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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.

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At least 1,189 records · Page 66
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Fabrication and field emission properties of vertical, tapered GaN nanowires etched via phosphoric acid

The controlled fabrication of vertical, tapered, and high-aspect ratio GaN nanowires via a two-step top-down process consisting of an inductively coupled plasma reactive ion etch followed by a hot, 85% H 3 PO 4 crystallographic wet etch is explored. The vertical nanowires are oriented in the $[0001]$ direction and are bound by sidewalls comprising of $\{33\bar{6}2\}$ semipolar planes which are at a 12° angle from the [0001] axis. High temperature H3PO4 etching between 60 °C and 95 °C result in smooth semipolar faceting with no visible micro-faceting, whereas a 50 °C etch reveals a micro-faceted etch evolution. High-angle annular dark-field scanning transmission electron microscopy imaging confirms nanowire tip dimensions down to 8–12 nanometers. The activation energy associated with the etch process is 0.90 ± 0.09 eV, which is consistent with a reaction-rate limited dissolution process. The exposure of the $\{33\bar{6}2\}$ type planes is consistent with etching barrier index calculations. The field emission properties of the nanowires were investigated via a nanoprobe in a scanning electron microscope as well as by a vacuum field emission electron microscope. Finally, the measurements show a gap size dependent turn-on voltage, with a maximum current of 33 nA and turn-on field of 1.92 V nm -1 for a 50 nm gap, and uniform emission across the array.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2026

Understanding polaronic transport in complex oxides by combining precise synthesis and first-principles many-body theory

In complex oxides, charge carriers often couple strongly with lattice vibrations to form polarons–entangled electron–phonon quasiparticles whose transport properties remain difficult to characterize. Experimental access to intrinsic polaronic transport requires ultraclean samples, while theoretical description demands methods beyond low-order perturbation theory. Here, we show a predictive theory–experiment workflow to study polaron transport in complex oxides. Focusing on a prototypical polaronic oxide, anatase TiO 2 , we combine growth of high-quality oxygen-vacancy-doped films using hybrid molecular beam epitaxy with a first-principles electron–phonon diagrammatic Monte-Carlo (FEP-DMC) framework recently developed for accurate polaron predictions. Our films exhibit record-high electron mobility for anatase TiO 2 , in excellent agreement with FEP-DMC calculations conducted prior to experiment, which predict a room-temperature mobility of 45 ± 15 cm −2 V −1 s −1 and a mobility-temperature scaling of μ ∝ T −1.9 ± 0.077 . Microscopic analysis using scanning transmission electron microscopy and x-ray photoelectron spectroscopy reveals the role of oxygen vacancies in modulating transport at lower temperatures. FEP-DMC further provides quantitative insight into polaron formation energy, phonon cloud distribution, lattice distortion around the polaron, and the polaronic contribution to mobility. Together, these results provide a deeper microscopic understanding of large-polaron transport in a complex oxide and provide the blueprint to characterize other polaronic materials.

anatase TiO2↗
DOE OSTI2020

Thermodynamics of optical Bloch equations

Abstract Optical Bloch equations (OBE) describe the coherent exchange of energy between a quantum bit (qubit) and a quasi-resonant driving field in the presence of a thermal bath. Despite it being an ubiquitous process in quantum technologies, a sound thermodynamic analysis is still missing. We hereby provide such an analysis, by deriving the relevant framework from first principles. We start from a complete microscopic description of the qubit-bath system where definitions of heat, work and entropy production are unambiguous. We trace out the bath and coarse-grain the resulting expressions in time, using a methodology similar to the derivation of the dynamical master equation, to derive closed expressions for the first and second law in terms of system properties. Long coarse graining times yield the Floquet Master equation and its already known thermodynamic description. Short coarse-graining times yield instead the OBE and a novel thermodynamic framework which explicitly depends on quantum coherences in the qubit’s energy basis which produce quantum signatures in the heat and entropy production flows. This allows us to characterize a genuinely quantum non-equilibrium situation, where the coherences created by the driving field are continuously erased by the bath. Our findings can be readily extended to larger open quantum systems. They carry the seeds for future thermodynamic analyses of quantum gates and the design of quantum engines in the strong coherent driving regime.

Elouard, Cyril↗
DOE OSTI2021

Electric-field-tunable electronic nematic order in twisted double-bilayer graphene

Graphene-based moiré systems have attracted considerable interest in recent years as they display a remarkable variety of correlated phenomena. Besides insulating and superconducting phases in the vicinity of integer fillings of the moiré unit cell, there is growing evidence for electronic nematic order both in twisted bilayer graphene and twisted double-bilayer graphene (tDBG), as signaled by the spontaneous breaking of the threefold rotational symmetry of the moiré superlattices. Here, we combine symmetry-based analysis with a microscopic continuum model to investigate the structure of the nematic phase of tDBG and its experimental manifestations. First, we perform a detailed comparison between the theoretically calculated local density of states and recent scanning tunneling microscopy data (arXiv:2009.11645) to resolve the internal structure of the nematic order parameter in terms of the layer, sublattice, spin, and valley degrees of freedom. We find strong evidence that the dominant contribution to the nematic order parameter comes from states at the moiré scale rather than at the microscopic scale of the individual graphene layers, which demonstrates the key role played by the moiré degrees of freedom and confirms the correlated nature of the nematic phase in tDBG. Secondly, our analysis reveals an unprecedented tunability of the orientation of the nematic director in tDBG by an externally applied electric field, allowing the director to rotate away from high-symmetry crystalline directions. Here, we compute the expected fingerprints of this rotation in both STM and transport experiments, providing feasible ways to probe it. Rooted in the strong sensitivity of the flat bands of tDBG to the displacement field, this effect opens an interesting route to the electrostatic control of electronic nematicity in moiré systems.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Assessing the quality of large-area monolayer graphene grown on liquid copper for size-selective ionic/molecular membrane separations

Monolayer graphene growth on liquid copper (Cu) has attracted attention due to advantages of a flat/smooth catalytic growth surface, high synthesis temperature (>1080 °C) as well as the possibility of forming graphene domains that are mobile on the liquid Cu with potential to minimize grain boundary defects and self-assemble into a continuous monolayer film. However, the quality of monolayer graphene grown on liquid copper and its suitability for size-selective ionic/molecular membrane separations has not been evaluated/studied. Here, we probe the quality of monolayer graphene grown on liquid Cu (via a metallurgical process, HSMG ® ) using Scanning Electron Microscope (SEM), High-resolution transmission electron microscope (HR-TEM), Raman spectroscopy and report on a facile approach to assess intrinsic sub-nanometer to nanometer-scale defects over centimeter-scale areas. We demonstrate high transfer yields of monolayer graphene (>93% coverage) from the growth substrate to polyimide track etched membrane (PITEM, pore diameter ~200 nm) supports to form centimeter-scale atomically thin membranes. Next, we use pressure-driven transport of ethanol to probe defects > 60 nm and diffusion-driven transport of analytes (KCl ~0.66 nm, L-Tryptophan ~0.7–0.9 nm, Vitamin B12 ~1–1.5 nm and Lysozyme ~3.8–4 nm) to probe nanoscale and sub-nanometer scale defects. Diffusive transport confirms the presence of intrinsic sub-nanometer to nanometer scale defects in monolayer graphene grown on liquid Cu are no less than that in high-quality graphene synthesized via chemical vapor deposition (CVD) on solid Cu. Our work not only benchmarks quality of graphene grown on liquid copper for membrane applications but also provides fundamental insights into the origin of intrinsic defects in large-area graphene synthesized via bottom-up processes for membrane applications.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Probe microscopy is all you need *

We pose that microscopy offers an ideal real-world experimental environment for the development and deployment of active Bayesian and reinforcement learning methods. Indeed, the tremendous progress achieved by machine learning (ML) and artificial intelligence over the last decade has been largely achieved via the utilization of static data sets, from the paradigmatic MNIST to the bespoke corpora of text and image data used to train large models such as GPT3, DALL·E and others. However, it is now recognized that continuous, minute improvements to state-of-the-art do not necessarily translate to advances in real-world applications. We argue that a promising pathway for the development of ML methods is via the route of domain-specific deployable algorithms in areas such as electron and scanning probe microscopy and chemical imaging. This will benefit both fundamental physical studies and serve as a test bed for more complex autonomous systems such as robotics and manufacturing. Favorable environment characteristics of scanning and electron microscopy include low risk, extensive availability of domain-specific priors and rewards, relatively small effects of exogenous variables, and often the presence of both upstream first principles as well as downstream learnable physical models for both statics and dynamics. Recent developments in programmable interfaces, edge computing, and access to application programming interfaces (APIs) facilitating microscope control, all render the deployment of ML codes on operational microscopes straightforward. We discuss these considerations and hope that these arguments will lead to create novel set of development targets for the ML community by accelerating both real world ML applications and scientific progress.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Automating STEM Aberration Correction via Bayesian Optimization

Multipole aberration correctors have given scanning transmission electron microscopes (STEM) the ability to produce high-quality, atomic-resolution images, enabling STEM to be a key tool in material sciences for characterizing the structure and composition of materials. However, the process of correcting these aberrations typically requires human input and is accomplished using scanned STEM or Ronchigram images at different focii and beam tilts. In this work, we demonstrate an automated on-sample aberration correction system using Bayesian Optimization. We have developed a Python-based server able to communicate with the CEOS DCOR aberration corrector and the Thermo Fischer microscope scripting interface. This server allows us to change aberrations, acquire images and perform basic image analysis.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Evaluating Stage Motion for Automated Electron Microscopy

Abstract Precise control is an essential and elusive quality of emerging self-driving transmission electron microscopes (TEMs). It is widely understood these instruments must be capable of performing rapid, high-volume, and arbitrary movements for practical self-driving operation. However, stage movements are difficult to automate at scale, owing to mechanical instability, hysteresis, and thermal drift. Such difficulties pose major barriers to artificial intelligence-directed microscope designs that require repeatable, precise movements. To guide design of emerging instruments, it is necessary to understand the behavior of existing mechanisms to identify rate limiting steps for full autonomy. Here, we describe a general framework to evaluate stage motion in any TEM. We define metrics to evaluate stage degrees of freedom, propose solutions to improve performance, and comment on fundamental limits to automated experimentation using present hardware.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Human-in-the-Loop: The Future of Machine Learning in Automated Electron Microscopy

Machine learning (ML) methods are progressively gaining acceptance in the electron microscopy community for de-noising, semantic segmentation, and dimensionality reduction of data post-acquisition. The introduction of the application programming interfaces (APIs) by major instrument manufacturers now allows the deployment of ML workflows in microscopes, not only for data analytics but also for real-time decision-making and feedback for microscope operation. However, the number of use cases for real-time ML remains remarkably small. Furthermore, we discuss some considerations in designing ML-based active experiments and pose that the likely strategy for the next several years will be human-in-the-loop automated experiments (hAE). In this paradigm, the ML learning agent directly controls beam position and image and spectroscopy acquisition functions, and a human operator monitors experiment progression in real and feature space of the system and tunes the policies of the ML agent to steer the experiment toward specific objectives.

47 OTHER INSTRUMENTATION↗
DOE OSTI2025

Stomata in-sight: Integrating live confocal microscopy with leaf gas exchange and environmental control

Stomatal anatomy (aperture area, length, and width) influences leaf-level physiology traits including conductance to water vapor. Stomatal anatomy can be visualized in situ by microscopy, but the difficulty of regulating the atmospheric environment of a microscope stage means that the conditions under which imaging is done are rarely physiologically relevant. Alternatively, leaf gas exchange instruments that measure gas fluxes reflect stomatal anatomical characteristics in aggregate, but the relative strengths of anatomical traits to control water use (e.g. size vs density) cannot be firmly established. To reconcile the microscopic stomatal characteristics with leaf-level gas exchange, we describe a tool that combines laser scanning confocal microscopy, gas exchange instruments, and machine-learning image analysis to simultaneously observe anatomical characteristics of many (>40) stomata alongside leaf-level traits like photosynthesis, transpiration, and stomatal conductance. We demonstrate how the tool has the resolution capable of quantifying aperture sizes and variability in maize (Zea mays) leaves under 5 steady-state light/pCO 2 treatments while tightly controlling other environmental variables like relative humidity and temperature. A model used to calculate stomatal conductance from measured apertures and stomatal density accurately matched stomatal conductance measured by gas exchange. This technical advancement will provide insight on how stomatal anatomy and function trade off to influence stomatal conductance and leaf-level water use efficiency.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Time-Dependent Density Functional Theory Description of 238 U⁡(n,f), 240,242 Pu⁢(n,f), and 237 Np(n,f) Reactions

In nuclei with an odd nucleon number the nonvanishing spin number density is the source of a pseudomagnetic field, which favors the splitting of the nucleon Cooper pairs. Such a pseudomagnetic field is generated always in the dynamics of any nucleus, but its effects on Cooper pairs are significantly enhanced in the dynamic evolution of nuclei with an odd number of nucleons. We present for the first time a microscopic study of the induced fission of the odd neutron compound nuclei 239 U, 241,243 Pu, and the odd proton, odd neutron compound nucleus 238 Np, performed within the time-dependent density functional theory extended to superfluid fermion systems, without any simplifying assumptions, with controlled numerical approximations, and for a very large number of initial conditions. Because of the presence of the unpaired odd nucleon(s), the time-reversal symmetry of the fission compound nucleus is spontaneously broken, an aspect routinely neglected in the most advanced microscopic approaches of the past. The emerging fission fragment properties are quite similar to the properties of fission fragments of neighboring even-even nuclei. The time from saddle-to-scission is often significantly longer in odd-odd or odd-mass nuclei than for even-even nuclei, since systems with unpaired nucleons are easier to excite and the potential energy surfaces of these nuclei have more structure, often resembling a very complicated obstacle course, rather than a more direct evolution of the nuclear shape from the top of the outer fission barrier to the scission configuration. The Pauli blocking approximation, often invoked in the literature, expected to inhibit the fission of nuclei with unpaired nucleons, is surprisingly strongly violated during the fission dynamics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Electronic Structure of Compressively Strained Bilayer Nickelate Thin Film

The discovery of superconductivity in bulk bilayer nickelates under high pressure, and its subsequent stabilization in compressively strained thin films at ambient pressure, has established a new platform for exploring high-𝑇 c superconductivity beyond the cuprates. Central to this development is the prominent role of the 3⁢𝑑$^2_𝑧$ orbital in shaping the low-energy electronic structure, imposing constraints on microscopic theories and fueling debate over the superconducting mechanism. Here we report a systematic in situ angle-resolved photoemission spectroscopy study of compressively strained bilayer nickelate thin films spanning Ca doping, oxygen stoichiometry and film thickness. Despite variations in oxygen-vacancy disorder and surface termination, the electronic structure remains robust and exhibits a systematic strain-driven evolution consistent with an intermediate-correlation regime. In particular, we demonstrate a Ca-doping-induced electronic structure evolution that is consistent with Fermi-level crossing of the 𝛾 band and is decoupled from the presence of superconductivity, suggesting that, while important for the 𝛾 band to be near the Fermi level, the debated 𝛾 crossing and the resulting Fermi pocket may not be a prerequisite for superconductivity. Together, our results establish key spectroscopic constraints on the minimal fermiology and correlation strength relevant to superconductivity in bilayer nickelates, providing an experimental foundation for microscopic theories of their pairing mechanism.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Orbital-spin locking and its optical signatures in altermagnets

Altermagnets, magnetic materials with zero magnetization and spin-split band structure, have gained tremendous attention recently for their rich physics and potential applications. Here, we report on a microscopic tight-binding model that unveils a unique coupling between orbitals and spins in d-wave altermagnets, which gives rise to momentum-dependent and spin-selective optical absorption. This coupling promotes the controlled optical excitation of up or down spins depending on the polarization direction of linearly polarized light. Such an effect originates from the coupling of orbitals to the sublattice degree of freedom through the crystal field, which is then coupled to spins through the antiferromagnetic interaction. Our crystal field analysis, which is general to any type of altermagnet, helps understand the onset of altermagnetism from a microscopic point of view, and we use our results to propose clear magneto-optical signatures of our predictions. Our findings shine light on the interplay between orbitals and spins in altermagnets, thus paving the way towards novel orbitronic and optospintronic devices.

Vila, Marc↗
DOE OSTI2025

Production of neutron-rich heavy nuclei in deep-inelastic 208 Pb + 208 Pb collisions within the stochastic mean-field theory

In deep-inelastic collisions of heavy nuclei, reaction products with a wide range of mass and charge are produced. Such collisions been considered as a possible way to produce superheavy nuclei, as an alternative to fusion reactions. To provide reliable theoretical predictions, it is desired to develop microscopic approaches that correctly and accurately describe nucleon transfer processes in dissipative collisions of heavy nuclei. The purpose of the present work is (1) to investigate the mechanism of nucleon transfers in dissipative collisions of two heavy nuclei, and (2) to explore possible pathways to produce neutron-rich heavy nuclei, through detailed theoretical analyses of fluctuations and correlations in nucleon transfers in 208 Pb + 208 Pb reactions. Three-dimensional time-dependent Hartree-Fock (TDHF) calculations are performed for the collisions of 208 Pb + 208 Pb at 𝐸 c.m. = 832, 936, and 1040 MeV, using the Skyrme SLy4d energy density functional. To calculate fluctuations and correlations in nucleon transfers, we employ the stochastic mean-field (SMF) theory, and the results are compared with another theoretical framework currently available, the time-dependent random phase approximation (TDRPA). Primary and secondary production cross sections are calculated with the SMF theory combined with a statistical model, GEMINI ++ . Using information of nucleon flow across a neck of colliding nuclei in TDHF calculations, we solve quantal diffusion equations for fluctuations and correlations in nucleon transfers based on the SMF theory. From the SMF calculations, we obtain the time evolution of diffusion coefficients as well as fluctuations and correlations in nucleon transfers for a range of initial orbital angular momenta. We compare the results of the SMF calculations with those of TDRPA, showing that TDRPA tends to predict substantially larger fluctuations and correlations in strongly damped collisions of heavy nuclei, which exhibit complex initial angular momentum dependence, while the SMF results provide almost constant (stable) values. Using the obtained fluctuations and correlations, we calculate primary and secondary production cross sections for the 208 Pb + 208 Pb collisions. From the results, we find that both lighter and heavier reaction products as compared to 208 Pb are produced for a wide region in the 𝑁−𝑍 plane as primary products, thanks to the quantal diffusion mechanism in the dissipative collisions. However, we show that cross sections for production of heavy nuclei with 𝑍 ≳ 90 or 𝑁 ≳ 135 are washed out due to secondary particle evaporation and/or fission processes. On the other hand, we find that there remain sizable cross sections for production of neutron-rich nuclei along 𝑁 = 126 with 𝑍< 82, even after secondary disintegration processes. We demonstrate that the secondary production cross sections depend weakly on incident energies, but lower (higher) energy is slightly preferred for production of nuclei with smaller (larger) atomic numbers as compared to 𝑍 = 82. Here, based on the microscopic SMF calculations, it has been shown that deep-inelastic collisions of heavy nuclei, such as 208 Pb + 208 Pb examined in this study, can be a promising means to produce neutron-rich heavy nuclei along 𝑁=126. Discrepancies between the SMF and TDRPA approaches are left unsolved for future investigations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Quantum Langevin theory for two coupled phase-conjugated electromagnetic waves

We provide a general macroscopic phenomenological formula of quantum Langevin equations for two coupled phase-conjugated electromagnetic fields with linear loss (gain) and complex nonlinear coupling coefficient. The macroscopic phenomenological formula is obtained from the coupling matrix to preserve the field commutation relations and correlations, which does not require knowing the microscopic details of light-matter interaction and internal atomic structures. To validate this phenomenological formula, we take spontaneous four-wave mixing in a double-Λ four-level atomic system as an example to numerically confirm that our macroscopic phenomenological result is consistent with that obtained from the microscopic Heisenberg-Langevin theory. We find that a complex-valued nonlinear coupling coefficient can lead to noises even without linear gain or loss. Lastly, we apply the quantum Langevin equations to study the effects of linear gain and loss, complex phase mismatching, as well as complex nonlinear coupling coefficient in entangled photon pair (biphoton) generation, particularly to their temporal quantum correlations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Polarization Selectivity of Aloof-Beam Electron Energy-Loss Spectroscopy in One-Dimensional ZnO Nanorods

Orientation-dependent electronic properties of wurtzite zinc oxide nanorods are characterized by aloof-beam electron energy-loss spectroscopy (EELS) carried out in a scanning transmission electron microscope (STEM). The two key crystal orientation differentiating transitions specific to the in-plane (13.0 eV) and out-of-plane (11.2 eV) directions with respect to the wurtzite structure are examined by first-principles density-functional theory calculations. We note some degree of orientation dependence at the onset of direct band gap transition near 3.4 eV. We demonstrate that good polarization selectivity can be achieved by placing the electron probe at different locations around the specimen with increasing impact parameter while keeping the beam-specimen orientation fixed. The observed results are qualitatively elucidated in terms of the perpendicular electric fields generated by the fast electron (60 kV) used in the microscope. The fact that good polarization selectivity can be achieved by aloof-beam EELS without the requirement of sample reorientation is an attractive aspect from the characterization method point of view in the STEM-EELS community.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

High-Precision Mapping of Diamond Crystal Strain Using Quantum Interferometry

Crystal-strain variation imposes significant limitations on many quantum sensing and information applications for solid-state defect qubits in diamond. Thus, the precision measurement and control of diamond crystal strain is a key challenge. Here, we report diamond strain measurements with a unique set of capabilities, including micron-scale spatial resolution, a millimeter-scale field of view, and a 2-order-of-magnitude improvement in volume-normalized sensitivity over previous work, reaching 5(2)×10 -8 /√Hzμm -3 (with spin-strain coupling coefficients representing the dominant systematic uncertainty). We use strain-sensitive spin-state interferometry on ensembles of nitrogen-vacancy (N-V) color centers in single-crystal bulk diamond with low strain gradients. This quantum interferometry technique provides insensitivity to magnetic-field inhomogeneity from the electronic and nuclear spin bath, thereby enabling long N-V–ensemble electronic spin dephasing times and enhanced strain sensitivity, as well as broadening the potential applications of the technique beyond isotopically enriched or high-purity diamond. We demonstrate the strain-sensitive measurement protocol first on a confocal scanning laser microscope, providing quantitative measurement of sensitivity as well as three-dimensional strain mapping; and second on a wide-field-imaging quantum diamond microscope. Our strain-microscopy technique enables fast, sensitive characterization for diamond material engineering and nanofabrication; as well as diamond-based sensing of strains applied externally, as in diamond anvil cells or embedded diamond stress sensors, or internally, as by crystal damage due to particle-induced nuclear recoils.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Lattice chain theories for dynamics of acoustic flexural phonons in nonpolar nanomaterials

Knowledge of lattice dynamics of acoustic flexural phonons is critically important in understanding the mechanical, electrical, and thermal properties of nanomaterials. However, the general nature of acoustic flexural phonons for the span of possible nanomaterials and the dependence of these on microscopic material properties remain unclear. Therefore, we develop general lattice chain theories to understand acoustic flexural vibrations in covalent and van der Waals lattices. Furthermore, the analytic theories suggest that the flexure branch has quadratic dispersion for low dimensional lattices in the long-wavelength limit, quite different from linear branches in bulk van der Waals bonded lattices like graphite. Surprisingly, interlayer van der Waals interactions in multilayer lattices do not determine the behavior of the flexural dispersion. The bonds of covalent interactions in multilayer and buckled monolayer lattices play different roles in determining the flexural dispersion with those in flat monolayer lattices, e.g., graphene. Further, based on the correspondence between microscopic and continuum dynamics, we provide a universal and effective approach to characterize the intrinsic bending rigidity of low dimensional nanomaterials using dispersion data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗