Chiral Stacking Identification of Two-Dimensional Triclinic Crystals Enabled by Machine Learning

Chiral materials possess broken inversion and mirror symmetry and show great potential in the application of next-generation optic, electronic, and spintronic devices. Two-dimensional (2D) chiral crystals have planar chirality, which is nonsuperimposable on their 2D enantiomers by any rotation about the axis perpendicular to the substrate. The degree of freedom to construct vertical stacking of 2D monolayer enantiomers offers the possibility of chiral manipulation for designed properties by creating multilayers with either a racemic or enantiomerically pure stacking order. However, the rapid recognition of the relative proportion of two enantiomers becomes demanding due to the complexity of stacking orders of 2D chiral crystals. Here, we report the unambiguous identification of racemic and enantiomerically pure stackings for layered ReSe2 and ReS2 using circular polarized Raman spectroscopy. The chiral Raman response is successfully manipulated by the enantiomer proportion, and the stacking orders of multilayer ReSe2 and ReS2 can be completely clarified with the help of second harmonic generation and scanning transmission electron microscopy measurements. Finally, we trained an artificial intelligent Spectra Classification Assistant to predict the chirality and the complete crystallographic structures of multilayer ReSe2 from a single circular polarized Raman spectrum with the accuracy reaching 0.9417 ± 0.0059.

Origin of Distinct Insulating Domains in the Layered Charge Density Wave Material 1T-TaS2

Vertical charge order shapes the electronic properties in layered charge density wave (CDW) materials. Various stacking orders inevitably create nanoscale domains with distinct electronic structures inaccessible to bulk probes. Here, the stacking characteristics of bulk 1T-TaS2 are analyzed using scanning tunneling spectroscopy (STS) and density functional theory (DFT) calculations. It is observed that Mott-insulating domains undergo a transition to band-insulating domains restoring vertical dimerization of the CDWs. Furthermore, STS measurements covering a wide terrace reveal two distinct band insulating domains differentiated by band edge broadening. These DFT calculations reveal that the Mott insulating layers preferably reside on the subsurface, forming broader band edges in the neighboring band insulating layers. Ultimately, buried Mott insulating layers believed to harbor the quantum spin liquid phase are identified. These results resolve persistent issues regarding vertical charge order in 1T-TaS2, providing a new perspective for investigating emergent quantum phenomena in layered CDW materials.

Probing Polymorphic Stacking Domains in Mechanically Exfoliated Two-Dimensional Nanosheets Using Atomic Force Microscopy and Ultralow-Frequency Raman Spectroscopy

As one of the key features of two-dimensional (2D) layered materials, stacking order has been found to play an important role in modulating the interlayer interactions of 2D materials, potentially affecting their electronic and other properties as a consequence. In this work, ultralow-frequency (ULF) Raman spectroscopy, electrostatic force microscopy (EFM), and high-resolution atomic force microscopy (HR-AFM) were used to systematically study the effect of stacking order on the interlayer interactions as well as electrostatic screening of few-layer polymorphic molybdenum disulfide (MoS2) and molybdenum diselenide (MoSe2) nanosheets. The stacking order difference was first confirmed by measuring the ULF Raman spectrum of the nanosheets with polymorphic stacking domains. The atomic lattice arrangement revealed using HR-AFM also clearly showed a stacking order difference. In addition, EFM phase imaging clearly presented the distribution of the stacking domains in the mechanically exfoliated nanosheets, which could have arisen from electrostatic screening. The results indicate that EFM in combination with ULF Raman spectroscopy could be a simple, fast, and high-resolution method for probing the distribution of polymorphic stacking domains in 2D transition metal dichalcogenide materials. Our work might be promising for correlating the interlayer interactions of TMDC nanosheets with stacking order, a topic of great interest with regard to modulating their optoelectronic properties.

Resolidified Chalcogen-Assisted Growth of Bilayer Semiconductors with Controlled Stacking Orders

Bilayer semiconductors have attracted much attention due to their stacking-order-dependent properties. However, as both 3R- and 2H-stacking are energetically stable at high temperatures, most of the high-temperature grown bilayer materials have random 3R- or 2H-stacking orders, leading to non-uniformity in optical and electrical properties. Here, a chemical vapor deposition method is developed to grow bilayer semiconductors with controlled stacking order by modulating the resolidified chalcogen precursors supply kinetics. Taking tungsten disulfide (WS2 ) as an example, pure 3R-stacking (100%) and 2H-stacking dominated (87.6%) bilayer WS2 are grown by using this method and both show high structural and optical quality and good uniformity. Importantly, the bilayer 3R-stacking WS2 shows higher field effect mobility than 2H-stacking samples, due to the difference in stacking order-dependent surface potentials. This method is universal for growing other bilayer semiconductors with controlled stacking orders including molybdenum disulfide and tungsten diselenide, paving the way to exploit stacking-order-dependent properties of these family of emerging bilayer materials.

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

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

Real-Space Observation of Ripple-Induced Symmetry Crossover in Ultrathin MnPS3

Stacking order is expected to have a significant impact on the properties of van der Waals layered magnets, as it determines the crystallographic and magnetic symmetry. Recent synchrotron-based optical studies on antiferromagnetic MnPS₃ have revealed a thickness-dependent symmetry crossover, suggesting possible different stackings in few-layer crystals from the bulk, which, however, has not been explicitly identified. Here, by using a combination of atomic-scale electron microscopy and theoretical calculations, we show that despite the bulk monoclinic stacking persists macroscopically down to bilayer, additional local rippling effect lifts the monoclinic symmetry of the few layers while preserving the trigonal symmetry of individual monolayers, leading to possible monolayer-like behavior in ultrathin MnPS₃ samples. This finding reveals the profound impact of rippling on the microscopic symmetry of two-dimensional materials with weak interlayer interactions and raises the possibility of approaching the paradigmatic two-dimensional Néel antiferromagnetic honeycomb lattice in MnPS₃ without reaching monolayer thickness.

Experimental Observation of ABCB Stacked Tetralayer Graphene

In tetralayer graphene, three inequivalent layer stackings should exist; however, only rhombohedral (ABCA) and Bernal (ABAB) stacking have so far been observed. The three stacking sequences differ in their electronic structure, with the elusive third stacking (ABCB) being unique as it is predicted to exhibit an intrinsic bandgap as well as locally flat bands around the K points. Here, we use scattering-type scanning near-field optical microscopy and confocal Raman microscopy to identify and characterize domains of ABCB stacked tetralayer graphene. We differentiate between the three stacking sequences by addressing characteristic interband contributions in the optical conductivity between 0.28 and 0.56 eV with amplitude and phase-resolved near-field nanospectroscopy. By normalizing adjacent flakes to each other, we achieve good agreement between theory and experiment, allowing for the unambiguous assignment of ABCB domains in tetralayer graphene. These results establish near-field spectroscopy at the interband transitions as a semiquantitative tool, enabling the recognition of ABCB domains in tetralayer graphene flakes and, therefore, providing a basis to study correlation physics of this exciting phase.

Unblocking Ion-occluded Pore Channels in Poly(triazine imide) Framework for Proton Conduction

Poly(triazine imide) or PTI is an ordered graphitic carbon nitride hosting Å-scale pores attractive for selective molecular transport. AA'-stacked PTI layers are synthesized by ionothermal route during which ions occupy the framework and occlude the pores. Synthesis of ion-free PTI hosting AB-stacked layers has been reported, however, pores in this configuration are blocked by the neighboring layer. The unavailability of open pore limits application of PTI in molecular transport. Herein, we demonstrate acid treatment for ion depletion which maintains AA' stacking and results in open pore structure. We provide first direct evidence of ion-depleted open pores by imaging with the atomic resolution using integrated differential phase-contrast scanning transmission electron microscopy. Depending on the extent of ion-exchange, AA' stacking with open channels and AB stacking with closed channels are obtained and imaged for the first time. The accessibility of open channels is demonstrated by enhanced proton transport through ion depleted PTI.

Effect of Metal-Precursor Stacking Order on Volume-Defect Formation in CZTSSe Thin Film: Formation Mechanism of Blisters and Nanopores

In this study, we investigated the effect of the stacking order of metal precursors on the formation of volume defects, such as blisters and nanopores, in CZTSSe thin-film solar cells. We fabricated CZTSSe thin films using three types of metal-precursor combinations, namely, Zn/Cu/Sn/Mo, Cu/Zn/Sn/Mo, and Sn/Cu/Zn/Mo, and studied the blister formation. The blister-formation mechanism was based on the delamination model, taking into consideration the compressive stress and adhesion properties. A compressive stress could be induced during the preferential formation of a ZnSSe shell. Under this stress, the adhesion between the ZnSSe film and the Mo substrate could be maintained by the surface tension of a metallic liquid phase with good wettability, or by the functioning of ZnSSe pillars as anchors, depending on the type of metal precursor used. Additionally, the nanopore formation near the back-contact side was found to be induced by the columnar microstructure of the metal precursor with the Cu/Zn/Mo stacking order and its dezincification. Based on the two volume-defect-formation mechanisms proposed herein, further development of volume-defect-formation suppression technology is expected to be made.

Realizing Spontaneously Regular Stacking of Pristine Graphene Oxide by a Chemical-Structure-Engineering Strategy for Mechanically Strong Macroscopic Films

Mechanical-electrical properties of macroscopic graphene films derived from graphene oxide (GO) sheets are substantially restricted by their surface wrinkles and structural misalignment. Herein, we propose a chemical-structure-engineering strategy to realize the spontaneously regular stacking of modified GO (GO-m) with trace carboxyl. The highly aligned GO-m film delivers a fracture strength and modulus of nearly 3- and 5-fold higher than a wrinkled film with conventional Hummer's method derived GO (GO-c). The favorable assembly pattern of GO-m sheets is attributed to their decreased interfacial friction on the atomic scale, which weakens their local gelation capability for freer configuration adjustment during the assembly process. The chemical structure of GO-m can be further engineered by an epoxide-to-hydroxyl reaction, achieving a record high tensile strength of up to 631 MPa for the pristine GO film. By exploring the relationship between the surface terminations of GO and its stacking mode, this work proves the feasibility to realize high-performance macroscopic materials with optimized microstructure through the chemical modulation of nanosheet assembly.

Interlayer Coupling Dependent Discrete H → T' Phase Transition in Lithium Intercalated Bilayer Molybdenum Disulfide

In this work, the interlayer coupling dependent lithium intercalation induced phase transition in bilayer MoS₂ (BL-MoS₂) was investigated using an atomic-resolution annual dark-field scanning transmission electron microscope (ADF-STEM). It was revealed that the lithiation induced H → T' phase transition in BL-MoS₂ strongly depended on the interlayer twist angle; i.e., the H → T' phase transition occurred in well-stacked H phase BL-MoS₂ (with a twist angle of θ_t = 0°) but not for θ_t ≠ 0° BL-MoS₂. The lithiated BL-MoS₂ appeared in homophase stacking, either T'/T' or H/H (locally, no phase transformation) stacking, without any heterophase stacking such as H/T' or T'/H observed. This finding indicated the H → T' phase transition occurred via a domain-by-domain mode rather than layer-by-layer. Up to 15 types of stacking orders were experimentally identified locally in lithiated bilayer T'-MoS₂, and the formation mechanism was attributed to the discrete interlayer translation with a unit step of (m/6a, n/6b) (m, n = 0, 1, 2, 3), where a and b were the primitive lattice vectors of T'-MoS₂. Our experimental results were further corroborated by ab initio density functional theory (DFT) calculations, where the occurrence of different stacking orders can be quantitatively correlated with the variation of intercalated lithium contents into the BL-MoS₂. The present study aids in the understanding of the phase transition mechanisms in atomically thin 2D transition metal dichalcogenides (TMDCs) and will also shed light on the precisely controlled phase engineering of 2D materials for memory applications.

Switchable Interlayer Magnetic Coupling of Bilayer CrI3

Due to the weak van der Waals (vdW) interlayer interaction, interfacial geometry of two-dimensional (2D) magnetic vdW materials can be freely assembled, and the stacking order between layers can be readily controlled, such as laterally shifting or rotating, which may trigger the variation of magnetic order. We investigate the H-type bilayer CrI3 where the two layers are aligned in anti-parallel directions. Based on first-principles calculations, we propose two states with different interlayer magnetic couplings, i.e., ferromagnetic and antiferromagnetic, and analyze the superexchange mechanism inside. It is found that the two magnetic coupling states are stacking-dependent, and could be switched by applying out-of-plane axial strain and electron doping. Our findings show great application potential in the design of heterostructural and spintronic devices based on 2D magnetic vdW 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.

Manipulation of Stacking Order in Td-WTe2 by Ultrafast Optical Excitation

Subtle changes in stacking order of layered transition metal dichalcogenides may have profound influence on the electronic and optical properties. The intriguing electronic properties of Td-WTe2 can be traced to the break of inversion symmetry resulting from the ground-state stacking sequence. Strategies for perturbation of the stacking order are actively pursued for intentional tuning of material properties, where optical excitation is of specific interest since it holds the potential for integration of ultrafast switches in future device designs. Here we investigate the structural response in Td-WTe2 following ultrafast photoexcitation by time-resolved electron diffraction. A 0.23 THz shear phonon, involving layer displacement along the b axis, was excited by a 515 nm laser pulse. Pump fluences in excess of a threshold of ∼1 mJ/cm2 result in formation, with an ∼5 ps time constant, of a new stacking order by layer displacement along the b axis in the direction toward the centrosymmetric 1T* phase. The shear displacement of the layers increases with pump fluence until saturation at ∼8 pm. We demonstrate that the excitation of the shear phonon and the stabilization of the metastable phase are decoupled when using an optical pump as evidenced by observation of a transition also in samples with a pinned shear phonon. The results are compared to dynamic first-principles simulations and the transition is interpreted in terms of a mechanism where transient local disorder is prominent before settling at the atomic positions of the metastable phase. This interpretation is corroborated by results from diffuse scattering. The correlation between excitation of intralayer vibrations and interlayer interaction demonstrates the importance of including both short- and long-range interactions in an accurate description of how optical fields can be employed to manipulate the stacking order in 2-dimensional transition metal dichalcogenides.

Stacking nuances modulate the mechanical properties of graphene/SnO2nanocomposites

Due to its superior mechanical properties, graphene is widely used as reinforcement materials in nanocomposites. In this work, a series of indentation simulations was performed, using finite element method, to investigate the mechanical properties of graphene/TiO₂and graphene/SnO₂nanocomposite films. The force-displacement curves obtained from simulations were first compared to analytical results, which demonstrates that with increasing the thicknesses of metal oxide layers, the mechanical responses of nanocomposites exhibit a transition from non-linear behaviors to linear behaviors. Furthermore, consistent with literature works, increasing graphene volume fraction can enhance the Young's modulus of the corresponding heterostructure. Interestingly, this enhancement can be modulated by nuances in stacking orders, i.e. layer arrangements, of nanocomposites. Through analyzing stress and strain distributions, the underlying mechanisms were proposed. Our results reported here provide comprehensive characterizations and understandings on the reinforcement effects of graphene on graphene/metal oxide nanocomposites.

Large-Area Single-Crystal Graphene via Self-Organization at the Macroscale

In 1665 Christiaan Huygens first noticed how two pendulums, regardless of their initial state, would synchronize.  It is now known that the universe is full of complex self-organizing systems, from neural networks to correlated materials. Here, graphene flakes, nucleated over a polycrystalline graphene film, synchronize during growth so as to ultimately yield a common crystal orientation at the macroscale. Strain and diffusion gradients are argued as the probable causes for the long-range cross-talk between flakes and the formation of a single-grain graphene layer. The work demonstrates that graphene synthesis can be advanced to control the nucleated crystal shape, registry, and relative alignment between graphene crystals for large area, that is, a single-crystal bilayer, and (AB-stacked) few-layer graphene can been grown at the wafer scale.

Controllable Epitaxial Growth of MoSe2 Bilayers with Different Stacking Orders by Reverse-Flow Chemical Vapor Deposition

The stacking order plays a critical role in the electronic and optical properties of two-dimensional materials. It is however of great challenge to achieve large-size and homogeneous bilayer crystals with precisely controlled stacking orders. Here, we demonstrate an optimized chemical vapor deposition strategy to grow MoSe₂ bilayers with controlled AA or AB stacking sequences. Reverse gas flow effectively suppresses the random nucleation centers, leading to uniform growth of the second layer of MoSe₂ on the first monolayer. A customized temperature profile selectively activates the growth of the MoSe₂ bilayer with different stacking orders: the AA stacking MoSe₂ bilayer tends to form at 810 °C, and the AB stacking MoSe₂ bilayer prefers to grow at a higher temperature of 860 °C. A series of characterization methods confirm that MoSe₂ bilayers with different stacking orders exhibit distinct crystal structures and physical properties. Our results demonstrate a robust and effective route for the controllable synthesis of transition metal dichalcogenide bilayers, which will benefit the development of two-dimensional materials and van der Waals heterostructures.

Layer-Dependent Electronic Structure of Atomically Resolved Two-Dimensional Gallium Selenide Telluride

Alloying two-dimensional (2D) semiconductors provides a powerful method to tune their physical properties, especially those relevant to optoelectronic applications. However, as the crystal structure becomes more complex, it becomes increasingly difficult to accurately correlate response characteristics to detailed atomic structure. We investigate, via annular dark-field scanning transmission electron microscopy, electron energy loss spectroscopy, and second harmonic generation, the layered III-VI alloy GaSe_0.5Te_0.5 as a function of layer number. The local atomic structure and stacking sequence for different layers is explicitly determined. We complement the measurements with first-principles calculations of the total energy and electronic band structure of GaSe_0.5Te_0.5 for different crystal structures and layer number. The electronic band gap as well as the π and π + σ plasmons are found to be sensitive to layer number.

Stacking-Dependent Magnetism in Bilayer CrI3

We report the connection between the stacking order and magnetic properties of bilayer CrI₃ using first-principles calculations. We show that the stacking order defines the magnetic ground state. By changing the interlayer stacking order, one can tune the interlayer exchange interaction between antiferromagnetic and ferromagnetic. To measure the predicted stacking-dependent magnetism, we propose using linear magnetoelectric effect. Our results not only gives a possible explanation for the observed antiferromagnetism in bilayer CrI₃ but also have direct implications in heterostructures made of two-dimensional magnets.

Stranski-Krastanov and Volmer-Weber CVD Growth Regimes To Control the Stacking Order in Bilayer Graphene

Aside from unusual properties of monolayer graphene, bilayer has been shown to have even more interesting physics, in particular allowing bandgap opening with dual gating for proper interlayer symmetry. Such properties, promising for device applications, ignited significant interest in understanding and controlling the growth of bilayer graphene. Here we systematically investigate a broad set of flow rates and relative gas ratio of CH₄ to H₂ in atmospheric pressure chemical vapor deposition of multilayered graphene. Two very different growth windows are identified. For relatively high CH₄ to H₂ ratios, graphene growth is relatively rapid with an initial first full layer forming in seconds upon which new graphene flakes nucleate then grow on top of the first layer. The stacking of these flakes versus the initial graphene layer is mostly turbostratic. This growth mode can be likened to Stranski-Krastanov growth. With relatively low CH₄ to H₂ ratios, growth rates are reduced due to a lower carbon supply rate. In addition bi-, tri-, and few-layer flakes form directly over the Cu substrate as individual islands. Etching studies show that in this growth mode subsequent layers form beneath the first layer presumably through carbon radical intercalation. This growth mode is similar to that found with Volmer-Weber growth and was shown to produce highly oriented AB-stacked materials. These systematic studies provide new insight into bilayer graphene formation and define the synthetic range where gapped bilayer graphene can be reliably produced.

Effects of Electrode Layer Band Structure on the Performance of Multilayer Graphene-hBN-Graphene Interlayer Tunnel Field Effect Transistors

Interlayer tunnel field-effect transistors based on graphene and hexagonal boron nitride (hBN) have recently attracted much interest for their potential as beyond-CMOS devices. Using a recently developed method for fabricating rotationally aligned two-dimensional heterostructures, we show experimental results for devices with varying thicknesses and stacking order of the graphene electrode layers and also model the current-voltage behavior. We show that an increase in the graphene layer thickness results in narrower resonance. However, due to a simultaneous increase in the number of sub-bands and decrease of sub-band separation with an increase in thickness, the negative differential resistance peaks becomes less prominent and do not appear for certain conditions at room temperature. Also, we show that due to the unique band structure of odd number of layer Bernal-stacked graphene, the number of closely spaced resonance conditions increase, causing interference between neighboring resonance peaks. Although this can be avoided with even number of layer graphene, we find that in this case the bandgap opening present at high biases tend to broaden the resonance peaks.

Coupling and Stacking Order of ReS2 Atomic Layers Revealed by Ultralow-Frequency Raman Spectroscopy

We investigate the ultralow-frequency Raman response of atomically thin ReS2, a special type of two-dimensional (2D) semiconductors with unique distorted 1T structure. Bilayer and few-layer ReS2 exhibit rich Raman spectra at frequencies below 50 cm(-1), where a panoply of interlayer shear and breathing modes are observed. The emergence of these interlayer phonon modes indicate that the ReS2 layers are coupled and orderly stacked. Whereas the interlayer breathing modes behave similarly to those in other 2D layered crystals, the shear modes exhibit distinctive behavior due to the in-plane lattice distortion. In particular, the two shear modes in bilayer ReS2 are nondegenerate and clearly resolved in the Raman spectrum, in contrast to the doubly degenerate shear modes in other 2D materials. By carrying out comprehensive first-principles calculations, we can account for the frequency and Raman intensity of the interlayer modes and determine the stacking order in bilayer ReS2.