Direct Measurement of the Tunable Electronic Structure of Bilayer MoS2 by Interlayer Twist

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.

CVD Synthesis of Twisted Bilayer WS2 with Tunable Second Harmonic Generation

The introduction of rotational freedom by twist angles in twisted bilayer (TB) transition metal dichalcogenides (TMDCs) can tailor the inherent properties of the TMDCs, which provides a promising platform to investigate the exotic physical properties. However, direct synthesis of high-quality TB-TMDCs with full twist angles is significantly challenging due to the substantial energy barriers during crystal growth. Here, a modified chemical vapor deposition strategy is proposed to synthesize TB-WS2 with a wide twist angle range from 0° to 120°. Utilizing a tilted SiO2/Si substrate, a gas flow disturbance is generated in the furnace tube to create a heterogeneous concentration gradient of the metal precursor, which provides an extra driving force for the growth of TB-WS2. The Raman and photoluminescence results confirm a weak interlayer coupling of the TB-WS2. High-quality periodic Moiré patterns are observed in the scanning transmission electron microscopy images. Moreover, owing to the strong correlation between the nonlinear optical response and the twisted crystal structure, tunable second harmonic generation behaviors are realized in the TB-WS2. This approach opens up a new avenue for the direct growth of high-crystalline-quality and pristine TB-TMDCs and their potential applications in nonlinear optical devices.

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.

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.

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.

Visualizing Giant Ferroelectric Gating Effects in Large-Scale WSe2/BiFeO3 Heterostructures

Multilayers based on quantum materials (complex oxides, topological insulators, transition-metal dichalcogenides, etc.) have enabled the design of devices that could revolutionize microelectronics and optoelectronics. However, heterostructures incorporating quantum materials from different families remain scarce, while they would immensely broaden the range of possible applications. Here we demonstrate the large-scale integration of compounds from two highly multifunctional families: perovskite oxides and transition-metal dichalcogenides (TMDs). We couple BiFeO₃, a room-temperature multiferroic oxide, and WSe₂, a semiconducting two-dimensional material with potential for photovoltaics and photonics. WSe₂ is grown by molecular beam epitaxy and transferred on a centimeter-scale onto BiFeO₃ films. Using angle-resolved photoemission spectroscopy, we visualize the electronic structure of 1 to 3 monolayers of WSe₂ and evidence a giant energy shift as large as 0.75 eV induced by the ferroelectric polarization direction in the underlying BiFeO₃. Such a strong shift opens new perspectives in the efficient manipulation of TMD properties by proximity effects.

Van der Waals-Interface-Dominated All-2D Electronics

The interface is the device. As the feature size rapidly shrinks, silicon-based electronic devices are facing multiple challenges of material performance decrease and interface quality degradation. Ultrathin 2D materials are considered as potential candidates in future electronics by their atomically flat surfaces and excellent immunity to short-channel effects. Moreover, due to naturally terminated surfaces and weak van der Waals (vdW) interactions between layers, 2D materials can be freely stacked without the lattice matching limit to form high-quality heterostructure interfaces with arbitrary components and twist angles. Controlled interlayer band alignment and optimized interfacial carrier behavior allow all-2D electronics based on 2D vdW interfaces to exhibit more comprehensive functionality and better performance. Especially, achieving the same computing capacity of multiple conventional devices with small footprint all-2D devices is considered to be the key development direction of future electronics. Herein, the unique properties of all-2D vdW interfaces and their construction methods are systematically reviewed and the main performance contributions of different vdW interfaces in 2D electronics are summarized, respectively. Finally, the recent progress and challenges for all-2D vdW electronics are discussed, and how to improve the compatibility of 2D material devices with silicon-based industrial technology is pointed out as a critical challenge.

Directed exfoliating and ordered stacking of transition-metal-dichalcogenides

Two-dimensional van der Waals crystals provide a limitless scope for designing novel combinations of physical properties by controlling the stacking order or twist angle of individual layers. Lattice orientation between stacked monolayers is significant not only for breaking the engineering symmetry but also for the study of many-body quantum phases and band topology. Thus far the state-of-the-art exfoliation approaches focus on the achievements of quality, size, yield, and scalability, while lacking sufficient information on lattice orientation. Consequently, interlayer alignment is usually determined by later experiments, such as the second harmonic generation spectroscopy, which increase the number of trials and errors for a designed artificial ordering and hampered the efficiency of systematic study. Herein, we report a lattice orientation distinguishable exfoliation method via gold favor epitaxy along the specific atomic step edges, meanwhile, fulfilling the requirements of high-quality, large-size, and high-yield monolayers. Hexagonal- and rhombohedral-stacking configurations of bilayer transition metal dichalcogenides are built directly at once as a result of foreseeing the lattice orientation. Optical spectroscopy, electron diffraction, and angle-resolved photoemission spectroscopy are used to study crystal quality, symmetric breaking, and band tuning, which support the exfoliating mechanism we proposed. This strategy shows the ability to facilitate the development of ordering stacking especially for multilayers assembling in the future.

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.

Accurate Atomic-Scale Imaging of Two-Dimensional Lattices Using Atomic Force Microscopy in Ambient Conditions

To facilitate the rapid development of van der Waals materials and heterostructures, scanning probe methods capable of nondestructively visualizing atomic lattices and moiré superlattices are highly desirable. Lateral force microscopy (LFM), which measures nanoscale friction based on the commonly available atomic force microscopy (AFM), can be used for imaging a wide range of two-dimensional (2D) materials, but imaging atomic lattices using this technique is difficult. Here, we examined a number of the common challenges encountered in LFM experiments and presented a universal protocol for obtaining reliable atomic-scale images of 2D materials under ambient environment. By studying a series of LFM images of graphene and transition metal dichalcogenides (TMDs), we have found that the accuracy and the contrast of atomic-scale images critically depended on several scanning parameters including the scan size and the scan rate. We applied this protocol to investigate the atomic structure of the ripped and self-folded edges of graphene and have found that these edges were mostly in the armchair direction. This finding is consistent with the results of several simulations results. Our study will guide the extensive effort on assembly and characterization of new 2D materials and heterostructures.

Electronic Structure of Quasi-Freestanding WS2/MoS2 Heterostructures

Growth of 2D materials under ultrahigh-vacuum (UHV) conditions allows for an in situ characterization of samples with direct spectroscopic insight. Heteroepitaxy of transition-metal dichalcogenides (TMDs) in UHV remains a challenge for integration of several different monolayers into new functional systems. In this work, we epitaxially grow lateral WS₂-MoS₂ and vertical WS₂/MoS₂ heterostructures on graphene. By means of scanning tunneling spectroscopy (STS), we first examined the electronic structure of monolayer MoS₂, WS₂, and WS₂/MoS₂ vertical heterostructure. Moreover, we investigate a band bending in the vicinity of the narrow one-dimensional (1D) interface of the WS₂-MoS₂ lateral heterostructure and mirror twin boundary (MTB) in the WS₂/MoS₂ vertical heterostructure. Density functional theory (DFT) is used for the calculation of the band structures, as well as for the density of states (DOS) maps at the interfaces. For the WS₂-MoS₂ lateral heterostructure, we confirm type-II band alignment and determine the corresponding depletion regions, charge densities, and the electric field at the interface. For the MTB, we observe a symmetric upward bend bending and relate it to the dielectric screening of graphene affecting dominantly the MoS₂ layer. Quasi-freestanding heterostructures with sharp interfaces, large built-in electric field, and narrow depletion region widths are proper candidates for future designing of electronic and optoelectronic devices.

Ultrafast Charge-Transfer Dynamics in Twisted MoS2/WSe2 Heterostructures

Two-dimensional transition metal dichalcogenides offer a fascinating platform for creating van der Waals heterojunctions with exciting physical properties. Because of their typical type-II band alignment, photoexcited electrons and holes can separate via interfacial charge transfer. Furthermore, the relative crystallographic alignment of the individual layers in these heterostructures represents an important degree of freedom. Based on both effects, various fascinating ideas for applications in optoelectronics and valleytronics have been suggested. Despite its utmost importance for the design and efficiency of potential devices, the nature and the dynamics of ultrafast charge transfer are not yet well understood. This is mainly because the charge transfer can be surprisingly fast, usually faster than the temporal resolution of previous experimental approaches. Here, we apply time- and polarization-resolved second-harmonic imaging microscopy to investigate the charge-transfer dynamics for three MoS₂/WSe₂ heterostructures with different stacking angles at a previously unattainable time resolution of ≈10 fs. For 1.70 eV excitation energy, electron transfer from WSe₂ to MoS₂ is found to depend considerably on the stacking angle with the fastest transfer time observed to be as short as 12 fs. At 1.85 eV excitation energy, ultrafast hole transfer from MoS₂ to hybridized states at the Γ-point and to the K-points of WSe₂ has to be considered. Surprisingly, the corresponding decay dynamics show only a minor stacking-angle dependence indicating that radiative recombination of momentum-space indirect Γ-K excitons becomes the dominant decay route for all samples.

Visualizing electron localization of WS2/WSe2 moiré superlattices in momentum space

The search for materials with flat electronic bands continues due to their potential to drive strong correlation and symmetry breaking orders. Electronic moirés formed in van der Waals heterostructures have proved to be an ideal platform. However, there is no holistic experimental picture for how superlattices modify electronic structure. By combining spatially resolved angle-resolved photoemission spectroscopy with optical spectroscopy, we report the first direct evidence of how strongly correlated phases evolve from a weakly interacting regime in a transition metal dichalcogenide superlattice. By comparing short and long wave vector moirés, we find that the electronic structure evolves into a highly localized regime with increasingly flat bands and renormalized effective mass. The flattening is accompanied by the opening of a large gap in the spectral function and splitting of the exciton peaks. These results advance our understanding of emerging phases in moiré superlattices and point to the importance of interlayer physics.

Superconducting Quantum Interference in Twisted van der Waals Heterostructures

We demonstrate the formation of both Josephson junctions and superconducting quantum interference devices (SQUIDs) using a dry transfer technique to stack and deterministically misalign mechanically exfoliated flakes of NbSe₂. The current-voltage characteristics of the resulting twisted NbSe₂-NbSe₂ junctions are found to be sensitive to the misalignment angle of the crystallographic axes, opening up a new control parameter for optimization of the device performance, which is not available in thin-film-deposited junctions. A single lithographic process has then been implemented to shape Josephson junctions into SQUID geometries with typical loop areas of ∼25 μm² and weak links ∼600 nm wide. At T = 3.75 K in an applied magnetic field, these devices display large stable current and voltage modulation depths of up to ΔI_c ∼ 75% and ΔV ∼ 1.4 mV, respectively.

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.

Electronically Weak Coupled Bilayer MoS2 at Various Twist Angles via Folding

Constructing a bilayer system with defined twist angles is an effective way to engineer the physical properties of two-dimensional (2D) materials, opening up a new research area of twistronics. How to achieve high-quality bilayer 2D materials in a controlled and mass production way is of primary importance to this emerging area. In this work, we present a strategy for the large-scale fabrication of twisted bilayer molybdenum disulfide (MoS₂) through photolithography patterning and folding of single-crystal monolayer MoS₂. Atomic resolution transmission electron spectroscopy directly confirms that the as-achieved folded bilayer MoS₂ is of high quality with targeted twist angles. Various twist angles result in tuning Raman mode frequencies and direct optical transition energies. Due to the weak interlayer coupling between the twisted layers, folded bilayers exhibit an extremely high photoluminescence with doubled intensity as compared to the unfolded monolayer, indicating a possible application in optoelectronic devices. Our work provides a new strategy to tailor the properties of MoS₂, which will be beneficial to twistable electronics.

Unveiling Atomic-Scale Moiré Features and Atomic Reconstructions in High-Angle Commensurately Twisted Transition Metal Dichalcogenide Homobilayers

Twisting the angle between van der Waals stacked 2D layers has recently sparked great interest as a new strategy to tune the physical properties of the materials. The twist angle and associated strain profiles govern the electrical and optical properties of the twisted 2D materials, but their detailed atomic structures remain elusive. Herein, using combined atomic-resolution electron microscopy and density functional theory (DFT) calculations, we identified five unique types of moiré features in commensurately twisted 7a×7a transition metal dichalcogenide (TMD) bilayers. These stacking variants are distinguishable only when the moiré wavelength is short. Periodic lattice strain is observed in various commensurately twisted TMD bilayers. Assisted by Zernike polynomial as a hierarchical active-learning framework, a hexagon-shaped strain soliton network has been atomically unveiled in nearly commensurate twisted TMD bilayers. Unlike stacking-polytype-dependent properties in untwisted structures, the stacking variants have the same electronic structures that suggest twisted bilayer systems are invariant against interlayer gliding.

Formation mechanism and twist-angle dependent optical properties of bilayer MoS2 grown by chemical vapor deposition

The main features of phonon vibrations of twisted bilayer MoS₂ are tuned by the twist angle.

Multi-shaped strain soliton networks and moiré-potential-modulated band edge states in twisted bilayer SiC

Tuning the interlayer twist angle provides a new degree of freedom to exploit the potentially excellent properties of two dimensional layered materials.

Directional ultrafast charge transfer in a WSe2/MoSe2 heterostructure selectively probed by time-resolved SHG imaging microscopy

Heterostructures of two-dimensional transition metal dichalcogenides (TMD) have shown promise for various optoelectronic and novel valleytronic applications. Due to their type-II band alignment, photoexcited electrons and holes can separate into different layers through ultrafast charge transfer. While this charge-transfer process is critical for potential applications, the underlying mechanisms still remain elusive. Here, we demonstrate for a rotationally mismatched WSe2/MoSe2 heterostructure that directional ultrafast charge transfer between the layers becomes accessible by time-resolved optical second-harmonic generation. By tuning the photon energy of the pump pulse, one of the two materials is resonantly excited, whereas the polarization of the probe pulse can be optimized to selectively detect the charge transfer into the other material. This allows us to explore the interlayer hole transfer from the WSe2 into the MoSe2 layer and vice versa, which appears within a few hundred femtoseconds via hybridized intermediate states at the Γ-point. Our approach enables systematic investigations of the charge transfer in dependence of the rotational layer mismatch in TMD heterostructures.

Electric Field Tuning of Interlayer Coupling in Noncentrosymmetric 3R-MoS2 with an Electric Double Layer Interface

Interlayer coupling in two-dimensional (2D) layered materials plays an important role in controlling their properties. 2H- and 3R-MoS₂ with different stacking orders and the resulting interlayer coupling have been recently discovered to have different band structures and a contrast behavior in valley physics. However, the role of carrier doping in interlayer coupling in 2D materials remains elusive. Here, based on the electric double layer interface, we demonstrated the experimental observation of carrier doping-enhanced interlayer coupling in 3R-MoS₂. A remarkable tuning of interlayer Raman modes can be observed by changing the stacking sequence and carrier doping near their monolayer limit. The modulated interlayer vibration modes originated from the interlayer coupling show a doping-induced blue shift and are supposed to be associated with the interlayer coupling enhancement, which is further verified using our first-principles calculations. Such an electrical control of interlayer coupling of layered materials in an electrical gating geometry provides a new degree of freedom to modify the physical properties in 2D materials.

Evolution of high-frequency Raman modes and their doping dependence in twisted bilayer MoS2

Twisted van der Waals heterostructures provide a new platform for studying strongly correlated quantum phases. The interlayer coupling in these heterostructures is sensitive to the twist angle (θ) and key to controllably tuning several interesting properties. Here, we demonstrate the systematic evolution of the interlayer coupling strength with twist angle in bilayer MoS₂ using a combination of Raman spectroscopy and classical simulations. At zero doping, we observe a monotonic increase in the separation between the A_1g and E_2g¹ mode frequencies as θ decreases from 10°→ 1°, and the separation approaches that of a bilayer at small twist angles. Furthermore, using doping dependent Raman spectroscopy, we reveal the θ dependent softening and broadening of the A_1g mode, whereas the E_2g¹ mode remains unaffected. Using first principles based simulations, we demonstrate large (weak) electron-phonon coupling for the A_1g (E_2g¹) mode, which explains the experimentally observed trends. Our study provides a non-destructive way to characterize the twist angle and the interlayer coupling and establishes the manipulation of phonons in twisted bilayer MoS₂ (twistnonics).

Second-harmonic imaging microscopy for time-resolved investigations of transition metal dichalcogenides

Two-dimensional transition metal dichalcogenides (TMD) have shown promise for various applications in optoelectronics and so-called valleytronics. Their operation and performance strongly depend on the stacking of individual layers. Here, optical second-harmonic generation in imaging mode is shown to be a versatile tool for systematic time-resolved investigations of TMD monolayers and heterostructures in consideration of the material's structure. Large sample areas can be probed without the need of any mapping or scanning. By means of polarization dependent measurements, the crystalline orientation of monolayers or the stacking angles of heterostructures can be evaluated for the whole field of view. Pump-probe experiments then allow to correlate observed transient changes of the second-harmonic response with the underlying structure. The corresponding time-resolution is virtually limited by the pulse duration of the used laser. As an example, polarization dependent and time-resolved measurements on mono- and multilayer MoS2flakes grown on a SiO2/ Si(001) substrate are presented.

Tuning Electrical Conductance in Bilayer MoS2 through Defect-Mediated Interlayer Chemical Bonding

Interlayer interaction could substantially affect the electrical transport in transition metal dichalcogenides, serving as an effective way to control the device performance. However, it is still challenging to utilize interlayer interaction in weakly interlayer-coupled materials such as pristine MoS₂ to realize layer-dependent tunable transport behavior. Here, we demonstrate that, by substitutional doping of vanadium atoms in the Mo sites of the MoS₂ lattice, the vanadium-doped monolayer MoS₂ device exhibits an ambipolar field effect characteristic, while its bilayer device demonstrates a heavy p-type field effect feature, in sharp contrast to the pristine monolayer and bilayer MoS₂ devices, both of which show similar n-type electrical transport behaviors. Moreover, the electrical conductance of the doped bilayer MoS₂ device is drastically enhanced with respect to that of the doped monolayer MoS₂ device. Employing first-principle calculations, we reveal that such striking behaviors arise from the presence of electrical transport networks associated with the enhanced interlayer hybridization of S-3p_z orbitals between adjacent layers activated by vanadium dopants in the bilayer MoS₂, which is nevertheless absent in its monolayer counterpart. Our work highlights that the effect of dopant not only is confined in the in-plane electrical transport behavior but also could be used to activate out-of-plane interaction between adjacent layers in tailoring the electrical transport of the bilayer transitional metal dichalcogenides, which may bring different applications in electronic and optoelectronic devices.

Hybridized intervalley moiré excitons and flat bands in twisted WSe2 bilayers

The large surface-to-volume ratio in atomically thin 2D materials allows to efficiently tune their properties through modifications of their environment. Artificial stacking of two monolayers into a bilayer leads to an overlap of layer-localized wave functions giving rise to a twist angle-dependent hybridization of excitonic states. In this joint theory-experiment study, we demonstrate the impact of interlayer hybridization on bright and momentum-dark excitons in twisted WSe2 bilayers. In particular, we show that the strong hybridization of electrons at the Λ point leads to a drastic redshift of the momentum-dark K-Λ exciton, accompanied by the emergence of flat moiré exciton bands at small twist angles. We directly compare theoretically predicted and experimentally measured optical spectra allowing us to identify photoluminescence signals stemming from phonon-assisted recombination of layer-hybridized dark excitons. Moreover, we predict the emergence of additional spectral features resulting from the moiré potential of the twisted bilayer lattice.

Light-matter interaction in van der Waals hetero-structures

Even if individual two-dimensional materials own various interesting and unexpected properties, the stacking of such layers leads to van der Waals solids which unite the characteristics of two dimensions with novel features originating from the interlayer interactions. In this topical review, we cover fabrication and characterization of van der Waals hetero-structures with a focus on hetero-bilayers made of monolayers of semiconducting transition metal dichalcogenides. Experimental and theoretical techniques to investigate those hetero-bilayers are introduced. Most recent findings focusing on different transition metal dichalcogenides hetero-structures are presented and possible optical transitions between different valleys, appearance of moiré patterns and signatures of moiré excitons are discussed. The fascinating and fast growing research on van der Waals hetero-bilayers provide promising insights required for their application as emerging quantum-nano materials.

Controlling interlayer excitons in MoS2 layers grown by chemical vapor deposition

Combining MoS2 monolayers to form multilayers allows to access new functionalities. Deterministic assembly of large area van der Waals structures requires concrete indicators of successful interlayer coupling in bilayers grown by chemical vapor deposition. In this work, we examine the correlation between the stacking order and the interlayer coupling of valence states in both as-grown MoS2 homobilayer samples and in artificially stacked bilayers from monolayers, all grown by chemical vapor deposition. We show that hole delocalization over the bilayer is only allowed in 2H stacking and results in strong interlayer exciton absorption and also in a larger A-B exciton separation as compared to 3R bilayers. Comparing 2H and 3R reflectivity spectra allows to extract an interlayer coupling energy of about t⊥ = 49 meV. Beyond DFT calculations including excitonic effects confirm signatures of efficient interlayer coupling for 2H stacking in agreement with our experiments.

Precise control of the interlayer twist angle in large scale MoS2 homostructures

Twist angle between adjacent layers of two-dimensional (2D) layered materials provides an exotic degree of freedom to enable various fascinating phenomena, which opens a research direction—twistronics. To realize the practical applications of twistronics, it is of the utmost importance to control the interlayer twist angle on large scales. In this work, we report the precise control of interlayer twist angle in centimeter-scale stacked multilayer MoS₂ homostructures via the combination of wafer-scale highly-oriented monolayer MoS₂ growth techniques and a water-assisted transfer method. We confirm that the twist angle can continuously change the indirect bandgap of centimeter-scale stacked multilayer MoS₂ homostructures, which is indicated by the photoluminescence peak shift. Furthermore, we demonstrate that the stack structure can affect the electrical properties of MoS₂ homostructures, where 30° twist angle yields higher electron mobility. Our work provides a firm basis for the development of twistronics.

Interlayer twist angle between vertically stacked 2D material layers can trigger exciting fundamental physics. Here, the authors report precise control of interlayer twist angle of stacked centimeter scale multilayer MoS₂ homostructures that enables continuous change in their indirect bandgap, Moiré phonons and electrical properties.

Self-organized twist-heterostructures via aligned van der Waals epitaxy and solid-state transformations

Vertical van der Waals (vdW) heterostructures of 2D crystals with defined interlayer twist are of interest for band-structure engineering via twist moiré superlattice potentials. To date, twist-heterostructures have been realized by micromechanical stacking. Direct synthesis is hindered by the tendency toward equilibrium stacking without interlayer twist. Here, we demonstrate that growing a 2D crystal with fixed azimuthal alignment to the substrate followed by transformation of this intermediate enables a potentially scalable synthesis of twisted heterostructures. Microscopy during growth of ultrathin orthorhombic SnS on trigonal SnS₂ shows that vdW epitaxy yields azimuthal order even for non-isotypic 2D crystals. Excess sulfur drives a spontaneous transformation of the few-layer SnS to SnS₂, whose orientation – rotated 30° against the underlying SnS₂ crystal – is defined by the SnS intermediate rather than the substrate. Preferential nucleation of additional SnS on such twisted domains repeats the process, promising the realization of complex twisted stacks by bottom-up synthesis.

Vertically stacked twisted layers of two-dimensional materials can trigger exciting fundamental physics. Here, authors report controlled growth of 30° twisted few-layer SnS₂ over SnS₂ via van der Waals epitaxy of an SnS intermediate and its transformation in the presence of excess sulfur.

Tailoring excitonic states of van der Waals bilayers through stacking configuration, band alignment, and valley spin

Excitons in monolayer semiconductors have a large optical transition dipole for strong coupling with light. Interlayer excitons in heterobilayers feature a large electric dipole that enables strong coupling with an electric field and exciton-exciton interaction at the cost of a small optical dipole. We demonstrate the ability to create a new class of excitons in hetero- and homobilayers that combines advantages of monolayer and interlayer excitons, i.e., featuring both large optical and electric dipoles. These excitons consist of an electron confined in an individual layer, and a hole extended in both layers, where the carrier-species-dependent layer hybridization can be controlled through rotational, translational, band offset, and valley-spin degrees of freedom. We observe different species of layer-hybridized valley excitons, which can be used for realizing strongly interacting polaritonic gases and optical quantum controls of bidirectional interlayer carrier transfer.

Ultraflatbands and Shear Solitons in Moiré Patterns of Twisted Bilayer Transition Metal Dichalcogenides

Ultraflatbands in twisted bilayers of two-dimensional materials have the potential to host strong correlations, including the Mott-insulating phase at half-filling of the band. Using first-principles density functional theory calculations, we show the emergence of ultraflatbands at the valence band edge in twisted bilayer MoS_{2}, a prototypical transition metal dichalcogenide. The computed band widths, 5 and 23 meV for 56.5° and 3.5° twist angles, respectively, are comparable to that of twisted bilayer graphene near "magic" angles. Large structural transformations in the moiré patterns lead to formation of shear solitons at stacking boundaries and strongly influence the electronic structure. We extend our analysis for twisted bilayer MoS_{2} to show that flatbands can occur at the valence band edge of twisted bilayer WS_{2}, MoSe_{2}, and WSe_{2} as well.

Misorientation-Angle-Dependent Phase Transformation in van der Waals Multilayers via Electron-Beam Irradiation

Misorientation-angle dependence on layer thickness is an intriguing feature of van der Waals materials, which causes stark optical gain and electrical transport modulation. However, the influence of misorientation angle on phase transformation is not determined yet. Herein, this phenomenon in a MoS₂ multilayer via in situ electron-beam irradiation is reported. An AA'-stacked MoS₂ bilayer undergoes structural transformation from the 2H semiconducting phase to the 1T' metallic phase, similar to a MoS₂ monolayer, which is confirmed via in situ transmission electron microscopy. Moreover, non-AA' stacking, which has no local AA' stacking order in the Moiré pattern, does not reveal such a phase transformation. While a collective sliding motion of chalcogen atoms easily occurs during the transformation in AA' stacking, in non-AA' stacking it is suppressed by the weak van der Waals strength and by the chalcogen atoms interlocked at different orientations, which disfavor their kinetics by the increased entropy of mixing.

A Perspective on the Application of Spatially Resolved ARPES for 2D Materials

In this paper, a perspective on the application of Spatially- and Angle-Resolved PhotoEmission Spectroscopy (ARPES) for the study of two-dimensional (2D) materials is presented. ARPES allows the direct measurement of the electronic band structure of materials generating extremely useful insights into their electronic properties. The possibility to apply this technique to 2D materials is of paramount importance because these ultrathin layers are considered fundamental for future electronic, photonic and spintronic devices. In this review an overview of the technical aspects of spatially localized ARPES is given along with a description of the most advanced setups for laboratory and synchrotron-based equipment. This technique is sensitive to the lateral dimensions of the sample. Therefore, a discussion on the preparation methods of 2D material is presented. Some of the most interesting results obtained by ARPES are reported in three sections including: graphene, transition metal dichalcogenides (TMDCs) and 2D heterostructures. Graphene has played a key role in ARPES studies because it inspired the use of this technique with other 2D materials. TMDCs are presented for their peculiar transport, optical and spin properties. Finally, the section featuring heterostructures highlights a future direction for research into 2D material structures.

Interlayer resistance of misoriented MoS2

Interlayer misorientation in transition metal dichalcogenides alters their interlayer distance, total energy, electronic band structure, and vibrational modes, but its effect on the interlayer resistance is not known. This study analyzes the interlayer resistance of misoriented bilayer MoS₂ as a function of the misorientation angle, and it shows that interlayer misorientation exponentially increases the electron resistivity while leaving the hole resistivity almost unchanged. The physics, determined by the wave functions at the high symmetry points, are generic among the popular semiconducting transition metal dichalcogenides (TMDs). The asymmetrical effect of misorientation on the electron and hole transport may be exploited in the design and optimization of vertical transport devices such as a bipolar transistor. Density functional theory provides the interlayer coupling elements used for the resistivity calculations.

Twisted MX2/MoS2 heterobilayers: effect of van der Waals interaction on the electronic structure

A comprehensive first-principles study of the electronic properties of twisted 2D transition metal dichalcogenide (TMDC) heterobilayers MX₂/MoS₂ (M = Mo, Cr, W; X = S, Se) with different rotation angles has been performed. The van der Waals (vdW) interaction is found to have an important effect on the electronic structure of two-dimensional (2D) TMDC heterobilayers. Compared to non-twisted heterobilayers, the interlayer distance of twisted heterobilayers increases appreciably, thereby changing the vdW interaction of the heterobilayers as well as the electronic structure of the MX₂/MoS₂ systems. As a result, for CrSe₂/MoS₂ and MoSe₂/MoS₂ systems, the indirect bandgap (Γ-K) exhibits a notable enlargement (about 0.1 eV), leading to the indirect-to-direct gap transition. At twisting angles between 13.2° and 46.8°, the interlayer distance is nearly constant for the mismatched lattices over the entire sample, resulting in nearly the same electronic structure. Even after considering the spin-orbit coupling (SOC) effect, the indirect-to-direct transition is still predicted to occur in the WS₂/MoS₂ heterobilayer due to the large spin-orbit splitting.

Anisotropic attosecond charge carrier dynamics and layer decoupling in quasi-2D layered SnS2

Strong quantum confinement effects lead to striking new physics in two-dimensional materials such as graphene or transition metal dichalcogenides. While spectroscopic fingerprints of such quantum confinement have been demonstrated widely, the consequences for carrier dynamics are at present less clear, particularly on ultrafast timescales. This is important for tailoring, probing, and understanding spin and electron dynamics in layered and two-dimensional materials even in cases where the desired bandgap engineering has been achieved. Here we show by means of core–hole clock spectroscopy that SnS₂ exhibits spin-dependent attosecond charge delocalization times (τ_deloc) for carriers confined within a layer, τ_deloc < 400 as, whereas interlayer charge delocalization is dynamically quenched in excess of a factor of 10, τ_deloc > 2.7 fs. These layer decoupling dynamics are a direct consequence of strongly anisotropic screening established within attoseconds, and demonstrate that important two-dimensional characteristics are also present in bulk crystals of van der Waals-layered materials, at least on ultrafast timescales.

Owing to their layered nature, transition metal dichalcogenides possess an anisotropic electronic structure whose impact on carrier dynamics is not fully known. Here, the authors use X-ray spectroscopy to unveil the electronic coupling and attosecond dynamics in SnS₂, a prototypical van der Waals layered crystal.

Ultrafast Interlayer Electron Transfer in Incommensurate Transition Metal Dichalcogenide Homobilayers

Two-dimensional materials, such as graphene, transition metal dichalcogenides, and phosphorene, can be used to construct van der Waals multilayer structures. This approach has shown potentials to produce new materials that combine novel properties of the participating individual layers. One key requirement for effectively harnessing emergent properties of these materials is electronic connection of the involved atomic layers through efficient interlayer charge or energy transfer. Recently, ultrafast charge transfer on a time scale shorter than 100 fs has been observed in several van der Waals bilayer heterostructures formed by two different materials. However, information on the transfer between two atomic layers of the same type is rare. Because these homobilayers are essential elements in constructing multilayer structures with desired optoelectronic properties, efficient interlayer transfer is highly desired. Here we show that electron transfer between two monolayers of MoSe₂ occurs on a picosecond time scale. Even faster transfer was observed in homobilayers of WS₂ and WSe₂. The samples were fabricated by manually stacking two exfoliated monolayer flakes. By adding a graphene layer as a fast carrier recombination channel for one of the two monolayers, the transfer of the photoexcited carriers from the populated to the drained monolayers was time-resolved by femtosecond transient absorption measurements. The observed efficient interlayer carrier transfer indicates that such homobilayers can be used in van der Waals multilayers to enhance their optical absorption without significantly compromising the interlayer transport performance. Our results also provide valuable information for understanding interlayer charge transfer in heterostructures.

Inversion Domain Boundary Induced Stacking and Bandstructure Diversity in Bilayer MoSe2

Interlayer rotation and stacking were recently demonstrated as effective strategies for tuning physical properties of various two-dimensional materials. The latter strategy was mostly realized in heterostructures with continuously varied stacking orders, which obscure the revelation of the intrinsic role of a certain stacking order in its physical properties. Here, we introduce inversion-domain-boundaries into molecular-beam-epitaxy grown MoSe₂ homobilayers, which induce uncommon fractional lattice translations to their surrounding domains, accounting for the observed diversity of large-area and uniform stacking sequences. Low-symmetry stacking orders were observed using scanning transmission electron microscopy and detailed geometries were identified by density functional theory. A linear relation was also revealed between interlayer distance and stacking energy. These stacking sequences yield various energy alignments between the valence states at the Γ and K points of the Brillouin zone, showing stacking-dependent bandgaps and valence band tail states in the measured scanning tunneling spectroscopy. These results may benefit the design of two-dimensional multilayers with manipulable stacking orders.

Orientation dependent interlayer stacking structure in bilayer MoS2 domains

We have studied the atomic structure of small secondary domains that nucleate on monolayer MoS₂ grown by chemical vapour deposition (CVD), which form the basis of bilayer MoS₂. The small secondary bilayer domains have a faceted geometry with three-fold symmetry and adopt two distinct orientations with 60° rotation relative to an underlying monolayer MoS₂ single crystal sheet. The two distinct orientations are associated with the 2H and 3R stacking configuration for bilayer MoS₂. Atomic resolution images have been recorded using annular dark field scanning transmission electron microscopy (ADF-STEM) that show the edge termination, lattice orientation and stacking sequence of the bilayer domains relative to the underlying monolayer MoS₂. These results provide important insights that bilayer MoS₂ growth from 60° rotated small nuclei on the surface of monolayer MoS₂ could lead to defective boundaries when merged to form larger continuous bilayer regions and that pure AA' or AB bilayer stacking may be challenging unless from a single seed.

Characterization of Rotational Stacking Layers in Large-Area MoSe2 Film Grown by Molecular Beam Epitaxy and Interaction with Photon

Transition metal dichalcogenides (TMDCs) are promising next-generation materials for optoelectronic devices because, at subnanometer thicknesses, they have a transparency, flexibility, and band gap in the near-infrared to visible light range. In this study, we examined continuous, large-area MoSe₂ film, grown by molecular beam epitaxy on an amorphous SiO₂/Si substrate, which facilitated direct device fabrication without exfoliation. Spectroscopic measurements were implemented to verify the formation of a homogeneous MoSe₂ film by performing mapping on the micrometer scale and measurements at multiple positions. The crystalline structure of the film showed hexagonal (2H) rotationally stacked layers. The local strain at the grain boundaries was mapped using a geometric phase analysis, which showed a higher strain for a 30° twist angle compared to a 13° angle. Furthermore, the photon-matter interaction for the rotational stacking structures was investigated as a function of the number of layers using spectroscopic ellipsometry. The optical band gap for the grown MoSe₂ was in the near-infrared range, 1.24-1.39 eV. As the film thickness increased, the band gap energy decreased. The atomically controlled thin MoSe₂ showed promise for application to nanoelectronics, photodetectors, light emitting diodes, and valleytronics.

Direct observation of multiple rotational stacking faults coexisting in freestanding bilayer MoS2

Electronic properties of two-dimensional (2D) MoS₂ semiconductors can be modulated by introducing specific defects. One important type of defect in 2D layered materials is known as rotational stacking fault (RSF), but the coexistence of multiple RSFs with different rotational angles was not directly observed in freestanding 2D MoS₂ before. In this report, we demonstrate the coexistence of three RSFs with three different rotational angles in a freestanding bilayer MoS₂ sheet as directly observed using an aberration-corrected transmission electron microscope (TEM). Our analyses show that these RSFs originate from cracks and dislocations within the bilayer MoS₂. First-principles calculations indicate that RSFs with different rotational angles change the electronic structures of bilayer MoS₂ and produce two new symmetries in their bandgaps and offset crystal momentums. Therefore, employing RSFs and their coexistence is a promising route in defect engineering of MoS₂ to fabricate suitable devices for electronics, optoelectronics, and energy conversion.

Wavelength-Tunable Electroluminescent Light Sources from Individual Ga-Doped ZnO Microwires

Electrically driven wavelength-tunable light emission from biased individual Ga-doped ZnO microwires (ZnO:Ga MWs) is demonstrated. Single crystalline ZnO:Ga MWs with different Ga-doping concentrations have been synthesized using a one-step chemical vapor deposition method. Strong electrically driven light emission from individual ZnO:Ga MW based devices is realized with tunable colors, and the emission region is localized toward the center of the wires. Increasing Ga-doping concentration in the MWs can lead to the redshift of electroluminescent emissions in the visible range. Interestingly, owing to the lack of rectification characteristics, relevant electrical measurement results show that the alternating current-driven light emission functions excellently on the ZnO:Ga MWs. Consequently, individual ZnO:Ga MWs, which can be analogous to incandescent sources, offer unique possibilities for future electroluminescence light sources. This typical multicolor emitter can be used to rival and complement other conventional semiconductor devices in displays and lighting.

Interlayer couplings, Moiré patterns, and 2D electronic superlattices in MoS2/WSe2 hetero-bilayers

By using direct growth, we create a rotationally aligned MoS2/WSe2 hetero-bilayer as a designer van der Waals heterostructure. With rotational alignment, the lattice mismatch leads to a periodic variation of atomic registry between individual van der Waals layers, exhibiting a Moiré pattern with a well-defined periodicity. By combining scanning tunneling microscopy/spectroscopy, transmission electron microscopy, and first-principles calculations, we investigate interlayer coupling as a function of atomic registry. We quantitatively determine the influence of interlayer coupling on the electronic structure of the hetero-bilayer at different critical points. We show that the direct gap semiconductor concept is retained in the bilayer although the valence and conduction band edges are located at different layers. We further show that the local bandgap is periodically modulated in the X-Y direction with an amplitude of ~0.15 eV, leading to the formation of a two-dimensional electronic superlattice.