Tailoring the electronic structure in bilayer molybdenum disulfide via interlayer twist

Moiré Superlattice in Two-Dimensional Materials: Fundamentals, Applications, and Recent Developments

Moiré superlattices, arising from the periodic Moiré patterns formed by two-dimensional (2D) materials stacked with a slight lattice mismatch, have attracted significant attention due to their unique electronic and optical performances. This review provides an overview of recent advances in Moiré superlattices, highlighting their formation mechanisms, structural characteristics, and emergent phenomena. First, we discuss the theoretical basis and experimental techniques employed in fabricating Moiré superlattices. Then we outline various characterization methods that enable the investigation of the structural and electronic performance of Moiré superlattices at the atomic scale. Afterward, we review the diverse range of emergent phenomena exhibited in Moiré superlattices. These phenomena include the appearance of electronic band engineering, unconventional superconductivity, and topologically nontrivial state. We explore how these phenomena arise from the interplay between the original electronic properties of the constituent materials and the Moiré pattern-induced modifications. Furthermore, we examine the potential applications of Moiré superlattices in fields such as electronics, optoelectronics, and quantum technologies. Finally, we summarize the challenges and directions in Moiré superlattice research, which include exploring more complex Moiré patterns, understanding the role of twist angle and strain engineering, and developing theoretical frameworks to describe the behaviors of Moiré systems. This review aims to provide a comprehensive understanding of the recent progress in Moiré superlattices, shedding light on their formation, performance, and potential applications. The insights gained from this research are expected to pave the way for the design and development of next-generation functional Moiré superlattices.

Control of Subband Energies via Interlayer Twisting in an Artificially Stacked WSe2 Bilayer

Tuning the electronic structure of artificially stacked bilayer crystals using their twist angle has attracted a significant amount of interest. In this study, resonant tunneling spectroscopy was performed on trilayer WSe2/h-BN/twisted bilayer (tBL) WSe2 devices with a wide range of twist angles (θBL) of tBL WSe2, from 0° to 34°. We observed two resonant tunneling peaks, identified as the first and second lowest hole subbands at the valence band Γ point of tBL WSe2. The subband separation, which directly measured the interlayer coupling strength, was tuned by ∼0.1 eV as θBL increased toward 6° and remained nearly constant for larger θBL values. The θBL dependence was attributed to the emergence of a stable W/Se (Se/W) stacking domain in the small θBL region, owing to the atomic reconstruction of the moiré lattice in tBL WSe2. Our findings demonstrate that the twist-controlled subband energies in tBL WSe2 are predominantly determined by local atomic reconstruction.

Delocalization of Quasiparticle Moiré States in Twisted Bilayer hBN

Twisted bilayers host many emergent phenomena in which the electronic excitations (quasiparticles, QPs) are closely intertwined with the local stacking order. By inspecting twisted hexagonal boron nitride (t-hBN), we show that nonlocal long-range interactions in large twisted systems cannot be reliably described by the local (high-symmetry) stacking and that the band gap variation (typically associated with the moiré excitonic potential) shows multiple minima with variable depth depending on the twist angle. We investigate twist angles of 2.45°, 2.88°, 3.48°, and 5.09° using the GW approximation together with stochastic compression to analyze the QP state interactions. We find that band-edge QP hybridization is suppressed for intermediate angles that exhibit two distinct local minima in the moiré potential (at AA region and saddle point (SP)) which become degenerate for the largest system (2.45°).

Helicity-Resolved Vibrational Coupling in Twist WS2/WSe2 Heterostructures

Helicity-resolved Raman spectra can provide an intricate view into lattice structural details. Through the analysis of peak positions, intensities, and circular polarized Raman signals, a wealth of information about chiral structure arrangement within the moiré superlattice, interlayer interaction strength, polarizability change in chemical bond, and beyond can be unveiled. However, the relationship between the circular polarization of high-frequency Raman and twist angle is still not clear. Here, we utilize helicity-resolved Raman spectroscopy to explore the interlayer interactions and the effect of the moiré superlattice in WS2/WSe2 heterostructures. For the out-of-plane Raman mode A1g of WS2 (A1g and 1E2g of WSe2), its intensity is significantly enhanced (suppressed) in WS2/WSe2 heterostructures when θ is less than 10° or greater than 50°. This observation could be attributed to the large polarizability changes in both W-S and W-Se covalent bonds. The circular polarization of 2LA(M) in WSe2 of the WS2/WSe2 heterostructure (θ < 10° or θ > 50°) is significantly enhanced compared to that of 2LA(M) in the monolayer WSe2. We deduce that the circular polarization of the Raman mode correlates with the proportion of high-symmetry area within a supercell of the moiré lattice. Our findings improve the understanding of twist-angle-modulated Raman modes in TMD heterostructures.

Twisted MoSe2 Homobilayer Behaving as a Heterobilayer

Heterostructures (HSs) formed by the transition-metal dichalcogenide materials have shown great promise in next-generation (opto)electronic applications. An artificially twisted HS allows us to manipulate the optical and electronic properties. In this work, we introduce the understanding of the energy transfer (ET) process governed by the dipolar interaction in a twisted molybdenum diselenide (MoSe2) homobilayer without any charge-blocking interlayer. We fabricated an unconventional homobilayer (i.e., HS) with a large twist angle (∼57°) by combining the chemical vapor deposition (CVD) and mechanical exfoliation (Exf.) techniques to fully exploit the lattice parameter mismatch and indirect/direct (CVD/Exf.) bandgap nature. These effectively weaken the interlayer charge transfer and allow the ET to control the carrier recombination channels. Our experimental and theoretical results explain a massive HS photoluminescence enhancement due to an efficient ET process. This work shows that the electronically decoupled MoSe2 homobilayer is coupled by the ET process, mimicking a "true" heterobilayer nature.

Identification and Structural Characterization of Twisted Atomically Thin Bilayer Materials by Deep Learning

Two-dimensional materials are expected to play an important role in next-generation electronics and optoelectronic devices. Recently, twisted bilayer graphene and transition metal dichalcogenides have attracted significant attention due to their unique physical properties and potential applications. In this study, we describe the use of optical microscopy to collect the color space of chemical vapor deposition (CVD) of molybdenum disulfide (MoS2) and the application of a semantic segmentation convolutional neural network (CNN) to accurately and rapidly identify thicknesses of MoS2 flakes. A second CNN model is trained to provide precise predictions on the twist angle of CVD-grown bilayer flakes. This model harnessed a data set comprising over 10,000 synthetic images, encompassing geometries spanning from hexagonal to triangular shapes. Subsequent validation of the deep learning predictions on twist angles was executed through the second harmonic generation and Raman spectroscopy. Our results introduce a scalable methodology for automated inspection of twisted atomically thin CVD-grown bilayers.

Second-harmonic generation in 2D moiré superlattices composed of bilayer transition metal dichalcogenides

Moiré superlattices (MSLs) in twisted two-dimensional van der Waals materials feature twist-angle-dependent crystal symmetry and strong optical nonlinearities. By adjusting the twist angle in bilayer van der Waals materials, the second-harmonic generation (SHG) can be controlled. Here, we focus on exploring the electronic and SHG properties of MSLs in 2D bilayer transition metal dichalcogenides (TMDs) with different twist angles through first-principles calculations. We constructed MSL structures of five TMD materials, including three single-phase materials (MoS2, WS2, and MoSe2) and two heterojunctions (MoS2/MoSe2 and MoS2/WS2) with twist angles of 9.4°, 13.2°, 21.8°, 32.2°, and 42.1° without lattice mismatch. Our findings demonstrate a consistent variation in the SHG susceptibility among different TMD MSLs as a response to twist-angle changes. The underlying reason for the twist-angle dependence of SHG is that the twist angle regulates the interlayer coupling strength, affecting the optical band gap of MSLs and subsequently tuning the SHG susceptibility. Through a comparison of the static SHG susceptibility values, we identified the twist angle of 9.4° as the configuration that yields the highest SHG susceptibility (e.g. 358.5 pm V-1 for the 9.4° MoSe2 MSL). This value is even twice that of the monolayer (173.3 pm V-1 for monolayer MoSe2) and AA'-stacked bilayer structures (139.8 pm V-1 for AA' MoSe2). This high SHG susceptibility is attributed to the strong interlayer coupling in the 9.4° MSL, which enhances the valence band energy (contributed by the antibonding orbitals of chalcogen-pz and transition metal-dz2) and consequently leads to a small optical band gap, thus improving the optical transitions. The findings of this study provide a straightforward way to improve the SHG performance of bilayer TMDs and also throw light on the sensitive relationship between the twist angle, band structure and SHG properties of TMD MSLs.

Patternable Process-Induced Strain in 2D Monolayers and Heterobilayers

Strain engineering in two-dimensional (2D) materials is a powerful but difficult to control approach to tailor material properties. Across applications, there is a need for device-compatible techniques to design strain within 2D materials. This work explores how process-induced strain engineering, commonly used by the semiconductor industry to enhance transistor performance, can be used to pattern complex strain profiles in monolayer MoS2 and 2D heterostructures. A traction-separation model is identified to predict strain profiles and extract the interfacial traction coefficient of 1.3 ± 0.7 MPa/μm and the damage initiation threshold of 16 ± 5 nm. This work demonstrates the utility to (1) spatially pattern the optical band gap with a tuning rate of 91 ± 1 meV/% strain and (2) induce interlayer heterostrain in MoS2-WSe2 heterobilayers. These results provide a CMOS-compatible approach to design complex strain patterns in 2D materials with important applications in 2D heterogeneous integration into CMOS technologies, moiré engineering, and confining quantum systems.

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.

Reconfiguring nucleation for CVD growth of twisted bilayer MoS2 with a wide range of twist angles

Twisted bilayer (TB) transition metal dichalcogenides (TMDCs) beyond TB-graphene are considered an ideal platform for investigating condensed matter physics, due to the moiré superlattices-related peculiar band structures and distinct electronic properties. The growth of large-area and high-quality TB-TMDCs with wide twist angles would be significant for exploring twist angle-dependent physics and applications, but remains challenging to implement. Here, we propose a reconfiguring nucleation chemical vapor deposition (CVD) strategy for directly synthesizing TB-MoS2 with twist angles from 0° to 120°. The twist angles-dependent Moiré periodicity can be clearly observed, and the interlayer coupling shows a strong relationship to the twist angles. Moreover, the yield of TB-MoS2 in bilayer MoS2 and density of TB-MoS2 are significantly improved to 17.2% and 28.9 pieces/mm2 by tailoring gas flow rate and molar ratio of NaCl to MoO3. The proposed reconfiguring nucleation approach opens an avenue for the precise growth of TB-TMDCs for both fundamental research and practical applications.

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.

Vitality of Intralayer Vibration in hBN for Effective Long-Range Interlayer Hole Transfer across High Barriers in MoSe2/hBN/WSe2 Heterostructures

Introducing the two-dimensional (2D) hexagonal boron nitride (hBN) between 2D transition metal dichalcogenide (TMD) layers promises convenient manipulation of the interlayer exciton (IX) and interlayer charge transfer in TMD/hBN/TMD heterostructures, while the role of inserted hBN layers during IX formation is controversial. Employing ab initio nonadiabatic molecular dynamics (NAMD) simulations and the electron-phonon coupling model, we systematically investigate interlayer hole transfer in MoSe2/WSe2 bilayers intercalated by hBN layers with various thicknesses. The conventional direct hole transfer from MoSe2 to WSe2 is decelerated by 2-3 orders of magnitude after the hBN insertion. Meanwhile, a novel channel intermediated by a deeper hole of WSe2 becomes dominant, where the intralayer shear mode of hBN plays a crucial role by reducing the energy barriers for this new channel. The unique role of hBN layers is revealed for the first time, enriching the knowledge of the underlying microscopic mechanisms and providing instructive guidance to practical van der Waals optoelectronic devices.

Polytypic Two-Dimensional FeAs with High Anisotropy

In the realm of two-dimensional (2D) crystal growth, the chemical composition often determines the thermodynamically favored crystallographic structures. This relationship poses a challenge in synthesizing novel 2D crystals without altering their chemical elements, resulting in the rarity of achieving specific crystallographic symmetries or lattice parameters. We present 2D polymorphic FeAs crystals that completely differ from bulk orthorhombic FeAs (Pnma), differing in the stacking sequence, i.e., polytypes. Preparing polytypic FeAs outlines a strategy for independently controlling each symmetry operator, which includes the mirror plane for 2Q-FeAs (I4/mmm) and the glide plane for 1Q-FeAs (P4/nmm). As such, compared to bulk FeAs, polytypic 2D FeAs shows highly anisotropic properties such as electrical conductivity, Young's modulus, and friction coefficient. This work represents a concept of expanding 2D crystal libraries with a given chemical composition but various crystal symmetries.

Single bacteria identification with second-harmonic generation in MoS2

Transition-metal dichalcogenides exhibit extraordinary optical nonlinearities, making them promising candidates for advanced photonic applications. Here, we present the microbial control over second-harmonic generation (SHG) in monolayer MoS2 and the identification of single-cell bacteria. Bacteria deposited on monolayer MoS2 induce a change in the SHG signal, in the form of anisotropic polarization responses that depend on the relative orientation of the bacteria with respect to the MoS2 crystallographic direction. The anisotropic enhancement is consistent with the presence of a tensile stress along the lateral direction of bacteria axis; SHG imaging is highly effective in monitoring biomaterial strain as low as 0.1%. We also investigate the ultraviolet-induced removal of single bacteria, through the SHG imaging of MoS2. By monitoring the transient SHG signals, we determine the rupture times for bacteria, which varies noticeably for each species. This allows us to distinguish specific bacteria that share habitats; SHG imaging is useful for label free identification of pathogens at the single cell levels such as E. coli and L. casei. This label-free detection and identification of pathogens at the single-cell level can have a profound impact on the development of diagnostic tools for various applications.

Large-scale and stacked transfer of bilayers MoS2devices on a flexible polyimide substrate

Two-dimensional transition metal dichalcogenides (TMDs), as flexible and stretchable materials, have attracted considerable attention in the field of novel flexible electronics due to their excellent mechanical, optical, and electronic properties. Among the various TMD materials, atomically thin MoS2has become the most widely used material due to its advantageous properties, such as its adjustable bandgap, excellent performance, and ease of preparation. In this work, we demonstrated the practicality of a stacked wafer-scale two-layer MoS2film obtained by transferring multiple single-layer films grown using chemical vapor deposition. The MoS2field-effect transistor cell had a top-gated device structure with a (PI) film as the substrate, which exhibited a high on/off ratio (108), large average mobility (∼8.56 cm2V-1s-1), and exceptional uniformity. Furthermore, a range of flexible integrated logic devices, including inverters, NOR gates, and NAND gates, were successfully implemented via traditional lithography. These results highlight the immense potential of TMD materials, particularly MoS2, in enabling advanced flexible electronic and optoelectronic devices, which pave the way for transformative applications in future-generation electronics.

Torsional deformation modulation of the electronic structure and optical properties of molybdenum ditelluride systems doped with halogen atoms X (X = F, Cl, Br, I): a first-principles study

CONTEXT

Using a first-principles plane-wave pseudopotential technique within the context of density-functional theory, the electronic structure and optical properties of the molybdenum ditelluride system doped with halogen atoms X (X = F, Cl, Br, I) were investigated. The electronic structure, density of states, charge transfer, and optical properties of halogen atom X doped on MoTe2 monolayer are systematically calculated and analyzed. It shows that the Fermi energy level is shifted upward after doping with halogen atoms. With F-MoTe2 doping, the geometrical distortion is the most pronounced, the charge transfer number is the highest, and the semiconductor shifts from a direct band gap to an indirect band gap. When the torsional deformation is between 1° and 5°, the F-doped MoTe2 system stays an indirect band gap semiconductor and transitions to quasi-metal at 6°. It is shown that the torsional deformation can modulate the electronic properties of the doped structure and realize the semiconductor-metal transition.

OPTICAL PROPERTIES

The F-doped system has a strong absorption peak reflection peak after torsion, and with the increase of torsion angle, the absorption peak is red-shifted, and the reflection peak is blue-shifted. Moreover, the absorption and reflection peaks start to decrease with the rise of the torsion angle.

METHODS

We apply the generalized gradient approximation plane-wave pseudopotential technique based on Perdew-Burke-Ernzerhof (PBE) generalized functions, under the first principles of the density-functional theory framework. The overall optimization of the intrinsic molybdenum ditelluride structure and the halogen atom X-doped molybdenum ditelluride structure was carried out. Then, the F-doped molybdenum ditelluride system was selected for torsional deformation with torsion angles from 1° to 6° for computational analysis.

SPECIFIC METHOD

To make the presentation more accessible, the atoms in the F-doped molybdenum ditelluride system were colored differently. The pink chain edge atoms were first reversed by θ°. Then, the blue chain edge atoms were reversed by θ° in the other direction. The middle row of atoms was adjusted accordingly to the different twisting angles of the two sides by doing the corresponding torsion with the torsion angle θ°/2 and fixing the individual atoms. The calculation employs the Monkhorst-Pack particular K-point sampling method. The 3 × 3 × 1 inverted-space K-point grid is utilized for material structure optimization calculations in each model, and the 9 × 9 × 1 K-point grid is used for material electronic structure calculations. A 15 Å vacuum layer is put on the crystal surface of vertical monolayer molybdenum ditelluride supercells to avoid interactions with adjoining cells.

Twist Angle-Dependent Intervalley Charge Carrier Transfer and Recombination in Bilayer WS2

A twist angle at a van der Waals junction provides a handle to tune its optoelectronic properties for a variety of applications, and a comprehensive understanding of how the twist modulates electronic structure, interlayer coupling, and carrier dynamics is needed. We employ time-dependent density functional theory and nonadiabatic molecular dynamics to elucidate angle-dependent intervalley carrier transfer and recombination in bilayer WS2. Repulsion between S atoms in twisted configurations weakens interlayer coupling, increases the interlayer distance, and softens layer breathing modes. Twisting has a minor influence on K valleys while it lowers Γ valleys and raises Q valleys because their wave functions are delocalized between layers. Consequently, the reduced energy gaps between the K and Γ valleys accelerate the hole transfer in the twisted structures. Intervalley electron transfer proceeds nearly an order of magnitude faster than hole transfer. The more localized wave functions at K than Q values and larger bandgaps result in smaller nonadiabatic couplings for intervalley recombination, making it 3-4 times slower in twisted than high-symmetry structures. B2g breathing, E2g in-plane, and A1g out-of-plane modes are most active during intervalley carrier transfer and recombination. The faster intervalley transfer and extended carrier lifetimes in twisted junctions are favorable for optoelectronic device performance.

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

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

Recent Advances in Moiré Superlattice Systems by Angle-Resolved Photoemission Spectroscopy

The last decade has witnessed a flourish in 2D materials including graphene and transition metal dichalcogenides (TMDs) as atomic-scale Legos. Artificial moiré superlattices via stacking 2D materials with a twist angle and/or a lattice mismatch have recently become a fertile playground exhibiting a plethora of emergent properties beyond their building blocks. These rich quantum phenomena stem from their nontrivial electronic structures that are effectively tuned by the moiré periodicity. Modern angle-resolved photoemission spectroscopy (ARPES) can directly visualize electronic structures with decent momentum, energy, and spatial resolution, thus can provide enlightening insights into fundamental physics in moiré superlattice systems and guides for designing novel devices. In this review, first, a brief introduction is given on advanced ARPES techniques and basic ideas of band structures in a moiré superlattice system. Then ARPES research results of various moiré superlattice systems are highlighted, including graphene on substrates with small lattice mismatches, twisted graphene/TMD moiré systems, and high-order moiré superlattice systems. Finally, it discusses important questions that remain open, challenges in current experimental investigations, and presents an outlook on this field of research.

Flattening conduction and valence bands for interlayer excitons in a moiré MoS2/WSe2 heterobilayer

We explore the flatness of conduction and valence bands of interlayer excitons in MoS2/WSe2 van der Waals heterobilayers, tuned by interlayer twist angle, pressure, and external electric field. We employ an efficient continuum model where the moiré pattern from lattice mismatch and/or twisting is represented by an equivalent mesoscopic periodic potential. We demonstrate that the mismatch moiré potential is too weak to produce significant flattening. Moreover, we draw attention to the fact that the quasi-particle effective masses around the Γ-point and the band flattening are reduced with twisting. As an alternative approach, we show (i) that reducing the interlayer distance by uniform vertical pressure can significantly increase the effective mass of the moiré hole, and (ii) that the moiré depth and its band flattening effects are strongly enhanced by accessible electric gating fields perpendicular to the heterobilayer, with resulting electron and hole effective masses increased by more than an order of magnitude - leading to record-flat bands. These findings impose boundaries on the commonly generalized benefits of moiré twistronics, while also revealing alternative feasible routes to achieve truly flat electron and hole bands to carry us to strongly correlated excitonic phenomena on demand.

Achieving near-perfect light absorption in atomically thin transition metal dichalcogenides through band nesting

Near-perfect light absorbers (NPLAs), with absorbance, [Formula: see text], of at least 99%, have a wide range of applications ranging from energy and sensing devices to stealth technologies and secure communications. Previous work on NPLAs has mainly relied upon plasmonic structures or patterned metasurfaces, which require complex nanolithography, limiting their practical applications, particularly for large-area platforms. Here, we use the exceptional band nesting effect in TMDs, combined with a Salisbury screen geometry, to demonstrate NPLAs using only two or three uniform atomic layers of transition metal dichalcogenides (TMDs). The key innovation in our design, verified using theoretical calculations, is to stack monolayer TMDs in such a way as to minimize their interlayer coupling, thus preserving their strong band nesting properties. We experimentally demonstrate two feasible routes to controlling the interlayer coupling: twisted TMD bi-layers and TMD/buffer layer/TMD tri-layer heterostructures. Using these approaches, we demonstrate room-temperature values of [Formula: see text]=95% at λ=2.8 eV with theoretically predicted values as high as 99%. Moreover, the chemical variety of TMDs allows us to design NPLAs covering the entire visible range, paving the way for efficient atomically-thin optoelectronics.

Expansion of the Materials Cloud 2D Database

Two-dimensional (2D) materials are among the most promising candidates for beyond-silicon electronic, optoelectronic, and quantum computing applications. Recently, their recognized importance sparked a push to discover and characterize novel 2D materials. Within a few years, the number of experimentally exfoliated or synthesized 2D materials went from a few to more than a hundred, with the number of theoretically predicted compounds reaching a few thousand. In 2018 we first contributed to this effort with the identification of 1825 compounds that are either easily (1036) or potentially (789) exfoliable from experimentally known 3D compounds. Here, we report on a major expansion of this 2D portfolio thanks to the extension of the screening protocol to an additional experimental database (MPDS) as well as the updated versions of the two databases (ICSD and COD) used in our previous work. This expansion leads to the discovery of an additional 1252 monolayers, bringing the total to 3077 compounds and, notably, almost doubling the number of easily exfoliable materials to 2004. We optimize the structural properties of all these monolayers and explore their electronic structure with a particular emphasis on those rare large-bandgap 2D materials that could be precious in isolating 2D field-effect-transistor channels. Finally, for each material containing up to 6 atoms per unit cell, we identify the best candidates to form commensurate heterostructures, balancing requirements on supercell size and minimal strain.

A natural indirect-to-direct band gap transition in artificially fabricated MoS2 and MoSe2 flowers

Twisted bilayer (tB) transition metal dichalcogenide (TMD) structures formed from two pieces of a periodic pattern overlaid with a relative twist manifest novel electronic and optical properties and correlated electronic phenomena. Here, twisted flower-like MoS₂ and MoSe₂ bilayers were artificially fabricated by the chemical vapor deposition (CVD) method. Photoluminescence (PL) studies demonstrated that an energy band structural transition from the indirect gap to the direct gap happened in the region away from the flower center in tB MoS₂ (MoSe₂) flower patterns, accompanied by an enhanced PL intensity. The indirect-to-direct-gap transition in the tB-MoS₂ (MoSe₂) flower dominantly originated from a gradually enlarged interlayer spacing and thus, interlayer decoupling during the spiral growth of tB flower patterns. Meanwhile, the expanded interlayer spacing resulted in a decreased effective mass of the electrons. This means that the charged exciton (trion) population was reduced and the neutral exciton density was increased to obtain the upgraded PL intensity in the off-center region. Our experimental results were further evidenced by the density functional theory (DFT) calculations of the energy band structures and the effective masses of electrons and holes for the artificial tB-MoS₂ flower with different interlayer spacings. The single-layer behavior of tB flower-like homobilayers provided a viable route to finely manipulate the energy band gap and the corresponding exotic optical properties by locally tuning the stacked structures and to satisfy the real requirement in TMD-based optoelectronic devices.

Two-dimensional superconducting MoSi2N4(MoN)4n homologous compounds

The number and stacking order of layers are two important degrees of freedom that can modulate the properties of 2D van der Waals (vdW) materials. However, the layers' structures are essentially limited to the known layered 3D vdW materials. Recently, a new 2D vdW material, MoSi2N4, without known 3D counterparts, was synthesized by passivating the surface dangling bonds of non-layered 2D molybdenum nitride with elemental silicon, whose monolayer can be viewed as a monolayer MoN (-N-Mo-N-) sandwiched between two Si-N layers. This unique sandwich structure endows the MoSi2N4 monolayer with many fascinating properties and intriguing applications, and the surface-passivating growth method creates the possibility of tuning the layer's structure of 2D vdW materials. Here we synthesized a series of MoSi2N4(MoN)4n structures confined in the matrix of multilayer MoSi2N4. These super-thick monolayers are the homologous compounds of MoSi2N4, which can be viewed as multilayer MoN (Mo4n+1N4n+2) sandwiched between two Si-N layers. First-principles calculations show that MoSi2N4(MoN)4 monolayers have much higher Young's modulus than MoN, which is attributed to the strong Si-N bonds on the surface. Importantly, different from the semiconducting nature of the MoSi2N4 monolayer, the MoSi2N4(MoN)4 monolayer is identified as a superconductor with a transition temperature of 9.02 K. The discovery of MoSi2N4(MoN)4n structures not only expands the family of 2D materials but also brings a new degree of freedom to tailor the structure of 2D vdW materials, which may lead to unexpected novel properties and applications.

Preparation, properties and applications of two-dimensional superlattices

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

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.

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

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

Bidirectional phonon emission in two-dimensional heterostructures triggered by ultrafast charge transfer

Photoinduced charge transfer in van der Waals heterostructures occurs on the 100 fs timescale despite weak interlayer coupling and momentum mismatch. However, little is understood about the microscopic mechanism behind this ultrafast process and the role of the lattice in mediating it. Here, using femtosecond electron diffraction, we directly visualize lattice dynamics in photoexcited heterostructures of WSe₂/WS₂ monolayers. Following the selective excitation of WSe₂, we measure the concurrent heating of both WSe₂ and WS₂ on a picosecond timescale-an observation that is not explained by phonon transport across the interface. Using first-principles calculations, we identify a fast channel involving an electronic state hybridized across the heterostructure, enabling phonon-assisted interlayer transfer of photoexcited electrons. Phonons are emitted in both layers on the femtosecond timescale via this channel, consistent with the simultaneous lattice heating observed experimentally. Taken together, our work indicates strong electron-phonon coupling via layer-hybridized electronic states-a novel route to control energy transport across atomic junctions.

Signature of Cascade Transitions between Interlayer Excitons in a Moiré Superlattice

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

Hybridization and localized flat band in the WSe2/MoSe2heterobilayer

Nearly localized moiré flat bands in momentum space, arising at particular twist angles, are the key to achieve correlated effects in transition-metal dichalcogenides. Here, we use angle-resolved photoemission spectroscopy (ARPES) to visualize the presence of a flat band near the Fermi level of van der Waals WSe₂/MoSe₂heterobilayer grown by molecular beam epitaxy. This flat band is localized near the Fermi level and has a width of several hundred meVs. By combining ARPES measurements with density functional theory calculations, we confirm the coexistence of different domains, namely the reference 2H stacking without layer misorientation and regions with arbitrary twist angles. For the 2H-stacked heterobilayer, our ARPES results show strong interlayer hybridization effects, further confirmed by complementary micro- Raman spectroscopy measurements. The spin-splitting of the valence band atKis determined to be 470 meV. The valence band maximum (VBM) position of the heterobilayer is located at the Γ point. The energy difference between the VBM at Γ and theKpoint is of -60 meV, which is a stark difference compared to individual single monolayer WSe₂and monolayer WSe₂, showing both a VBM atK.

Emergent Moiré Phonons Due to Zone Folding in WSe2-WS2 Van der Waals Heterostructures

Bilayers of 2D materials offer opportunities for creating devices with tunable electronic, optical, and mechanical properties. In van der Waals heterostructures (vdWHs) where the constituent monolayers have different lattice constants, a moiré superlattice forms with a length scale larger than the lattice constant of either constituent material regardless of twist angle. Here, we report the appearance of moiré Raman modes from nearly aligned WSe₂-WS₂ vdWHs in the range of 240-260 cm^-1, which are absent in both monolayers and homobilayers of WSe₂ and WS₂ and in largely misaligned WSe₂-WS₂ vdWHs. Using first-principles calculations and geometric arguments, we show that these moiré Raman modes are a consequence of the large moiré length scale, which results in zone-folded phonon modes that are Raman active. These modes are sensitive to changes in twist angle, but notably, they occur at identical frequencies for a given small twist angle away from either the 0-degree or 60-degree aligned heterostructure. Our measurements also show a strong Raman intensity modulation in the frequency range of interest, with near 0 and near 60-degree vdWHs exhibiting a markedly different dependence on excitation energy. In near 0-degree aligned WSe₂-WS₂ vdWHs, a nearly complete suppression of both the moiré Raman modes and the WSe₂ A_1g Raman mode (∼250 cm^-1) is observed when exciting with a 532 nm CW laser at room temperature. Temperature-dependent reflectance contrast measurements demonstrate the significant Raman intensity modulation arises from resonant Raman effects.

Anomalous optical excitations from arrays of whirlpooled lattice distortions in moiré superlattices

Moiré superlattices formed by stacking two-dimensional crystals have reinvigorated the pursuit for emergent functionalities of engineered superlattices. Unique optical characteristics can be realized from the interplay between the electronic excitations and the atomic rearrangements owing to their intrinsic softness. Although large-scale reconstructions have been identified at small twist angles, they have been treated as being rigid at large twist angles. Here, we report that moiré superlattices made from single layers of MoS₂ and WSe₂ exhibit a pair of torsional strains with opposite chirality irrespective of the twist angle. The whirlpool-shaped periodic lattice distortions introduce fuzziness in the Raman spectra and universal redshifts to the intralayer excitons for all twist angles. We show that both of these modulations become weaker as the twist angle increases but do not disappear, whereas they are turned off when the constituent layers are not tightly coupled, thus establishing an essential structure-property relationship for moiré superlattices.

Determining the interlayer shearing in twisted bilayer MoS2 by nanoindentation

The rise of twistronics has increased the attention of the community to the twist-angle-dependent properties of two-dimensional van der Waals integrated architectures. Clarification of the relationship between twist angles and interlayer mechanical interactions is important in benefiting the design of two-dimensional twisted structures. However, current mechanical methods have critical limitations in quantitatively probing the twist-angle dependence of two-dimensional interlayer interactions in monolayer limits. Here we report a nanoindentation-based technique and a shearing-boundary model to determine the interlayer mechanical interactions of twisted bilayer MoS₂. Both in-plane elastic moduli and interlayer shear stress are found to be independent of the twist angle, which is attributed to the long-range interaction of intermolecular van der Waals forces that homogenously spread over the interfaces of MoS₂. Our work provides a universal approach to determining the interlayer shear stress and deepens the understanding of twist-angle-dependent behaviours of two-dimensional layered materials.

The study of the mechanical properties of twisted van der Waals structures can provide important information about their interlayer coupling and electronic behaviour. Here, the authors report a nanoindentation-based technique to determine the interlayer shear stress in bilayer MoS2, showing its independence as a function of the twist angle.

Controlling the harmonic generation in transition metal dichalcogenides and their heterostructures

The growing interest in transition metal dichalcogenides (TMDs) has encouraged researchers to focus on their nonlinear optical properties, such as harmonic generation (HG), which has potential for fundamental science and applications. HG is a nonlinear phenomenon used to study low-dimensional physics and has applications in bioimaging, optical signal processing, and novel coherent light sources. In this review, we present the state-of-the-art advances of HG in atomically-thin TMDs and their heterostructures. Different factors affecting the HG in TMDs such as strain, electric gating, excitonic resonance, phase and edge modulation, and valley-induced HG are discussed with a particular emphasis on the HG in heterostructure van der Waals TMDs. Moreover, we discuss the enhancement of HG in TMDs by incorporating cavities and nanostructures including the bound states in the continuum with extreme Q-factor. This work provides a concise summary of recent progress in engineering HG in atomically-thin TMDs and their heterostructures and a compact reference for researchers entering the field.

Interlayer Excitons in Transition Metal Dichalcogenide Semiconductors for 2D Optoelectronics

Optoelectronic materials that allow on-chip integrated light signal emitting, routing, modulation, and detection are crucial for the development of high-speed and high-throughput optical communication and computing technologies. Interlayer excitons in 2D van der Waals heterostructures, where electrons and holes are bounded by Coulomb interaction but spatially localized in different 2D layers, have recently attracted intense attention for their enticing properties and huge potential in device applications. Here, a general view of these 2D-confined hydrogen-like bosonic particles and the state-of-the-art developments with respect to the frontier concepts and prototypes is presented. Staggered type-II band alignment enables expansion of the interlayer direct bandgap from the intrinsic visible in monolayers up to the near- or even mid-infrared spectrum. Owing to large exciton binding energy, together with ultralong lifetime, room-temperature exciton devices and observation of quantum behaviors are demonstrated. With the rapid advances, it can be anticipated that future studies of interlayer excitons will not only allow the construction of all-exciton information processing circuits but will also continue to enrich the panoply of ideas on quantum phenomena.

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.

Probing Nanoscale Exciton Funneling at Wrinkles of Twisted Bilayer MoS2 Using Tip-Enhanced Photoluminescence Microscopy

In twisted bilayer (t2L) two-dimensional (2D) transition metal dichalcogenides, local strain at wrinkles strongly modulates the local exciton density and PL energy resulting in an exciton funneling effect. Probing such exciton behaviors especially at nanometer length scales is beyond the limit of conventional analytical tools due to the limited spatial resolution and low sensitivity. To address this challenge, herein we applied high-resolution tip-enhanced photoluminescence (TEPL) microscopy to investigate exciton funneling at a wrinkle in a t2L MoS₂ sample with a small twist angle of 0.5°. Owing to a spatial resolution of <10 nm, excitonic behavior at nanoscale sized wrinkles could be visualized using TEPL imaging. Detailed investigation of nanoscale exciton funneling at the wrinkles revealed a deformation potential of -54 meV/%. The obtained results provide novel insights into the inhomogeneities of excitonic behaviors at nanoscale and would be helpful in facilitating the rational design of 2D material-based twistronic devices.

V. P. L, N. M, Nayak PK. Twist-Dependent Tuning of Excitonic Emissions in Bilayer WSe2

Monolayer (ML) transition metal dichalcogenides (TMDCs) have been rigorously studied to comprehend their rich spin and valley physics, exceptional optical properties, and ability to open new avenues in fundamental research and technology. However, intricate analysis of twisted homobilayer (t-BL) systems is highly required due to the intriguing twist angle (t-angle)-dependent interlayer effects on optical and electrical properties. Here, we report the evolution of the interlayer effect on artificially stacked BL WSe2, grown using chemical vapor deposition (CVD), with t-angle in the range of 0 ≤ θ ≤ 60°. Systematic analyses based on Raman and photoluminescence (PL) spectroscopies suggest intriguing deviations in the interlayer interactions, higher-energy exciton transitions (in the range of ∼1.6-1.7 eV), and stacking. In contrast to previous observations, we demonstrate a red shift in the PL spectra with t-angle. Density functional theory (DFT) is employed to understand the band-gap variations with t-angle. Exciton radiative lifetime has been estimated theoretically using temperature-dependent PL measurements, which shows an increase with t-angle that agrees with our experimental observations. This study presents the groundwork for further investigation of the evolution of various interlayer excitons and their dynamics with t-angle in homobilayer systems, critical for optoelectronic applications.

Strong Moiré Excitons in High-Angle Twisted Transition Metal Dichalcogenide Homobilayers with Robust Commensuration

The burgeoning field of twistronics, which concerns how changing the relative twist angles between two materials creates new optoelectronic properties, offers a novel platform for studying twist-angle dependent excitonic physics. Herein, by surveying a range of hexagonal phase transition metal dichalcogenides (TMD) twisted homobilayers, we find that 21.8 ± 1.0°-twisted (7a×7a) and 27.8 ± 1.0°-twisted (13a×13a) bilayers account for nearly 20% of the total population of twisted bilayers in solution-phase restacked bilayers and can be found also in chemical vapor deposition (CVD) samples. Examining the optical properties associated with these twisted angles, we found that 21.8 ± 1.0° twisted MoS₂ bilayers exhibit an intense moiré exciton peak in the photoluminescence (PL) spectra, originating from the refolded Brillouin zones. Our work suggests that commensurately twisted TMD homobilayers with short commensurate wavelengths can have interesting optoelectronic properties that are different from the small twist angle counterparts.

P=O Functionalized Black Phosphorus/1T-WS2 Nanocomposite High Efficiency Hybrid Photocatalyst for Air/Water Pollutant Degradation

Research on layered two-dimensional (2D) materials is at the forefront of material science. Because 2D materialshave variousplate shapes, there is a great deal of research on the layer-by-layer-type junction structure. In this study, we designed a composite catalyst with a dimension lower than two dimensions and with catalysts that canbe combined so that the band structures can be designed to suit various applications and cover for each other’s disadvantages. Among transition metal dichalcogenides, 1T-WS₂ can be a promising catalytic material because of its unique electrical properties. Black phosphorus with properly controlled surface oxidation can act as a redox functional group. We synthesized black phosphorus that was properly surface oxidized by oxygen plasma treatment and made a catalyst for water quality improvement through composite with 1T-WS₂. This photocatalytic activity was highly efficient such that the reaction rate constant k was 10.31 × 10⁻² min⁻¹. In addition, a high-concentration methylene blue solution (20 ppm) was rapidly decomposed after more than 10 cycles and showed photo stability. Designing and fabricating bandgap energy-matching nanocomposite photocatalysts could provide a fundamental direction in solving the future’s clean energy problem.

Controlled Synthesis of Ultrathin PtSe2 Nanosheets with Thickness-Tunable Electrical and Magnetoelectrical Properties

Thickness-dependent chemical and physical properties have gained tremendous interest since the emergence of two-dimensional (2D) materials. Despite attractive prospects, the thickness-controlled synthesis of ultrathin nanosheets remains an outstanding challenge. Here, a chemical vapor deposition (CVD) route is reported to controllably synthesize high-quality PtSe2 nanosheets with tunable thickness and explore their thickness-dependent electronic and magnetotransport properties. Raman spectroscopic studies demonstrate all Eg , A1 g , A2 u , and Eu modes are red shift in thicker nanosheets. Electrical measurements demonstrate the 1.7 nm thick nanosheet is a semiconductor with room temperature field-effect mobility of 66 cm2 V-1 s-1 and on/off ratio of 106 . The 2.3-3.8 nm thick nanosheets show slightly gated modulation with high field-effect mobility up to 324 cm2 V-1 s-1 at room-temperature. When the thickness is over 3.8 nm, the nanosheets show metallic behavior with conductivity and breakdown current density up to 6.8 × 105 S m-1 and 6.9 × 107 A cm-2 , respectively. Interestingly, magnetoresistance (MR) studies reveal magnetic orders exist in this intrinsically non-magnetic material system, as manifested by the thickness-dependent Kondo effect, where both metal to insulator transition and negative MR appear upon cooling. Together, these studies suggest that PtSe2 is an intriguing system for both developing novel functional electronics and conducting fundamental 2D magnetism study.

Spectroscopic Signatures of Interlayer Coupling in Janus MoSSe/MoS2 Heterostructures

The interlayer coupling in van der Waals heterostructures governs a variety of optical and electronic properties. The intrinsic dipole moment of Janus transition metal dichalcogenides (TMDs) offers a simple and versatile approach to tune the interlayer interactions. In this work, we demonstrate how the van der Waals interlayer coupling and charge transfer of Janus MoSSe/MoS₂ heterobilayers can be tuned by the twist angle and interface composition. Specifically, the Janus heterostructures with a sulfur/sulfur (S/S) interface display stronger interlayer coupling than the heterostructures with a selenium/sulfur (Se/S) interface as shown by the low-frequency Raman modes. The differences in interlayer interactions are explained by the interlayer distance computed by density-functional theory (DFT). More intriguingly, the built-in electric field contributed by the charge density redistribution and interlayer coupling also play important roles in the interfacial charge transfer. Namely, the S/S and Se/S interfaces exhibit different levels of photoluminescence (PL) quenching of MoS₂ A exciton, suggesting enhanced and reduced charge transfer at the S/S and Se/S interface, respectively. Our work demonstrates how the asymmetry of Janus TMDs can be used to tailor the interfacial interactions in van der Waals heterostructures.

Lattice reconstruction induced multiple ultra-flat bands in twisted bilayer WSe2

Moiré superlattices in van der Waals heterostructures provide a tunable platform to study emergent properties that are absent in the natural crystal form. Twisted bilayer transition metal dichalcogenides (TB-TMDs) can host moiré flat bands over a wide range of twist angles. For twist angle close to 60°, it was predicted that TB-TMDs undergo a lattice reconstruction which causes the formation of ultra-flat bands. Here, by using scanning tunneling microscopy and spectroscopy, we show the emergence of multiple ultra-flat bands in twisted bilayer WSe₂ when the twist angle is within 3° of 60°. The ultra-flat bands are manifested as narrow tunneling conductance peaks with estimated bandwidth less than 10 meV, which is only a fraction of the estimated on-site Coulomb repulsion energy. The number of these ultra-flat bands and spatial distribution of the wavefunctions match well with the theoretical predictions, strongly evidencing that the observed ultra-flat bands are induced by lattice reconstruction. Our work provides a foundation for further study of the exotic correlated phases in TB-TMDs.

It was predicted that lattice reconstruction can lead to the emergence of multiple ultra-flat electronic bands in twisted bilayer transition metal dichalcogenides. Here, by using scanning tunneling microscopy and spectroscopy, the authors demonstrate such bands in twisted bilayer WSe₂.

The optical response of artificially twisted MoS[Formula: see text] bilayers

Two-dimensional layered materials offer the possibility to create artificial vertically stacked structures possessing an additional degree of freedom-the interlayer twist. We present a comprehensive optical study of artificially stacked bilayers (BLs) MoS[Formula: see text] encapsulated in hexagonal BN with interlayer twist angle ranging from 0[Formula: see text] to 60[Formula: see text] using Raman scattering and photoluminescence spectroscopies. It is found that the strength of the interlayer coupling in the studied BLs can be estimated using the energy dependence of indirect emission versus the A[Formula: see text]-E[Formula: see text] energy separation. Due to the hybridization of electronic states in the valence band, the emission line related to the interlayer exciton is apparent in both the natural (2H) and artificial (62[Formula: see text]) MoS[Formula: see text] BLs, while it is absent in the structures with other twist angles. The interlayer coupling energy is estimated to be of about 50 meV. The effect of temperature on energies and intensities of the direct and indirect emission lines in MoS[Formula: see text] BLs is also quantified.

A simple fabrication strategy for orientationally accurate twisted heterostructures

Van der Waals (vdW) heterostructure is a type of metamaterial where multiple layers of 2D materials are vertically aligned at controlled misorientation. The relative rotation in between the adjacent layers, or the twist angle between them plays a crucial role in changing the electronic band structure of the superlattice. The assembly of multi-layers of precisely twisted two dimensional layered materials requires knowledge of the atomic structure at the edge of the flake. It may be artificially created by the 'tear and stack' process. Otherwise, the crystallographic orientation needs to be determined through invasive processes such as transmission electron microscopy or scanning tunneling microscopy, and via second-harmonic generation (SHG). Here, we demonstrate a simple and elegant transfer protocol using only an optical microscope as a edge identifier tool through which, controlled transfer of twisted homobilayer and heterobilayer transition metal dichalcogenides is performed with close to 100% yield. The fabricated twisted vdW heterostructures have been characterized by SHG, Raman spectroscopy and photoluminiscence spectroscopy, confirming the desired twist angle within ∼0.5° accuracy. The presented method is reliable, quick and prevents the use of invasive tools which is desirable for reproducible device functionalities.

Giant Photoluminescence Enhancement and Carrier Dynamics in MoS2 Bilayers with Anomalous Interlayer Coupling

Fundamental researches and explorations based on transition metal dichalcogenides (TMDCs) mainly focus on their monolayer counterparts, where optical densities are limited owing to the atomic monolayer thickness. Photoluminescence (PL) yield in bilayer TMDCs is much suppressed owing to indirect-bandgap properties. Here, optical properties are explored in artificially twisted bilayers of molybdenum disulfide (MoS₂). Anomalous interlayer coupling and resultant giant PL enhancement are firstly observed in MoS₂ bilayers, related to the suspension of the top layer material and independent of twisted angle. Moreover, carrier dynamics in MoS₂ bilayers with anomalous interlayer coupling are revealed with pump-probe measurements, and the secondary rising behavior in pump-probe signal of B-exciton resonance, originating from valley depolarization of A-exciton, is firstly reported and discussed in this work. These results lay the groundwork for future advancement and applications beyond TMDCs monolayers.

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.

High-Speed Imaging of Second-Harmonic Generation in MoS2 Bilayer under Femtosecond Laser Ablation

We report an in situ characterization of transition-metal dichalcogenide (TMD) monolayers and twisted bilayers using a high-speed second-harmonic generation (SHG) imaging technique. High-frequency laser modulation and galvano scanning in the SHG imaging enabled a rapid identification of the crystallinity in the TMD, including the orientation and homogeneity with a speed of 1 frame/s. For a twisted bilayer MoS2, we studied the SHG peak intensity and angles as a function of the twist angle under a strong interlayer coupling. In addition, rapid SHG imaging can be used to visualize laser-induced ablation of monolayer and bilayer MoS2 in situ under illumination by a strong femtosecond laser. Importantly, we observed a characteristic threshold behavior; the ablation process occurred for a very short time duration once the preheating condition was reached. We investigated the laser thinning of the bilayer MoS2 with different twist angles. When the twist angle was 0°, the SHG decreased by approximately one-fourth of the initial intensity when one layer was removed. Conversely, when the twist angle was approximately 60° (the SHG intensity was suppressed), the SHG increased abruptly close to that of the nearby monolayer when one layer was removed. Precise layer-by-layer control was possible because of the unique threshold behavior of the laser-induced ablation.

Interferometric 4D-STEM for Lattice Distortion and Interlayer Spacing Measurements of Bilayer and Trilayer 2D Materials

Van der Waals materials composed of stacks of individual atomic layers have attracted considerable attention due to their exotic electronic properties that can be altered by, e.g., manipulating the twist angle of bilayer materials or the stacking sequence of trilayer materials. To fully understand and control the unique properties of these few-layer materials, a technique that can provide information about their local in-plane structural deformations, twist direction, and out-of-plane structure is needed. In principle, interference in overlap regions of Bragg disks originating from separate layers of a material encodes 3D information about the relative positions of atoms in the corresponding layers. Here, an interferometric 4D scanning transmission electron microscopy technique is described that utilizes this phenomenon to extract precise structural information from few-layer materials with nm-scale resolution. It is demonstrated how this technique enables measurement of local pm-scale in-plane lattice distortions as well as twist direction and average interlayer spacings in bilayer and trilayer graphene, and therefore provides a means to better understand the interplay between electronic properties and precise structural arrangements of few-layer 2D materials.

Structural Monoclinicity and Its Coupling to Layered Magnetism in Few-Layer CrI3

Using polarization-resolved Raman spectroscopy, we investigate layer number, temperature, and magnetic field dependence of Raman spectra in one- to four-layer CrI₃. Layer-number-dependent Raman spectra show that in the paramagnetic phase a doubly degenerated E_g mode of monolayer CrI₃ splits into one A_g and one B_g mode in N-layer (N > 1) CrI₃ due to the monoclinic stacking. Their energy separation increases in thicker samples until an eventual saturation. Temperature-dependent measurements further show that the split modes tend to merge upon cooling but remain separated until 10 K, indicating a failed attempt of the monoclinic-to-rhombohedral structural phase transition that is present in the bulk crystal. Magnetic-field-dependent measurements reveal an additional monoclinic distortion across the magnetic-field-induced layered antiferromagnetism-to-ferromagnetism phase transition. We propose a structural change that consists of both a lateral sliding toward the rhombohedral stacking and a decrease in the interlayer distance to explain our experimental observations.