped in a confinement potential, e.g., generated by strain field, we find that intralayer excitons are valley and orbital angular momentum (OAM) entangled. By tuning the trap profile and external magnetic field, one can engineer the exciton states at the ground state and realize a series of valley-OAM entangled states. We further show that the OAM of excitons can be transferred to emitted photons, and these novel exciton states can naturally serve as polarization-OAM locked single photon emitters, which under certain circumstance become polarization-OAM entangled, highly tunable by strain trap and magnetic field. Our proposal demonstrates a novel scheme to generate polarization-OAM locked/entangled photons at the nanoscale with a high degree of integrability and tunability, pointing to exciting opportunities for quantum information applications.

Complex Strain Scapes in Reconstructed Transition-Metal Dichalcogenide Moiré Superlattices

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

Research Process on Photodetectors based on Group-10 Transition Metal Dichalcogenides

Rapidly evolving group-10 transition metal dichalcogenides (TMDCs) offer remarkable electronic, optical, and mechanical properties, making them promising candidates for advanced optoelectronic applications. Compared to most TMDCs semiconductors, group-10-TMDCs possess unique structures, narrow bandgap, and influential physical properties that motivate the development of broadband photodetectors, specifically infrared photodetectors. This review presents the latest developments in the fabrication of broadband photodetectors based on conventional 2D TMDCs. It mainly focuses on the recent developments in group-10 TMDCs from the perspective of the lattice structure and synthesis techniques. Recent progress in group-10 TMDCs and their heterostructures with different dimensionality of materials-based broadband photodetectors is provided. Moreover, this review accounts for the latest applications of group-10 TMDCs in the fields of nanoelectronics and optoelectronics. Finally, conclusions and outlooks are summarized to provide perspectives for next-generation broadband photodetectors based on group-10 TMDCs.

Pair-Density-Wave and Chiral Superconductivity in Twisted Bilayer Transition Metal Dichalcogenides

We theoretically explore possible orders induced by weak repulsive interactions in twisted bilayer transition metal dichalcogenides (e.g., WSe_{2}) in the presence of an out-of-plane electric field. Using renormalization group analysis, we show that superconductivity survives even with the conventional van Hove singularities. We find that topological chiral superconducting states with Chern number N=1, 2, 4 (namely, p+ip, d+id, and g+ig) appear over a large parameter region with a moiré filling factor around n=1. At some special values of applied electric field and in the presence of a weak out-of-plane Zeeman field, spin-polarized pair-density-wave (PDW) superconductivity can emerge. This spin-polarized PDW state can be probed by experiments such as spin-polarized STM measuring spin-resolved pairing gap and quasiparticle interference. Moreover, the spin-polarized PDW could lead to a spin-polarized superconducting diode effect.

An Atomistic Insight into Moiré Reconstruction in Twisted Bilayer Graphene beyond the Magic Angle

Twisted bilayer graphene exhibits electronic properties strongly correlated with the size and arrangement of moiré patterns. While rigid rotation of the two graphene layers results in a moiré interference pattern, local rearrangements of atoms due to interlayer van der Waals interactions result in atomic reconstruction within the moiré cells. Manipulating these patterns by controlling the twist angle and externally applied strain provides a promising route to tuning their properties. Atomic reconstruction has been extensively studied for angles close to or smaller than the magic angle (θ _m = 1.1°). However, this effect has not been explored for applied strain and is believed to be negligible for high twist angles. Using interpretive and fundamental physical measurements, we use theoretical and numerical analyses to resolve atomic reconstruction in angles above θ _m . In addition, we propose a method to identify local regions within moiré cells and track their evolution with strain for a range of representative high twist angles. Our results show that atomic reconstruction is actively present beyond the magic angle, and its contribution to the moiré cell evolution is significant. Our theoretical method to correlate local and global phonon behavior further validates the role of reconstruction at higher angles. Our findings provide a better understanding of moiré reconstruction in large twist angles and the evolution of moiré cells under the application of strain, which might be potentially crucial for twistronics-based applications.

Real-Space Mapping of Local Subdegree Lattice Rotations in Low-Angle Twisted Bilayer Graphene

In two-dimensional small-angle twisted bilayers, van der Waals (vdW) interlayer interaction introduces an atomic-scale reconstruction, which consists of a moiré-periodic network of local subdegree lattice rotations. However, real-space measurement of the subdegree lattice rotation requires extremely high spatial resolution, which is an outstanding challenge in an experiment. Here, a topmost small-period graphene moiré pattern is introduced as a magnifying lens to magnify sub-Angstrom lattice distortions in small-angle twisted bilayer graphene (TBG) by about 2 orders of magnitude. Local moiré periods of the topmost graphene moiré patterns and low-energy van Hove singularities of the system are spatially modified by the atomic-scale reconstruction of the underlying TBG, thus enabling real-space mapping of the networks of the subdegree lattice rotations both in structure and in electronic properties. Our results indicate that it is quite facile to study subdegree lattice rotation in vdW systems by measuring the periods of the topmost moiré superlattice.

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

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

Inversion Symmetry and Exotic Interlayer Exciton Behavior in Twisted Trilayer MoS2 Produced by Vapor Deposition

Two-dimensional materials (2DMs) that are stacked vertically with a certain twist angle provide new degrees of freedom for designing novel physical properties. Twist-related properties of homogeneous bilayer and heterogeneous bilayer 2DMs, such as excitons and phonons, have been described in many pioneering works. However, twist-related properties of homogeneous trilayer 2DMs have been rarely reported. In this work, trilayer MoS₂ with the twisted angle of 12° by optimized vapor deposition rather than the conventional mechanical stacking method was successfully fabricated. The inversion symmetry of trilayer MoS₂ is changed by twist. Phonons and excitons produced by twist have an enormous influence on the interlayer interaction of trilayer MoS₂, making trilayer MoS₂ appear to have exotic optical properties. Compared with monolayer MoS₂, the phonon vibration and photoluminescence intensity of trilayer MoS₂ with one-interlayer-twisted are significantly improved, and the second harmonic generation response in the non-twist region of trilayer MoS₂ is ∼3 times that of monolayer MoS₂. In addition, interlayer coupling, inversion symmetry, and exciton behavior of the twist region show regional differences. This work provides a new way for designing twist and exploring the influence of twist on the structures of 2DMs with few layers.