Interlayer Modes Research Articles

Unveiling the Key Obstacle in Photocatalytic Overall Water Splitting Reaction on Poly (heptazine imide) Semiconductors.

Poly (heptazine imide) (PHI), a classic 2D polymeric photocatalyst, represents a promising organic semiconductor for photocatalytic overall water splitting (POWS). However, since the key bottleneck in POWS of PHI remains unclear, its quantum efficiency of POWS is extremely restrained. To identify the key obstacle in POWS on the PHI, a series of PHI with different stacking modes is synthesized by tuning interlayer cations. The structural characterizations revealed that tuning the interlayer cations of PHI can induce rearrangements in interlayer stacking modes. Additionally, charge carriers dynamics uncover that optimizing the interlayer stacking modes of PHI can promote exciton diffusion and prolong the photoexcited electron lifetimes, thus improving the concentration of surface-reaching charge. More importantly, this confirms that the POWS activity of PHI is closely correlated with the interlayer stacking modes. This work offers new insight into structural regulation for governing charge-transport dynamics and the activity of 2D polymeric photocatalysts.

Precise Regulation of Interlayer Stacking Modes in Trinuclear Copper Organic Frameworks for Efficient Photocatalytic Reduction of Uranium(VI).

The interlayer stacking modes of 2D covalent-organic frameworks (COFs) directly influence their structural features, ultimately determining their functional output. However, controllably modulating the interlayer stacking structure in traditional 2D metal-free COFs, based on the same building blocks, remains challenging. Here, two trinuclear copper organic frameworks are synthesized successfully with different interlayer stacking structures: eclipsed AA stacking in Cu3-PA-COF-AA and staggered ABC stacking in Cu3-PA-COF-ABC, using the same monomers. Remarkably, various functionalities, including porosity and electronic and optical properties, can be effectively regulated by interlayer stacking. As a result, Cu3-PA-COF-AA and Cu3-PA-COF-ABC exhibit significantly different activities toward the photoreduction of U(VI), presenting a promising strategy for removing radioactive uranium pollution. Due to its broader visible-light absorption range and superior photogenerated carrier migration and separation efficiency, Cu3-PA-COF-AA achieves a U(VI) removal ratio of 93.6% without additional sacrificial agents in an air atmosphere-≈2.2 times higher than that of Cu3-PA-COF-ABC (42.0%). To the best of the knowledge, this is the first study to elucidate the effect of interlayer stacking in COFs on the photocatalytic activity of U(VI) reduction. This finding may inspire further exploration of the structure-function relationship in COFs as photocatalysts and their potential for photoinduced removal of radionuclides.

Raman spectroscopy of atomically thin HfX2 (X=S, Se)

Abstract We investigated interlayer modes of few-layer HfX2 (X=S, Se) by using low-frequency micro-Raman spectroscopy with three excitation energies (1.96 eV, 2.33 eV, 2.54 eV) under vacuum condition (10−6 Torr). We observed interlayer modes in HfSe2 when the 2.54-eV excitation energy was used. The low-frequency Raman spectra reveal a series of shear and breathing modes (<50 cm−1) that are helpful for identifying the number of layers. The in-plane Eg and out-of-plane A1g modes of HfSe2 are located at ~150 cm−1 and ~200 cm−1, respectively. In HfS2, in-plane Eg and out-of-plane A1g optical phonons are observed at ~260 cm−1 and ~337 cm−1, respectively. The in-plane and out-of-plane force constants of atomically thin HfSe2 are obtained to be 1.87 ×1019 N/m3 and 6.55×1019 N/m3, respectively, by fitting the observed interlayer modes using the linear chain model. These results provide valuable information on materials parameters for device designs using atomically-thin layered HfX2 (X=S, Se).

Interlayer coupling modulated for thermoelectric transport characterization of black arsenic nanoscale devices

Modulating interlayer coupling modes can effectively enhance the thermoelectric properties of nanomaterials or nanoscale devices. By using density functional theory combined with non-equilibrium Green’s function method, we investigate the thermoelectric properties of zigzag-type black arsenic nanoscale devices with varying interlayer coupling modes. Our results show that altering the interlayer coupling mode significantly modulates the thermoelectric properties of the system. Specifically, we consider four coupling modes with different strengths, by modulating different interlayer overlap patterns. Notably, in the weaker interlayer coupling mode, the system exhibits enhanced thermoelectric properties due to increased interface phonon scattering, for example, the M4 reaching a peak value of 2.23 at μ = −0.73 eV. Furthermore, we explore the temperature-dependent behavior of each coupling model. The results suggest that the thermoelectric characteristics are more sensitive to temperature variations in the weaker coupling modes. These insights provide valuable guidance for enhancing the thermoelectric performance of nanoscale devices through precise interlayer coupling modulation.

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

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

Model of cross-flow interference index and application for multi-layer commingled production in Sulige tight sandstone gas reservoir, Ordos Basin, China

Multi-layer commingled production is the main feature of gas well development in Sulige tight sandstone gas reservoir, Ordos Basin. Identifying potential interference between layers and devising methods for their characterization are crucial considerations for optimizing the development of gas reservoirs. To address these issues, we designed a physical simulation experiment process and interlayer commingled mining schemes, implementing various interlayer combination modes. The results show that a common occurrence in the process of multi-layer commingled production of tight gas and water layers, whether it involves gas layers production alone or simultaneous production of gas and water layers. This phenomenon involves the crossflow of gas and water between layers, resulting in interlayer interference and a subsequent reduction in gas reservoir recovery. Based on these observations, the concept of an interlayer interference index in multi-layer commingled production in tight sandstone gas reservoirs is proposed. The interference index model is obtained by fitting the multiple linear regression method, showcasing its correlation with the physical properties of the reservoir. High water saturation and a significant permeability ratio of the water layer to the gas layer (exceeding the critical value of 1) can result in the early occurrence of interlayer interference and yield a higher interference index. Furthermore, based on the interference index model, a novel method for productivity evaluation of gas wells in tight gas reservoirs is established. The calculations demonstrate that the interference index curve effectively characterizes the interlayer interference performance of gas wells. The productivity and production performance predictions derived from this model align closely with historical production data, affirming the model's effectiveness and accuracy. Therefore, the interference index model emerges as a valuable tool for predicting the productivity and production performance of gas wells in Sulige tight sandstone gas reservoirs. The research results have important theoretical guidance and practical significance for the efficient development of Sulige tight sandstone gas reservoirs.

Anomalous interlayer vibrations in few-layer InSe induced by weak intralayer bonding

Atomically thin InSe is a promising semiconductor that possesses exceptional plasticity, high electron mobility, and wide bandgap tunability, which are thought to be highly sensitive to interlayer coupling. Since the interlayer vibration modes can provide direct access to the interlayer coupling strength, in this study, we systematically investigated the interlayer modes in few-layer InSe using low-frequency Raman spectroscopy. We found that the commonly used linear chain model (LCM), which treats the single layer as a rigid entity, is inadequate in accurately describing the frequencies of interlayer shear modes in InSe due to the influence of weak in-plane intralayer In–In bonding. This issue can be addressed with a modified model that accounts for both the in-plane interlayer coupling between InSe layers and the in-plane intralayer interaction within InSe layers. However, the out-of-plane intralayer In–In bonding is strong enough so that it has negligible impact on the frequency of the interlayer layer-breathing modes, which can be well understood by the LCM. Our study reveals how the weak intralayer bonding in two-dimensional materials gives a non-negligible contribution to the corresponding interlayer vibrations.

Direct Observation of the Anisotropic Transport Behavior of Li+ in Graphite Anodes and Thermal Runaway Induced by the Interlayer Polarization.

Graphite is one of the major anode materials for commercial lithium-ion batteries. Li+ transport in a single graphite granule along intra and interlayer modes is a crucial factor for the battery performance. However, direct evidence and visualized details of the Li+ transports are hardly provided. Here, we report the direct observation of the anisotropic transport behavior of Li+ and investigate the electro-chemo-structure evolution during the lithiation of graphite through both the intra and interlayer pathways via in situ transmission electron microscopy. The in situ experiments of nano batteries give two extreme conditions, in which thermal runaway induced by polarization only occurs along the interlayer, not along the intralayer. The high diffusion energy barrier induced large polarization when the interlayer Li+ transport became dominant. The energy of the polarization electric field would be instantaneously released like a short electric pulse, which generated a substantial amount of joule heat and created an extremely high temperature, causing the melting of the tungsten tip. We provide another possible fundamental mechanism of thermal failure in graphite-based Li-ion batteries and hope this insightful work would help the safety management of graphite-based lithium-ion batteries.

Raman and Far-Infrared Synchrotron Nanospectroscopy of Layered Crystalline Talc: Vibrational Properties, Interlayer Coupling, and Symmetry Crossover

Talc is an insulating layered material that is stable at ambient conditions and has high-quality basal cleavage, which is a major advantage for its use in van der Waals heterostructures. Here, we use near-field synchrotron infrared nanospectroscopy, Raman spectroscopy, and first-principles calculations to investigate the structural and vibrational properties of talc crystals, ranging from monolayer to bulk, in the 300-750 cm-1 and <60 cm-1 spectral windows. We observe a symmetry crossover from mono to bilayer talc samples, attributed to the stacking of adjacent layers. The in-plane lattice parameters and frequencies of intralayer modes of talc display weak dependence with the number of layers, consistent with a weak interlayer interaction. On the other hand, the low-frequency (<60 cm-1) rigid-layer (interlayer) modes of talc are suitable to identify the number of layers in ultrathin talc samples, besides revealing strong in-plane and out-of-plane anisotropy in the interlayer force constants and related elastic stiffnesses of single crystals. The shear and breathing force constants of talc are found to be 66% and 28%, respectively, lower than those of graphite, making talc an excellent lubricant that can be easily exfoliated. Our results broaden the understanding of the structural and vibrational properties of talc at the nanoscale regime and serve as a guide for future ultrathin heterostructures applications.

A unified inferring framework of multiplex epidemic networks under multiple interlayer interaction modes

Different epidemic transmissions on multiplex networks may interact and display intertwined effects, leading to a challenge and urgently needed problem of the inference of multiplex epidemic network structures under multiple interlayer interaction modes (IIMs). However, in reality, few existing studies have focused on multiplex epidemic network inference responding to the intertwined IIMs, much less the corresponding consistency analysis. To fill these two gaps, we first propose an inference framework of multiplex epidemic networks under a unified form of IIMs. In particular, we develop a Hamming distance-based two-step estimator for an intricate IIM called infection-probability-dependent interaction (IPDI). The proposed two-step estimator overcomes the problems of unobservable and time-varying variable inference in the IPDI mode. Second, we solve the theoretical difficulty of consistency analysis for the network inference under multiple IIMs and obtain sufficient conditions for exponentially decaying inferring error. Under the guarantee of consistently sufficient conditions, the sample size scale enables our framework's high-dimensional inferring ability. The synthetic network simulations show the validity of the proposed algorithm and consistency analysis. In addition, the analysis of real data of Twitter and Foursquare indicates the effectiveness and practicality of the proposed inferring framework.

Probing the interfacial coupling in ternary van der Waals heterostructures

Good interfacial coupling between each constituent of van der Waals Heterostructures (vdWHs) is the prerequisite for the distinguished performance of related devices. Since vdWHs-based devices commonly consist of three or more constituents, an effective evaluation of interfacial coupling quality in multiple heterointerfaces is critical during the device fabrication process. Here, in ternary vdWHs composed of hBN, graphene (Gr) and transition metal dichalcogenide (TMD) flakes, which are essential building blocks for low-dimensional vdWHs-based electronic and optoelectronic devices, we realized probe and quantification of the interfacial coupling by low-frequency Raman spectroscopy under resonant excitation through the C exciton energy in TMD constituents. Based on the frequencies of emerging interlayer vibration modes in hBN/TMD/Gr ternary vdWHs, the interfacial coupling force constants of hBN/TMD and TMD/Gr interfaces are estimated as parameters to quantitatively evaluate the interfacial coupling strength at the corresponding interfaces. Moreover, the interfacial coupling strength at Gr/hBN interface is also successfully revealed in Gr/hBN/MoTe2 ternary vdWHs, which cannot be directly characterized from Gr/hBN binary vdWH due to its unobservable interlayer modes with weak electron-phonon coupling. This general strategy can be further extended to probe and quantify the interfacial coupling quality in polynary vdWHs and related devices.

Phonon physics in twisted two-dimensional materials

As one of the most effective manipulation means to control the physical properties of two-dimensional van der Waals stacking materials, the twisted angle periodically regulates the interlayer interaction potential by generating moiré patterns. The decrease in Brillouin zone size and the change of high symmetry direction caused by the interlayer twisted angle lead to the emergence of the hybrid folded phonons—moiré phonons, which have noticeable impacts on phonon properties. This paper reviews the recent developments and discoveries on phonon properties in twisted two-dimensional stacking homogeneous and heterogeneous systems and focuses on the impacts of the interlayer twisted angle on phonon dispersion, such as interlayer coupling phonon modes and moiré phonons. Meanwhile, we introduced the recent research on the influence of the interlayer twisted angle on phonon transport behavior along the in-plane and out-of-plane directions. In addition, the theoretical and experimental open questions and challenges faced in the phonon characteristics of twisted two-dimensional materials are discussed, and some possible solutions are put forward.

Three coordination polymers as a multi-responsive luminescent probe for the detection of Fe3+, Cr2O72− and antibiotic in aqueous media

Three coordination polymers (CPs), namely {[Co(L)(dpa)]·H2O}n (1), {[Zn(L)2(dpb)]}n (2) and {[Zn(L)(dpe)]}n (3), have been assembled through a dual-ligand strategy of a semi-rigid dicarboxylic acid (H2L = 1,4-bis(4-phenoxy)benzenedicarboxylic acid) with the help of different N-donor co-ligands (dpa = di(pyridin-4-yl)amine, dpb = 1,4-di(pyridin-4-yl)benzene), dpe = trans-1,2-di(4-pyridyl)ethylene). Single crystal X-ray diffraction analyses reveals that compound 1 is a 4-fold interpenetrating 2D sql network and compound 2 is a 2-fold interpenetrating 2D sql network, although the final structures are different because of various inter-layer stacking modes. Compound 3 is a 8-fold interpenetrating 3D dia framework containing an octahedral cage. A photoluminescence investigation shows that compounds 2 and 3 exhibit strong fluorescence originating from the intra-ligand charge transfer transitions. Benefiting from its chemical stability and luminescent properties, compound 2 possesses multi-functional fluorescent responses toward the Fe3+ ion, the Cr2O72− ion and the NZF antibiotic in aqueous medium. The KSV values of compound 2 are 4.68 × 104 M−1 for the Fe3+ ion, 7.23 × 104 M−1 for the Cr2O72− anion, and 1.03 × 104 M−1 for the NZF antibiotic. Additionally, the possible mechanism for the luminescence quenching has been investigated.

Ultrafast nonlinear phonon response of few-layer hexagonal boron nitride

Ultrafast optical-phonon dynamics and the related nonlinear lattice response of few-layer hexagonal boron nitride ($h$-BN) are elucidated in a combined experimental and theoretical study. The lifetimes of transverse optical (TO) phonons and interlayer modes are 1.2 and 20 ps. In-plane TO phonon displacements are shown to couple to interlayer shear and breathing motions. In the nonlinear phonon response, a transient reduction of the TO phonon frequency arises from this anharmonic coupling, which is a particular property of few-layer $h$-BN.

Intrinsic effect of interfacial coupling on the high-frequency intralayer modes in twisted multilayer MoTe2.

The interfacial coupling at the interface makes the van der Waals heterostructures (vdWHs) exhibit many unique properties that cannot be realized in its constituents. Such a study usually starts with a twisted stack of two flakes exfoliated from the same layered materials to form twisted multilayers, in which the impact of interfacial coupling on the low-frequency interlayer modes had been well understood. However, it is not clear how interfacial coupling affects the high-frequency intralayer modes of twisted multilayers. Herein, we perform high-resolution resonance Raman spectroscopy of the high-frequency intralayer modes in twisted multilayer MoTe2 (tMLM). All the Davydov entities of the out-of-plane intralayer mode are observed and distinguished at 4 K. It is found that the out-of-plane intralayer modes in tMLM are sensitive to its interfacial layer-breathing coupling so that the out-of-plane intralayer modes in tMLM do not show a direct relationship with those of the two constituents. However, the case is quite different for the in-plane intralayer modes in tMLM, whose spectral profile can be fitted by those of the corresponding modes of its constituents. This indicates that the in-plane intralayer modes are localized within the constituents in tMLM because of its negligible interfacial shear coupling at the interface. All the results can be well understood using the vdW model in which only the nearest neighbor interlayer/interfacial interaction is taken into account. This work directly builds the relationship between the Davydov splitting of the high-frequency intralayer vibrations and the low-frequency interlayer vibrations in tMLM, which can be further extended to other twisted materials and the related vdWHs.

Plasmonic tuning of near-field heat transfer between graphene monolayers

We discuss the non-radiative heat transfer in non-equilibrium double layer graphene system. We show that at the neutrality point the heat exchange is dominated by the inter-layer plasmon modes and derive analytic expressions for the heat current as a function of temperature and the interlayer separation. These results show that for a range of low temperatures the two graphene layers are much more efficient heat exchanger than conventional metals. The physical reason behind this phenomenon is the presence of inter-band excitations with a large energy, and a small momentum in graphene spectrum. Plasmonic mechanism of the heat transfer is sharply suppressed by electrostatic doping. This allows for tuning of the heat exchange by a small applied voltage between the two layers.

Controllability of Deep-Coupling Dynamical Networks

This paper explores the state controllability of deep-coupling networks with inter-layer couplings, where the nodes of each layer are higher-dimensional linear time-invariant dynamical systems. The collective effects on the network controllability from intra-layer network topologies, node dynamics, external control inputs and inner interactions are extensively explored under two representative inter-layer coupling modes, where the integrated network can be controllable even if the intra-layer network topology is uncontrollable by external inputs. Some necessary and/or sufficient conditions for the network controllability are obtained for the representative two-layer intra-layer couplings of interdependent and drive-response modes. Simulated examples reveal the important role of inter-layer couplings of a controllable deep-coupling dynamical network assembled from uncontrollable intra-layer networks.

Ballistic performance and damage simulation of fiber metal laminates under high-velocity oblique impact

Fiber metal laminates have been successfully applied in military aircrafts, armor vehicles and other modern engineering industries as protective structures due to their outstanding impact resistant properties. Prediction of the ballistic performance and investigation on the damage mechanism of the fiber metal laminates under general oblique impact conditions still remain a very challenging issue. In this study, a nonlinear dynamic finite element model in terms of continuum damage mechanics including intra- and inter-layer failure modes is presented. The accuracy of this model is validated with available experimental data. The damage and ballistic performance of two different structural fiber metal laminates subjected to high-velocity oblique impact by rigid hemispherical nose projectile with angles of 0°, 30°, 45° and 60° are studied. The numerical results show that the projectile deflects when the oblique impact occurs and the deflection angle decreases with increasing the impact velocity. The residual velocity of the projectile and the energy absorption of the target are related to the initial impact velocity and impact angle of the projectile. The proposed simulation approach offers a new proper reference for numerical investigations of common oblique impact problems in other fiber metal laminates.

Raman Activity of Multilayer Phosphorene under Strain.

Using computational tools, we study the behavior of activities of lattice vibrational Raman modes in few-layered phosphorene of up to four layers subjected to a uniaxial strain of −2 to +6% applied in the armchair and zigzag directions. We study both high- and low-frequency modes and find very appreciable frequency shifts in response to the applied strain of up to ≈20 cm–1. The Raman activities are characterized by Ag2/Ag1 activity ratios, which provide very meaningful characteristics of functionalization via layer- and strain-engineering. The ratios exhibit a pronounced vibrational anisotropy, namely a linear increase with the applied armchair strain and a highly nonlinear behavior with a strong drop of the ratio with the strain applied along the zigzag direction. For the low-frequency modes, which are Raman active exclusively in few-layered systems, we find the breathing interlayer modes of primary importance due to their strong activities. For few-layered structures with a thickness ≥4, a splitting of the breathing modes into a pair of modes with complementary activities is found, with the lower frequency mode being strain activated. Our calculated database of results contains full angular information on activities of both low- and high-frequency Raman modes. These results, free of experimental complexities, such as dielectric embedding, defects, and size and orientation of the flakes, provide a convenient benchmark for experiments. Combined with high-spatial-resolution Raman scattering experiments, our calculated results will aid in the understanding of the complicated inhomogeneous strain distributions in few-layered phosphorene or the manufacture of materials with desired electronic properties via strain- or layer-engineering.

Lattice vibration and Raman scattering of two-dimensional van der Waals heterostructure

Research on two-dimensional (2D) materials and related van der Waals heterostructures (vdWHs) is intense and remains one of the leading topics in condensed matter physics. Lattice vibrations or phonons of a vdWH provide rich information, such as lattice structure, phonon dispersion, electronic band structure and electron–phonon coupling. Here, we provide a mini review on the lattice vibrations in vdWHs probed by Raman spectroscopy. First, we introduced different kinds of vdWHs, including their structures, properties and potential applications. Second, we discussed interlayer and intralayer phonon in twist multilayer graphene and MoS2. The frequencies of interlayer and intralayer modes can be reproduced by linear chain model (LCM) and phonon folding induced by periodical moiré potentials, respectively. Then, we extended LCM to vdWHs formed by distinct 2D materials, such as MoS2/graphene and hBN/WS2 heterostructures. We further demonstrated how to calculate Raman intensity of interlayer modes in vdWHs by interlayer polarizability model.