Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “stacking two-dimensional structure”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Collinear antiferromagnetic order in a quasi-two-dimensional triangular lattice compound DyNiAl 4 Ge 2

The two-dimensional magnetic triangular lattice, with rare-earth local moments coupled through long-range interactions and hosting strong spin-orbit coupling, serves as an ideal platform for exploring novel quantum phenomena. Here, we report the physical properties of DyNiAl 4 Ge 2 single crystals through comprehensive structural, magnetic, heat capacity, electrical transport, and neutron powder diffraction measurements. DyNiAl 4 Ge 2 crystallizes in a trigonal lattice with the space group $R\bar{3}m$, where Dy atoms form two-dimensional triangular lattice layers within the 𝑎𝑏 plane and stack along the 𝑐 axis. Magnetic susceptibility measurement reveals a magnetic phase transition at 𝑇 𝑁 = 9.0 K, further confirmed by the 𝜆-shaped peak in the heat capacity curve. The obtained temperature-magnetic field phase diagram is relatively simple compared to other isostructural compounds, suggesting the absence of magnetic frustration. This is further evidenced by neutron powder diffraction, which shows a collinear antiferromagnetic ground state with a propagation vector 𝒌 = (0, 0, 1.5), implying the absence of magnetic frustration in DyNiAl 4 Ge 2 . In this magnetic structure, Dy moments are aligned ferromagnetically within each triangular layer and arranged antiferromagnetically between adjacent layers along the 𝑐 axis. In conclusion, our results establish DyNiAl 4 Ge 2 as a model system for understanding the interplay between RKKY interaction and geometrical frustration in this family of compounds.

Wu, HengHeng [Chinese Academy of Sciences (CAS), S↗
DOE OSTI2026

Vapor-phase pillarization of MXenes for engineering hierarchical interlayer porosity

MXenes, a family of two-dimensional (2D) multilamellar materials, possess excellent thermal and electronic properties for a range of applications. Their use in heterogeneous catalysis, however, is limited by the low surface area resulting from stacked layers. Pillarization with inorganic oxides can create more open, mesoporous MXene structures, improving accessibility for guest species to diffuse, reside or react in the space between 2D layers. A previous liquid-phase pillarization method, however, involves excessive use of solvent-based precursors and multiple processing steps. Here, we report a vapor-phase pillarization (VPP) strategy to introduce pillars, exemplified by silica pillars, with high pillar precursor usage efficiency and a simplified processing workflow. The resulting silica-pillared mesoporous MXene exhibits significantly increased surface area and porosity. These textural properties can be easily tuned by the VPP synthesis conditions. When applied as a ruthenium (Ru) catalyst support for the hydrogenolysis of low-density polyethylene (LDPE), the silica-pillared MXene enabled high Ru dispersion and catalytic activity. This study highlights the potential of the VPP method for engineering mesoporous, 2D MXene materials and demonstrates the effectiveness of mesoporous MXene as a catalyst support in overcoming mass transport and active-site accessibility challenges in heterogeneous catalysis involving bulky substances, such as plastics upcycling.

Luo, Song [University of Delaware, Newark, DE (Uni↗
DOE OSTI2025

Squeezing quantum states in three-dimensional twisted crystals

Bloch's theorem provides a conventional starting point for describing wave propagation in periodic media, but in ordered materials where competing spatial periods coexist it is rendered ineffective, often with dramatic consequences. Here we develop an alternate approach that uses coherent free-particle vortex states to study quantum states in supertwisted crystals: three-dimensional stacks of atomically thin two-dimensional layers. Here, this formalism leads naturally to the representation of the spectrum using squeezed coherent states, and it reveals the crucial role of a Coriolis coupling in the equations of motion. This identifies an underlying noncommutative geometry and novel edge state structure in a family of complex ordered structures.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Substrate-Directed Dimensional and Phase Control of Peptide Assemblies on Two-Dimensional van der Waals Materials

Understanding and controlling biomolecular self-assembly on van der Waals (vdW) materials has the potential to advance hybrid bioelectronic devices by enabling precise tuning of the interface and modulation of the resulting electronic properties of the biomolecule-vdW heterostructure. However, how surface properties of vdW materials direct biomolecule assembly remains poorly understood. To fill this knowledge gap, we investigated the assembly of a peptide known to assemble into two-dimensional (2D) crystalline films on MoS 2 on three representative vdW surfaces: WS 2 , MoS 2 , and highly oriented pyrolytic graphite (HOPG). Using in situ atomic force microscopy (AFM), we find that assembly is substrate-dependent, resulting in multilayers on WS 2 , monolayers on MoS 2 , and multiple coexisting phases on HOPG. WS 2 exhibits a higher negative charge, strong long-range electrostatic interactions, and extensive hydration layering that may promote multilayer stacking. In contrast, MoS 2 has stronger short-range interactions with the peptides but much weaker long-range interactions and hydration structure, which may favor monolayer formation. Molecular dynamics simulations predict a corresponding switch from monolayer to multilayer aggregates of the adsorbed monomers, reflected in their relative mobilities. On hydrophobic HOPG, the peptides bind most strongly and remain as monomers with high surface mobility. The peptide dimers comprising the basic unit of the crystals are more compact on HOPG, which has a smaller lattice constant than WS 2 or MoS 2 , suggesting strain contributes to stabilizing multiple phases. Our results provide mechanistic insights into how surface charge and hydration structure, and the lattice structure of the substrates governs peptide assembly on vdW materials, offering a framework to rationally control the 2D peptide-vdW heterostructures.

Molecular dynamics simulations↗
DOE OSTI2025

Truncating 2D Framework Materials Down to a Single Pore: Synthetic Approaches and Opportunities

Here, in this Accounts article, we summarize our recent work on truncating conjugated two-dimensional framework materials down to a single pore, or a single macrocycle. Conjugated 2D architectures have emerged as one of the most synthetically adaptable motifs for coupling semiconductivity and porosity in metal–organic frameworks (MOFs) and covalent organic frameworks (COFs). However, despite their prevalence, 2D architectures have several limitations. In particular, the strong interlayer π–π stacking can limit both processability and the accessibility of internal active sites. We have found that simple macrocycles preserve key aspects of 2D framework structure and function, including porosity and out-of-plane electrical conductivity, while providing improved processability, surface tunability, and mass transport properties. In this article, we first describe our synthetic approach and general design considerations. Specifically, we show how ditopic analogues of the tritopic ligands commonly found in the synthesis of 2D MOFs and COFs can be used to achieve a diverse library of conjugated macrocycles that resemble fragments of semiconducting frameworks in both form and function. The length of the peripheral side chains, the size of the aromatic core, and the solubility of intermediates are all key variables in favoring selective macrocycle formation over undesired linear polymers and oligomers. Next, we highlight the unique advantages that macrocycles provide, including improved processability, atomically precise surface tunability, and greater active site accessibility. In particular, the identity of the peripheral side chains dramatically impacts both solubility and colloidal stability as well as crystal size and morphology. We further show how the solution processability and nanoscale dimensions of macrocycles can simplify electronic device fabrication and improve electrochemical performance. Finally, we end with a forward-looking discussion on how macrocycles offer a unique bridge between conjugated molecules and extended frameworks, enabling new application areas and fundamental science.

charge transport↗
DOE OSTI2025

Van der Waals Sandwich Structures for Surface-Enhanced Raman Scattering

Surface-enhanced Raman scattering (SERS) intensity of two-dimensional (2D) materials critically depends on the resonant conditions and factors such as the substrate interferences and molecule adsorption fluctuations, making comprehensive investigation, understanding, and optimization of 2D materials-assisted SERS challenging. Here, in this work, the wavelength-dependent SERS of van der Waals structures of 2D materials is systematically investigated, focusing on the intrinsic frequency-dependent Raman tensors by first-principles method while ruling out other extrinsic factors in experiments. Distinct enhancement profiles are found for different 2D materials, among which MoS2 and graphene exhibit remarkably strong and broadband enhancement effects. For stacked multilayers and heterostructures of 2D materials, the calculated SERS addresses the significance of the first contact monolayer effect. Based on the above theory, the van der Waals sandwich structures are proposed and investigated as the SERS substrates, verifying a further significantly enhanced SERS performance. This resonant first-principles study demonstrates a comprehensive and analytical way to explore and promote the SERS of van der Waals structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Simulations of a hypersonic turbulent boundary layer over wavy surfaces

Here, we conduct large-eddy simulations of a Mach 5.84 cold wall turbulent boundary layer over one-dimensional wavy walls with varying amplitudes and wavelengths. Across all wall topologies, a series of alternating shock and expansion waves is shown to influence the entire boundary layer, and generate repeating wave patterns in the turbulent stresses, dispersive stresses, and turbulent kinetic energy budget. The series of alternating shocks and expansions imposes repeating adverse and favourable pressure gradients across the wavy wall, and at sufficient wall amplitude, triggers flow separation in the trough of the wave. Flow separation is demonstrated to influence the behaviour of wall pressure fluctuations over the wavy wall. In attached flows, the prominent frequencies are consistent with integral-scale boundary layer turbulence, whereas in separated flows, a two-decade frequency range is present, akin to two-dimensional shock–boundary layer interactions. Counter-rotating streamwise-oriented structures are observed on the windward side of the wave, which diminish over the wave crest. A conditional analysis demonstrates that these structures are present in the upstream boundary layer, and are amplified with increasing wall amplitude. An examination of the Görtler number and probability density function (PDF) of the fluctuating lateral wall shear stress demonstrates the strong correlation between a large Görtler number and growth of the PDF tail density, suggesting that the amplification of the counter-rotating streamwise-oriented structures are linked to centrifugal instabilities in regions of streamline concavity.

boundary layers↗
DOE OSTI2026

In Situ Insights into Enhanced Cooperative Ligand Exchange Kinetics via Solvent-Induced Restacking in a 2D Metal–Organic Framework

Understanding the reaction kinetics at catalytically active sites is crucial for integrating catalytic two-dimensional (2D) materials into industrial processes. This study focuses on in situ observation of ligand exchange kinetics and solvent-assisted structural restacking transition in the 2D paddle wheel-based MOF [Cu 2 (dttc) 2 ] n (DUT-134(Cu), dttc = dithieno[3,2-b:2′,3′- d]thiophene-2,6-dicarboxylate). The ligand exchange process, involving the replacement of dimethylformamide (DMF) with nitriles such as acetonitrile (ACN), pentanenitrile, and heptanenitrile, was investigated using advanced in situ characterization techniques with high temporal resolution, including powder X-ray diffraction and Raman spectroscopy. The larger analytes exhibited reduced exchange rates, consistent with enhanced steric hindrance and greater diffusion constraints. Interestingly, the study revealed that the exchange of DMF with ACN induces a structural transition to higher symmetry within few seconds, a transition from AB to AA stacking mode of the layers, and a widening of the interlayer distance. Crucially, this structural transition dramatically accelerates the solvent exchange process through cooperative effects, offering critical advantages for catalytic applications. Notably, the reverse exchange from ACN to DMF proceeds more slowly and does not reverse the structural changes, but a new phase is formed with preserved AA stacking. By isotope labeling of linker molecules in combination with two complementary theoretical vibrational simulation methods, the precise assignment of Raman bands and the vibrational modes associated with the ligand exchange process could be achieved. These pioneering insights into the dynamic behavior of 2D MOFs, coupled with ligand exchange, establish a highly promising and transformative approach to achieving enhanced tunability and responsiveness in future catalytic applications.

Layers↗
DOE OSTI2026

Identifying Strain Stacking Boundaries between Multiphase Domains in Atomically Thin Two-Dimensional Magnets

Stacking engineering of van der Waals materials is an important strategy to control the materials’ properties, such as electronic correlations, ferroelectricity, and layer-dependent two-dimensional magnetism. A timely testbed for the study of the latter is atomically thin chromium trihalides (CrX 3 , X = Cl, Br, I). Notably, by understanding the sliding mechanism between different stacking sequences, control of the stacking arrangement, and thus magnetic properties in CrX 3 , can be achieved. Such insight, however, is currently lacking. Here, in this study, advanced electron microscopy methods are used to identify multiple stacking sequences corresponding to different bulk phases in atomically thin CrX 3 (X = Cl and Br) down to bilayer thickness and with lateral domain sizes as small as tens of nanometers. Indications of nanometer scale transitions and interactions at the stacking boundaries are found, including a universally preferred sliding direction that is consistent with density functional theory calculations and the strain fields at lateral heterostructure boundaries. This study demonstrates the necessity to consider local stacking structures when interpreting averaged magnetic properties measured with macroscale probes. Additionally, the preferred sliding direction insight from this study provides a strategy to control stacking sequence in atomically thin CrX 3 samples during the exfoliation and sample fabrication process.

DFT calculations↗
DOE OSTI2025

Roadmap for Photonics with 2D Materials

Triggered by advances in atomic-layer exfoliation and growth techniques, along with the identification of a wide range of extraordinary physical properties in self-standing films consisting of one or a few atomic layers, two-dimensional (2D) materials such as graphene, transition metal dichalcogenides (TMDs), and other van der Waals (vdW) crystals now constitute a broad research field expanding in multiple directions through the combination of layer stacking and twisting, nanofabrication, surface-science methods, and integration into nanostructured environments. Photonics encompasses a multidisciplinary subset of those directions, where 2D materials contribute remarkable nonlinearities, long-lived and ultraconfined polaritons, strong excitons, topological and chiral effects, susceptibility to external stimuli, accessibility, robustness, and a completely new range of photonic materials based on layer stacking, gating, and the formation of moiré patterns. These properties are being leveraged to develop applications in electro-optical modulation, light emission and detection, imaging and metasurfaces, integrated optics, sensing, and quantum physics across a broad spectral range extending from the far-infrared to the ultraviolet, as well as enabling hybridization with spin and momentum textures of electronic band structures and magnetic degrees of freedom. The rapid expansion of photonics with 2D materials as a dynamic research arena is yielding breakthroughs, which this Roadmap summarizes while identifying challenges and opportunities for future goals and how to meet them through a wide collection of topical sections prepared by leading practitioners.

2D materials↗
DOE OSTI2026

Supramolecular Assembly of Multielement Ribbon-like Structures Derived from Halide Perovskites

Halide perovskites are crucial materials with broad applications owing to their exceptional optoelectronic properties. Vacancy-ordered double perovskites, featuring highly tunable transition metal sites, enable controllable optoelectronic properties through multielement compositional design. Here, in this study, we introduced 18-crown-6 into the vacancy-ordered double perovskites system and developed two-dimensional ribbon-like single crystals (18C6@K) 2 {PtSnTeIrRe} 1 Cl 6 via an antisolvent supramolecular assembly method, demonstrating morphology modulation through multielement composition design. The crystals crystallize in the centrosymmetric space group $P\bar{1}$. The dumbbell-shaped structural units (crown ether@A)2MX6 pack along a and b axes to form a 2-dimensional (2D) monolayer, and these monolayers further stack along the c axis to generate the ribbon-like single crystals. Energy-dispersive X-ray spectroscopy (EDX) qualitatively confirmed the uniform distribution of the five transition metals throughout the crystal, while inductively coupled plasma atomic emission spectroscopy (ICP–AES) quantitatively verified their atomic ratios. We further investigated the origin of the morphology, distinct from the previously reported cube-like single crystals with the $R\bar{3}$ space group. When acetonitrile was used as the solvent, three-dimensional crystals with $R\bar{3}$ symmetry were obtained, whereas dimethylformamide (DMF) was essential for forming two-dimensional ribbon-like single crystals. The essential role of DMF could be ascribed to its capability to maintain a higher concentration of the building blocks. Moreover, Ir 4+ and Pt 4+ cations also played critical roles in inducing the two-dimensional ribbon-like morphology. The three-element (18C6@K) 2 {PtSnTe}1Cl 6 single crystals exhibited bright yellow emission under 375 nm laser excitation, demonstrating the tunability of optoelectronic properties of this class of material.

Zhu, Heqing [University of California, Berkeley, C↗
DOE OSTI2025

Emergent Above-Gap Photoluminescence in Molecularly Engineered Hybrid Bilayer Crystals

Bilayer crystals, built by stacking two-dimensional (2D) covalent monolayers, give rise to coupled excitonic states whose properties are constrained by fixed lattice symmetry and orientation. Replacing one covalent monolayer with a 2D molecular crystal––held together by non-covalent forces––overcomes this limitation, as molecular functional groups afford tunable in-plane lattice geometry, intermolecular spacing, and interlayer coupling, providing a powerful knob for exciton engineering. Here, in this study, we report four-atom-thick hybrid bilayer crystals (HBCs) synthesized by directly growing single-crystalline PDI molecular crystal atop WS 2 monolayers, which exhibit a robust photoluminescence (PL) peak 120 meV above the WS 2 optical band gap alongside a belowgap emission. Both peaks display strong polarization anisotropy—nearing unity for the above-gap emission—and maintain a perfectly linear power-law dependence up to an excitation density of ~10 7 mW/cm 2 , indicative of coexisting localized and delocalized excitonic states. Substituting PDI with a PTCDA monolayer on WS 2 fully quenches PL, demonstrating molecular control over excitonic emission. Lattice scale ab initio GW and GW-BSE calculations reveal a significantly hybridized bilayer band structure in PDI/WS 2 that supports interlayer excitonic species both above and below the WS 2 gap with strong polarization anisotropy, in excellent agreement with experiment. Our work introduces a molecule-based bilayer platform for the bottom-up design and control of excitonic phenomena in atomically thin optoelectronic and quantum materials.

2D materials↗
DOE OSTI2025

Stacking polymorphism of PtSe 2 : its implication to layer-dependent metal-insulator transitions

Using diffusion Monte Carlo (DMC) and density functional theory (DFT) calculations, we examine the structural stability and interlayer binding properties of PtSe 2 . Our DMC study reveals that AA and AB-r bilayer stacking modes are nearly degenerate, highlighting the significant role of interlayer hybridization in offsetting the energy cost due to larger interlayer separations in the AB-r mode. Additionally, our DMC-benchmarked DFT calculations with the r 2 SCAN+rVV10 functional uncover pronounced stacking polymorphism in few-layer PtSe 2 , driven by degenerate AA and AB-r interfaces, which leads to substantial band gap variations across different stacking configurations. This polymorphism, along with selenium vacancies, influences a layer-dependent metal-insulator transition observed in few-layer PtSe 2 . Our findings emphasize the importance of both van der Waals interactions and interlayer hybridization in determining the phase stability and electronic properties of PtSe 2 , advancing our understanding of its fundamental properties and refining theoretical models for practical applications in nanoelectronic devices.

Electronic materials↗
DOE OSTI2025

Screw-Dislocation-Driven Growth of 2D Perovskite Spiral Microplates

Two-dimensional (2D) organic–inorganic halide perovskites are solution-processable semiconductors that are promising for optoelectronic applications. Understanding crystallization mechanisms to achieve control over nanostructures is important for optimizing desired properties. Here we introduce a versatile strategy to synthesize spiral microplates of diverse 2D perovskites at the air–water interface through screw-dislocation-driven growth. Spirals of 11 2D perovskite compositions (LA) 2 (A) n−1 Pb n X 3n+1 with different spacer (LA) cations, A-cations, halide (X) anions, and n-number can be grown. They typically consist of single- or few-layer perovskite step heights but exhibit stacking complexity when multiple dislocations interact. The spiral microplates exhibit the characteristic optical properties (photoluminescence and second-harmonic generation) of the underlying 2D perovskites. Fluorescence-detected circular dichroism imaging shows that the chirality of the spiral center does not translate to the observed chiroptical properties of the microplate, consistent with the length scale of the chiral distortion. Furthermore, this solution growth of perovskite spirals diversifies the perovskite microstructures for optoelectronics and other applications.

2D halide perovskites↗
DOE OSTI2025

Ligand-induced self-assembly of twisted two-dimensional halide perovskites

Two-dimensional (2D) halide perovskites (HPs) exhibit intriguing optoelectronic functionalities. Conventionally, 2D HPs have been synthesized with linear and planar molecular spacers, resulting in nominal modifications of their optoelectronic properties. In contrast, lower-dimensional HPs (0D and 1D) have proved accommodating to the incorporation of bulky molecular spacers. Fundamental insights into the incorporation of bulky molecular spacers in 2D HP structures remains elusive. Here, in this study, by implementing a high-throughput autonomous exploration workflow, the crystallization behaviours of 2D HPs based on a bulky 3,3-diphenylpropylammonium (DPA) spacer are comprehensively explored. Counterintuitive to conventional HP chemistry, synthesis of 2D DPA 2 PbI 4 HPs is indeed feasible when the steric hindrance is mediated by minute incorporation of 3D HP precursors. Furthermore, a moiré superlattice is observed from the DPA 2 PbI 4 flakes, indicating the spontaneous formation of twisted stacks of 2D HPs.We hypothesize that the unconventional van der Waals surface of DPA 2 PbI 4 facilitates the self-assembly of the twisted stacks of 2D HPs. This work exemplifies how high-throughput experimentation can discover unconventional material systems in which the synthetic principle lies beyond conventional chemical intuition. Furthermore, these findings provide hints for how to chemically manipulate the twist stacking in 2D HPs, thus rendering a straightforward way for bespoke realization of functionalities in exotic materials systems via a bottom-up approach.

materials chemistry↗
DOE OSTI2025

A General and Modular Approach to Solid-State Integration of Zero-Dimensional Quantum Systems

Here, we present an all-electrical readout mechanism for quasi-0D quantum states (0D-QS), such as point defects, adatoms, and molecules, that is modular and general, providing an approach that is amenable to scaling and integration with other solid-state quantum technologies. Our approach relies on the creation of high-quality tunnel junctions via the mechanical exfoliation and stacking of multilayer graphene (MLG) and hexagonal boron nitride (hBN) to encapsulate the target system in an MLG/hBN/0D-QS/hBN/MLG heterostructure. This structure allows for all-electronic spectroscopy and readout of candidate systems through a combination of coulomb and spin-blockade. As a proof of principle, we demonstrate electronic tunneling spectroscopy of point defects in hBN and the molecular qubit vanadyl phthalocyanine. Our approach demonstrates a new pathway for the incorporation of molecules and atomic defects into solid-state quantum devices and circuits along with a readout scheme that does not rely on highly constrained optical processes for photonic readout.

defects in hexagonal boron nitride↗
DOE OSTI2025

Robust supermoiré pattern in large-angle single-twist bilayers

Forming long-wavelength moiré superlattices in van der Waals bilayers that have a small-angle twist between the two layers has been a key approach for creating moiré flat bands. However, for small twist angles, strong lattice reconstruction creates domain walls and other forms of disorder in the moiré pattern, posing considerable challenges for engineering such platforms. At large twist angles, the lattices are more rigid, but it is difficult to produce flat bands in shorter-wavelength moiré superlattices. Here, in this study, we introduce an approach for tailoring robust supermoiré structures in bilayers of transition-metal dichalcogenides using only a single twist near a commensurate angle. Structurally, we show the spontaneous formation of a periodic arrangement of three inequivalent commensurate moiré stackings, where the angle deviation from the commensurate angle determines the periodicity. Electronically, we reveal a large set of van Hove singularities that indicate strong band hybridization, leading to flat bands near the valence band maximum. Our study extends the study of the interplay among band topology, quantum geometry and moiré superconductivity to the large twist angle regime.

electronic properties and materials↗
DOE OSTI2025

Surface acoustic waves and lattice vibrations in two-dimensional Ti 3 ⁢C 2 ⁢𝑇 𝑥 (𝑇 =O, F) MXene films

We investigated surface acoustic wave (SAW) propagation and lattice vibrations in two-dimensional (2D) titanium carbide (Ti 3 ⁢C 2 ⁢𝑇 x ) MXene films as a function of surface termination and layer stacking, using atomistic simulations. We found that SAW propagation velocity is highly sensitive to both single-layer properties and interlayer bonding. Surface terminations significantly modulate wave behavior, with oxygen and fluorine terminations producing distinct effects on wave propagation, with oxygen-terminated monolayers exhibiting 20% higher wave speeds than fluorine counterparts due to strengthened intralayer bonds. Key observations include the transition from one to two layers causing wave speed variations, and the development of interlayer modes that generate more dispersed lattice vibrations. As the film layer thickness increases, SAW propagation becomes predominantly confined to the upper surface, with coherence of vibrational modes diminishing in multilayer structures. These findings suggest MXene terminations and layer stacking are crucial parameters for controlling SAW behavior, offering promising avenues for novel acoustic wave device applications.

2-dimensional systems↗