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At least 127 records · Page 7

Molecular-Scale Characterization of Photoinduced Charge Separation in Mixed-Dimensional InSe–Organic van der Waals Heterostructures

Layered indium selenide (InSe) is an emerging two-dimensional semiconductor that has shown significant promise for high-performance transistors and photodetectors. The range of optoelectronic applications for InSe can potentially be broadened by forming mixed-dimensional van der Waals heterostructures with zero-dimensional molecular systems that are widely employed in organic electronics and photovoltaics. Here, we report the spatially resolved investigation of photoinduced charge separation between InSe and two molecules (C 70 and C 8 -BTBT) using scanning tunneling microscopy combined with laser illumination. We experimentally and computationally show that InSe forms type-II and type-I heterojunctions with C 70 and C 8 -BTBT, respectively, due to an interplay of charge transfer and dielectric screening at the interface. Laser-excited scanning tunneling spectroscopy reveals a ~0.25 eV decrease in the energy of the lowest unoccupied molecular orbital of C 70 with optical illumination. Furthermore, photoluminescence spectroscopy and Kelvin probe force microscopy indicate that electron transfer from InSe to C 70 in the type-II heterojunction induces a photovoltage that quantitatively matches the observed downshift in the tunneling spectra. In contrast, no significant changes are observed upon optical illumination in the type-I heterojunction formed between InSe and C 8 -BTBT. Density functional theory calculations further show that, despite the weak coupling between the molecular species and InSe, the band alignment of these mixed-dimensional heterostructures strongly differs from the one suggested by the ionization potential and electronic affinities of the isolated components. Self-energy-corrected density functional theory indicates that these effects are the result of the combination of charge redistribution at the interface and heterogeneous dielectric screening of the electron–electron interactions in the heterostructure. In addition to providing specific insight for mixed-dimensional InSe–organic van der Waals heterostructures, this work establishes a general experimental methodology for studying localized charge transfer at the molecular scale that is applicable to other photoactive nanoscale systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Toward a First-Principles Framework for Predicting Collective Properties of Electrolytes

Conspectus Given the universal importance of electrolyte solutions, it is natural to expect that we have a nearly complete understanding of the fundamental properties of these solutions (e.g., the chemical potential) and that we can therefore explain, predict, and control the phenomena occurring in them. In fact, reality falls short of these expectations. But, recent advances in the simulation and modeling of electrolyte solutions indicate that it should soon be possible to make progress toward these goals. In this Account, we will discuss the use of first-principles interaction potentials based in quantum mechanics (QM) to enhance our understanding of electrolyte solutions. Specifically, we will focus on the use of quantum density functional theory (DFT) combined with molecular dynamics simulation (DFT-MD) as the foundation for our approach. The overarching concept is to understand and accurately reproduce the balance between local or short-ranged (SR) structural details and long-range (LR) correlations, allowing the prediction of the thermodynamics of both single ions in solution as well as the collective interactions characterized by activity/osmotic coefficients. In doing so, relevant collective motions and driving forces characterized by chemical potentials can be determined. Here, in this Account, we will make the case that understanding electrolyte solutions requires a faithful QM representation of the SR nature of the ion–ion, ion–water, and water–water interactions. However, the number of molecules that is required for collective behavior makes the direct application of high-level QM methods that contain the best SR physics untenable, making methods that balance accuracy and efficiency a practical goal. Alternatives such as continuum solvent models (CSMs) and empirically based classical molecular dynamics have been extensively employed to resolve this problem but without yet overcoming the fundamental issue of SR accuracy. We will demonstrate that accurately describing the SR interaction is imperative for predicting both intrinsic properties, namely, at infinite dilution, and collective properties of electrolyte solutions. DFT has played an important role in our understanding of condensed phase systems, e.g., bulk liquid water, the air–water interface, ions in bulk, and at the air–water interface. This approach holds huge promise to provide benchmark calculations of electrolyte solution properties that will allow for the development and improvement of more efficient methods, as well as an enhanced understanding of fundamental phenomena. However, the standard protocol using the generalized gradient approximation with van der Waals (vdW) correction requires improvement in order to achieve a high level of quantitative accuracy. Simply simulating with higher level DFT functionals may not be the best route considering the significant computational cost. Alternative methods of incorporating information from higher levels of QM should be explored; e.g., using force matching techniques on small clusters, where high level benchmark calculations are possible, to develop ideal correction terms to the DFT functional is a promising possibility. We argue that DFT with statistical mechanics is becoming an increasingly useful framework enabling the prediction of collective electrolyte properties.

Duignan, Timothy T.↗

A Physical Model for Understanding the Activation of MoS 2 Basal-plane Sulfur Atoms for the Hydrogen Evolution Reaction

All the DFT calculations are done with the Vienna Ab Initio Simulation Package (VASP) using the projector augmented wave method. The Bayesian error estimation exchange-correlation functionals (BEEF) with van der Waals interactions are employed. A plane-wave cutoff energy of 400 eV is used together with PAW-PBE potentials where semi core p states are treated as valence. All the calculations allow for spin-polarization. The structures are relaxed until the force is converged to < 0.01 eV/Å. The lattice parameter of MoS 2 unit cell, optimized with this functional, is 3.19 Å. A (4×4) supercell is used to model all the transition metal doped MoS 2 systems studied here, including those with S vacancies. For calculations in the initial dopant structure exploration, the Brillouin zone is sampled with a 3x3x1 Monkhorst-Pack k-point mesh. A 6×6×1 Monkhorst-Pack k-point mesh is used for the H binding energy and density of states calculations. In all calculations, the vacuum layer is set as 15 Å to eliminate periodic interaction perpendicular to the basal plane.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Ultrafast laser-induced spin–lattice dynamics in the van der Waals antiferromagnet CoPS 3

CoPS 3 stands out in the family of the van der Waals antiferromagnets XPS 3 (X = Mn, Ni, Fe, and Co) due to the unquenched orbital momentum of the magnetic Co 2+ ions, which is known to facilitate the coupling of spins to both electromagnetic waves and lattice vibrations. Here, using a time-resolved magneto-optical pump–probe technique, we experimentally study the ultrafast laser-induced dynamics of mutually correlated spins and lattice. It is shown that a femtosecond laser pulse acts as an ultrafast heater and, thus, results in the melting of the antiferromagnetic order. At the same time, the resonant pumping of the 4 T 1g → 4 T 2g electronic transition in Co 2+ ions effectively changes their orbital momentum, giving rise to a mechanical force that moves the ions in the direction parallel to the orientation of their spins, thus generating a coherent B g phonon mode at the frequency of about 4.7 THz.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Unraveling Strain Gradient Induced Electromechanical Coupling in Twisted Double Bilayer Graphene Moiré Superlattices

Moiré superlattices of 2D materials with a small twist angle are thought to exhibit appreciable flexoelectric effect, though unambiguous confirmation of their flexoelectricity is challenging due to artifacts associated with commonly used piezoresponse force microscopy (PFM). For example, unexpectedly small phase contrast (≈8°) between opposite flexoelectric polarizations is reported in twisted bilayer graphene (tBG), though theoretically predicted value is 180°. We report a methodology is developed to extract intrinsic moiré flexoelectricity using twisted double bilayer graphene (tDBG) as a model system, probed by lateral PFM. For small twist angle samples, it is found that a vectorial decomposition is essential to recover the small intrinsic flexoelectric response at domain walls from a large background signal. The obtained threefold symmetry of commensurate domains with significant flexoelectric response at domain walls is fully consistent with the theoretical calculations. Incommensurate domains in tDBG with relatively large twist angles can also be observed by this technique. A general strategy is provided here for unraveling intrinsic flexoelectricity in van der Waals moiré superlattices while providing insights into engineered symmetry breaking in centrosymmetric materials.

36 MATERIALS SCIENCE↗

Nonlinear effects in manybody van der Waals interactions

Van der Waals interactions are ubiquitous and they play an important role for the stability of materials. Current understanding of this type of coupling is based on linear response theory, while optical nonlinearities are rarely considered in this context. Many materials, however, exhibit strong optical nonlinear response, which prompts further evaluation of dispersive forces beyond linear response. Here we present a approach that takes into account linear and nonlinear properties of all dipolar nanoparticles in a given system. This method is based on a Hamiltonian for nonlinear dipoles, which we apply in different systems uncovering a complex interplay of distance, anisotropy, polarizabilities, and hyperpolarizabilities in the vdW energy. This investigation broadens our basic understanding of dispersive interactions, especially in the context of nonlinear materials. Published by the American Physical Society 2024

Le, Dai-Nam (ORCID:0000000307568742)↗

Low-frequency Raman signature of Ag-intercalated few-layer MoS 2

Density functional theory based calculations and experimental analysis on a limited number of real samples are performed to study how the presence of silver intercalated in the van der Waals gap of few-layer MoS 2 affects the low-frequency Raman active modes of this material. Silver is found to predominantly affect the breathing-like and shear-like vibrational modes of MoS 2 . These modes correspond to quasi-rigid movements of each individual layer with a restoring force (and, in turn, frequency) that is determined by modulations in the weak interlayer interactions. Noticeable red-shifts with increasing Ag concentration are found for all low-frequency modes. This finding indicates the potential for low-frequency vibrations as useful gauges for practical determination of silver concentration using low-frequency Raman spectroscopy. Finally, this work also describes a semi-classical linear chain model that allows to extrapolate results to a large number of layers. Further, first-principles calculations show how Raman spectroscopy can be used to characterize the quality of the two-dimensional interface between MoS 2 and a silver substrate.

36 MATERIALS SCIENCE↗

Nanoscale Control of Polar Surface Phases in Layered van der Waals CuInP 2 S 6

Antiferroelectric (AFE) materials, in which alternating dipole moments cancel out to a zero net macroscopic polarization, can be used for high-density energy storage and memory applications. The AFE phase can exist in bulk CuInP 2 Se 6 , CuBiP 2 S 6 , and a few other transition-metal thiophosphates below 200 K. The required low temperature poses challenges for practical applications. In this work, we report the coexistence of ferrielectric (FE) states and a stable surface phase that does not show piezoelectric response (“zero-response phase”) in bulk CuInP 2 S 6 at room temperature. Using piezoresponse force microscopy (PFM) tomographic imaging together with density functional theory, we find that direct and alternating voltages can locally and stably convert FE to zero-response phases and vice versa. While PFM loops show pinched hystereses reminiscent of antiferroelectricity, PFM tomography reveals that the zero-response areas form only on top of the FE phase in which the polarization vector is pointing up. Theoretical calculations suggest that the zero-response phase may correspond to AFE ordering where stacked CuInP 2 S 6 layers have alternating polarization orientations thereby leading to a net-zero polarization. Consistent with experimental findings, theory predicts that the FE polarization pointing down is robust up to the top surface, whereas FE polarization pointing up energetically favors the formation of an AFE surface layer, whose thickness is likely to be sensitive to local strains. AFE order is likely to be more robust against detrimental size effects than polar order, therefore providing additional opportunities to create multifunctional heterostructures with 2D electronic materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Direct Observation of Twin van der Waals Molecular Chains

The van der Waals (vdW) assemblies are the most common structures of materials. However, directly mapping intermolecular electron clouds of a vdW assembly has never been obtained, even though the intramolecular electron clouds were visualized by atomic-resolution techniques. In this report, we unprecedently mapped the intermolecular electron cloud of the assembles of ethanol molecules via ethyl groups with noncontact atomic force microscopy at 5 K, leading to the first visualization of vdW molecular chains, in which ethanol molecules assemble into twin vdW molecular chains in a reverse parallel configuration on Ag(111) plane. Furthermore, spontaneous order-disorder transitions in the chain were dynamically observed, suggesting its unusual properties different from 2D vdW materials. In conclusion, these findings provide an "eye" to see the atomic world of vdW materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Assembly of Arbitrary Designer Heterostructures with Atomically Clean Interfaces

Van der Waals heterostructures are an excellent platform for studying intriguing interface phenomena, such as moiré and proximity effects. Many of these phenomena occurring in such heterostructures' interfaces and surfaces have so far been hampered because of their high sensitivity to disorder and interface contamination. Here, it reports a dry polymer-based assembly technique to fabricate arbitrary designer van der Waals heterostructures with atomically clean surfaces. The key features of the suspended dry pick-up and flip-over assembly technique are: 1) the heterostructure surface never comes into contact with polymers, 2) the assemble is entirely solvent-free, 3) it is entirely performed in a glovebox, and 4) it only requires temperatures below 130 °C. By performing ambient atomic force microscopy and atomically-resolved scanning tunneling microscopy on example heterostructures, it demonstrates the fabrication of air-sensitive heterostructures with ultra-clean interfaces and surfaces. It envisions that, due to the avoidance of polymer melting, this technique is potentially compatible with heterostructure assembly under ultra-high vacuum conditions, which promises ultimate heterostructure quality.

2D materials↗

Chemistry and Interfacial Structure Promoting Quasi-van der Waals Epitaxial Growth of WS 2 Nanosheets on Sapphire for Prospective Application in Field-Effect Transistors

How do chemical and structural modifications to the supporting crystal surface affect the subsequent van der Waals (vdW) or quasi(Q)-vdW epitaxial growth of 2D nanocrystals? Developing an atomic-scale picture of such an interfacial system is crucial for understanding its impact on the physical and chemical properties of the supported 2D materials. The elucidation of the interfacial structure and chemistry needed to promote the Q-vdW epitaxial growth of 2D tungsten disulfide (WS 2 ) nanocrystals contributes to the growth mechanism understanding, thus pushing forward the integration of such atomically thin semiconductors toward real field-effect transistor applications. In addition to an atomic-force microscopy top view, we showcase a combination of X-ray techniques for a top-to-bottom investigation of the complexities of the buried interface structures. Furthermore, this approach uses X-ray photoelectron spectroscopy, X-ray standing wave excited X-ray fluorescence, and crystal truncation rod scattering to produce a highly resolved chemical-state-specific 3D atomic map for the extended interface structure of WS 2 /α-Al 2 O 3 (001). Employing these detailed analysis methods, along with density functional theory to further refine the picoscale structure, we demonstrate how two different types of interface engineering during the pregrowth stage lead to significant differences in the chemical and structural modifications to the terminal surface of c-face sapphire, which in turn leads to substantial differences in the submonolayer growth of supported WS 2 2D nanocrystals in terms of lateral domain sizes, epitaxial registry, vdW gaps, and stability.

36 MATERIALS SCIENCE↗

Impact of the adhesion-force lever-arm “a” on the Rock ‘n’ Roll resuspension model and how to compute it from contact mechanics

The paper proposes a methodology to fill a gap in the context of mechanistic particle resuspension models related to the adhesion and lift force lever arms ( a ): to date, only one experimental observation exists from a centrifuge experiment with a specific particle/surface pair which found r P / a = 100 and assumed that the contact points were symmetric with respect to the particle center. However, the Reeks and Hall’s (2001) model is highly sensitive to this parameter, which therefore cannot be used as-is for different particle diameters or materials. This paper proposes a methodology to compute the adhesion and lift force lever arms ( a A and a L , respectively) based on Atomic Force Microcopy (AFM) surface roughness measurements and contact mechanics arguments. In practice, a spherical, perfectly smooth particle is brought in contact (computationally) with the measured surface roughness and is then rotated by the point of contact to determine the two or more asperities over which the particle would sit on the surface. A method to compute the asperity radius of curvature is devised to compute the asperity deformation and the correct partitioning of the total deformation between the particle and the asperity is presented. For the glass surface under consideration, the asperity deformation was negligible, i.e., it was below the van der Waals radius, which is the limit of applicability of contact mechanics. The Reeks and Hall’s (2001) model is then extended to account for the joint probability of a A and a L . Significant differences in particle resuspended after a day in common atmospheric conditions are found between the approach that uses the lever-arm distributions or their mean values. Also, important differences are found when comparing the lever-arm distribution and r P / a = 100. Hence, one should be cautious of using r P / a = 100 for surface/particle pairs differing from those in the original study. Finally, limits of applicability of the theories used are presented together with considerations regarding how to extend the method to non-spherical particles and different materials.

42 ENGINEERING↗

Fluidic Flow Assisted Deterministic Folding of Van der Waals Materials

Origami offers a distinct approach for designing and engineering new material structures and properties. The folding and stacking of atomically thin van der Waals (vdW) materials, for example, can lead to intriguing new physical properties including bandgap tuning, Van Hove singularity, and superconductivity. On the other hand, achieving well-controlled folding of vdW materials with high spatial precision has been extremely challenging and difficult to scale toward large areas. In this paper, a deterministic technique is reported to fold vdW materials at a defined position and direction using microfluidic forces. Electron beam lithography (EBL) is utilized to define the folding area, which allows precise control of the folding geometry, direction, and position beyond 100 nm resolution. Using this technique, single-atomic-layer vdW materials or their heterostructures can be folded without the need for any external supporting layers in the final folded structure. In addition, arrays of patterns can be folded across a large area using this technique and electronic devices that can reconfigure device functionalities through folding are also demonstrated. Such scalable formation of folded vdW material structures with high precision can lead to the creation of new atomic-scale materials and superlattices as well as opening the door to realizing foldable and reconfigurable electronics.

2D materials↗

Sensitivity of magnetohydrodynamic simulations of Joule-heated conductors to the vaporization curve in equations of state

Magnetohydrodynamic (MHD) simulations of electrically exploded aluminum and copper rods demonstrate a technique to validate equations of state (EOS) for rapidly Joule-heated conductors. The balance of internal and magnetic forces at the conductor-insulator interface drives the metal there along the vaporization phase boundary. Variations between critical points and vaporization curves in existing models predict differing densities and temperatures in MHD simulations for these models. Here, the inclusion of Maxwell constructs in the liquid-vapor biphase region of the EOS caused the rod surface to vaporize earlier in time than unmodified tables with van der Waals loops. Velocimetry of recent experiments is used to validate the location of the vaporization curve in existing EOS models and differentiate between the vapor dome treatments. Dielectric coatings applied to the metal surface restricted the conductor’s expansion and diverted the metal into the warm dense matter regime.

36 MATERIALS SCIENCE↗

Experimental and Theoretical Studies of the Surface Oxidation Process of Rare–Earth Tritellurides

Recent studies have established Van der Waals (vdW) layered and 2D rare-earth tritellurides (RTe 3 ) as superconductors and near room-temperature charge density wave (CDW) materials. Their environmental stability raises natural concern owing to aging/stability effects observed in other tellurium-based layered crystals. Here, the results establish the stability and environmental aging characteristics of these RTe 3 systems involving a variety of metals such as La, Nd, Sm, Gd, Dy, and Ho. The atomic force microscopy (AFM) and scanning electron microscopy (SEM) results show that all the RTe 3 sheets oxidize to form thin TeO x layers that are primarily confined to the surface, edges, and grain boundaries. Time-resolved in situ Raman spectroscopy measurements are used to understand the kinetics of the oxidization process for different lanthanide metal cations and establish their relative stability/resilience to oxidization. Overall results indicate that the vdW layers show higher air stability as the 4f electron number decreases going from Ho to La, resulting in the most stable LaTe 3 compared to the least stable HoTe 3 . Comprehensive quantum mechanical simulations reveal that environmental degradation originates from a strong oxidizing reaction with O 2 molecules, while humidity (H 2 O) plays a negligible role unless Te vacancies are present. Moreover, the simulations explain the effects of 4f electrons on the work function and Te vacancies formation, which directly impact the aging characteristics of RTe 3 layers. Interestingly, optical and electrical measurements show that the CDW response is still observed in aged RTe 3 layers owing to the presence of underlying pristine/nonoxidized RTe 3 layers, except CDW transition temperatures increase due to the thickness effect. Overall results offer the first in-depth environmental aging studies on these materials, which can be applied to engineer and design their chemical stability, surface properties, and overall CDW characteristics.

36 MATERIALS SCIENCE↗

Magnetic properties of intercalated quasi-2D Fe 3-x GeTe 2 van der Waals magnet

Among several well-known transition metal-based compounds, cleavable van der Waals (vdW) Fe 3-x GeTe 2 (FGT) magnet is a strong candidate for use in two-dimensional (2D) magnetic devices due to its strong perpendicular magnetic anisotropy, sizeable Curie temperature (T C ~154 K), and versatile magnetic character that is retained in the low-dimensional limit. While the T C remains far too low for practical applications, there has been a successful push toward improving it via external driving forces such as pressure, irradiation, and doping. Here we present experimental evidence of a room temperature (RT) ferromagnetic phase induced by the electrochemical intercalation of common tetrabutylammonium cations (TBA+) into quasi-2D FGT. We obtained Curie temperatures as high as 350 K with chemical and physical stability of the intercalated compound. The temperature-dependent Raman measurements, in combination with vdW-corrected ab initio calculations, suggest that charge transfer (electron doping) upon intercalation could lead to the observation of RT ferromagnetism. This work demonstrates that molecular intercalation is a viable route in realizing high-temperature vdW magnets in an inexpensive and reliable manner and has the potential to be extended to bilayer and few-layer vdW magnets.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Substituent and Heteroatom Effects on π–π Interactions: Evidence That Parallel-Displaced π-Stacking is Not Driven by Quadrupolar Electrostatics

Stacking interactions are a recurring motif in supramolecular chemistry and biochemistry, where a persistent theme is a preference for parallel-displaced aromatic rings rather than face-to-face π-stacking. This is usually explained in terms of quadrupole–quadrupole interactions between the arene moieties but that interpretation is inconsistent with accurate calculations, which reveal that the quadrupolar picture is qualitatively wrong. At typical π-stacking distances, quadrupolar electrostatics may differ in sign from an exact calculation based on charge densities of the interacting arenes. We apply symmetry-adapted perturbation theory to dimers composed of substituted benzene and various aromatic heterocycles, which display a wide range of electrostatic interactions, and we investigate the interplay of Pauli repulsion, dispersion, and electrostatics as it pertains to parallel-displaced π-stacking. Profiles of energy components along cofacial slip-stacking coordinates support a prominent role for the “van der Waals model” (dispersion in competition with Pauli repulsion), even for polar monomers where electrostatic interactions are significant. While electrostatic interactions are necessary to explain the optimal face-to-face π-stacking distance and to account for the relative orientation of one polar arene with respect to another, we find no evidence to support continued invocation of quadrupolar electrostatics as a basis for π-stacking. Our results suggest that a driving force for offset-stacking exists even in the absence of electrostatic interactions. Consequently, tuning electrostatics via functionalization does not guarantee that slip-stacking can be avoided. This has implications for rational design of soft materials and other supramolecular architectures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Heteroepitaxial control of thickness, strain, and domain architecture in few-layer ferroelectric tin monochalcogenides

Thin-film epitaxy and epitaxial strain have been widely exploited to tune domain configurations, switching behavior, and ferroic properties in conventional three-dimensional ferroelectric thin films; however, its application to controlling the properties of two-dimensional (2D) ferroelectrics has remained largely unexplored. Here, using SnX (X = Se, S) as a model system, we demonstrate heteroepitaxial control of thickness, strain state, and domain architecture in few-layer ferroelectric SnX via growth on monolayer MoS2 van der Waals (vdW) templates. Compared with conventional growth, MoS2-templated heteroepitaxy promotes epitaxial alignment, yielding ultrathin SnSe films with improved crystalline quality, full areal coverage, and enlarged lateral dimensions. Strong interfacial epitaxial coupling induces pronounced in-plane strain and stabilizes a hierarchical ferroelastic domain architecture, in which long-range 90° stripe domains are further subdivided into nanoscale rotational variants, as revealed by scanning transmission electron microscopy and synchrotron X-ray microscopy. Piezoresponse force microscopy and second-harmonic polarimetry confirm robust in-plane polarization, while ferroelectricity in SnSe is established through polarization-electric field hysteresis and nonvolatile ferroelectric resistive switching with on/off ratios approaching 1000. A nonvolatile, switchable ferroelectric diode effect further evidences direct coupling between polarization and charge transport. Notably, ferroelectric switchability exhibits a strong thickness dependence and is preserved only below ∼10 layers. This vdW heteroepitaxial strategy is further extended to ferroelectric SnS. The seamless heteroepitaxial integration of 2D ferroelectrics with CMOS-compatible, wafer-scale MoS2 templates provides a general and scalable route for strain-enabled structural and ferroelectric engineering in emerging memory and low-power optoelectronic applications.

Wang, Yueyin↗