Phonon Spectroscopy at Atomic Resolution

Phonon mode at interface and its impact on interfacial thermal transport

Due to the minimization and integration of micro/nano-devices, the high density of interfaces becomes a significant challenge in various applications. Phonon modes at interface resulting from the mismatch between inhomogeneous functional counterparts are crucial for interfacial thermal transport and overall thermal management of micro/nano-devices, making it a topic of great research interest recently. Here, we comprehensively review the recent advances on the theoretical and experimental investigations of interfacial phonon mode and its impact on interfacial thermal transport. Firstly, we summarize the recent progresses of the theoretical and experimental characterization of interfacial phonon modes at various interfaces, along with the overview of the development of diverse methodologies. Then, the impact of interfacial phonon modes on interfacial thermal transport process are discussed from the normal modal decomposition and inelastic scattering mechanisms. Meanwhile, we examine various factors influencing the interfacial phonon modes and interfacial thermal transport, including temperature, interface roughness, interfacial mass gradient, interfacial disorder, and so on. Finally, an outlook is provided for future studies. This review provides a fundamental understanding of interfacial phonon modes and their impact on interfacial thermal transport, which would be beneficial for the exploration and optimization of thermal management in various micro/nano-devices with high density interfaces.

Dynamic STEM-EELS for single-atom and defect measurement during electron beam transformations

This study introduces the integration of dynamic computer vision-enabled imaging with electron energy loss spectroscopy (EELS) in scanning transmission electron microscopy (STEM). This approach involves real-time discovery and analysis of atomic structures as they form, allowing us to observe the evolution of material properties at the atomic level, capturing transient states traditional techniques often miss. Rapid object detection and action system enhances the efficiency and accuracy of STEM-EELS by autonomously identifying and targeting only areas of interest. This machine learning (ML)-based approach differs from classical ML in that it must be executed on the fly, not using static data. We apply this technology to V-doped MoS2, uncovering insights into defect formation and evolution under electron beam exposure. This approach opens uncharted avenues for exploring and characterizing materials in dynamic states, offering a pathway to increase our understanding of dynamic phenomena in materials under thermal, chemical, and beam stimuli.

Toward Optimum Coupling between Free Electrons and Confined Optical Modes

Free electrons are excellent tools to probe and manipulate nanoscale optical fields with emerging applications in ultrafast spectromicroscopy and quantum metrology. However, advances in this field are hindered by the small probability associated with the excitation of single optical modes by individual free electrons. Here, we theoretically investigate the scaling properties of the electron-driven excitation probability for a wide variety of optical modes including plasmons in metallic nanostructures and Mie resonances in dielectric cavities, spanning a broad spectral range that extends from the ultraviolet to the infrared region. The highest probabilities for the direct generation of three-dimensionally confined modes are observed at low electron and mode energies in small structures, with order-unity (∼100%) coupling demanding the use of <100 eV electrons interacting with eV polaritons confined down to tens of nanometers in space. Electronic transitions in artificial atoms also emerge as practical systems to realize strong coupling to few-eV free electrons. In contrast, conventional dielectric cavities reach a maximum probability in the few-percent range. In addition, we show that waveguide modes can be generated with higher-than-unity efficiency by phase-matched interaction with grazing electrons, suggesting a practical method to create multiple excitations of a localized optical mode by an individual electron through funneling the so-generated propagating photons into a confining cavity─an alternative approach to direct electron-cavity interaction. Our work provides a roadmap to optimize electron-photon coupling with potential applications in electron spectromicroscopy as well as nonlinear and quantum optics at the nanoscale.

Current opinion on the prospect of mapping electronic orbitals in the transmission electron microscope: State of the art, challenges and perspectives

The concept of electronic orbitals has enabled the understanding of a wide range of physical and chemical properties of solids through the definition of, for example, chemical bonding between atoms. In the transmission electron microscope, which is one of the most used and powerful analytical tools for high-spatial-resolution analysis of solids, the accessible quantity is the local distribution of electronic states. However, the interpretation of electronic state maps at atomic resolution in terms of electronic orbitals is far from obvious, not always possible, and often remains a major hurdle preventing a better understanding of the properties of the system of interest. In this review, the current state of the art of the experimental aspects for electronic state mapping and its interpretation as electronic orbitals is presented, considering approaches that rely on elastic and inelastic scattering, in real and reciprocal spaces. This work goes beyond resolving spectral variations between adjacent atomic columns, as it aims at providing deeper information about, for example, the spatial or momentum distributions of the states involved. The advantages and disadvantages of existing experimental approaches are discussed, while the challenges to overcome and future perspectives are explored in an effort to establish the current state of knowledge in this field. The aims of this review are also to foster the interest of the scientific community and to trigger a global effort to further enhance the current analytical capabilities of transmission electron microscopy for chemical bonding and electronic structure analysis.

Atomic-scale observation of localized phonons at FeSe/SrTiO3 interface

In single unit-cell FeSe grown on SrTiO3, the superconductivity transition temperature features a significant enhancement. Local phonon modes at the interface associated with electron-phonon coupling may play an important role in the interface-induced enhancement. However, such phonon modes have eluded direct experimental observations. The complicated atomic structure of the interface brings challenges to obtain the accurate structure-phonon relation knowledge. Here, we achieve direct characterizations of atomic structure and phonon modes at the FeSe/SrTiO3 interface with atomically resolved imaging and electron energy loss spectroscopy in an electron microscope. We find several phonon modes highly localized (~1.3 nm) at the unique double layer Ti-O terminated interface, one of which (~ 83 meV) engages in strong interactions with the electrons in FeSe based on ab initio calculations. This finding of the localized interfacial phonon associated with strong electron-phonon coupling provides new insights into understanding the origin of superconductivity enhancement at the FeSe/SrTiO3 interface.

Nanoscale Localized Phonons at Al2O3 Grain Boundaries

Nanoscale defects like grain boundaries (GBs) would introduce local phonon modes and affect the bulk materials' thermal, electrical, optical, and mechanical properties. It is highly desirable to correlate the phonon modes and atomic arrangements for individual defects to precisely understand the structure-property relation. Here we investigated the localized phonon modes of Al2O3 GBs by combination of the vibrational electron energy loss spectroscopy (EELS) in scanning transmission electron microscope and density functional perturbation theory (DFPT). The differences between GB and bulk obtained from the vibrational EELS show that the GB exhibited more active vibration at the energy range of <50 meV and >80 meV, and further DFPT results proved the wide distribution of bond lengths at GB are the main factor for the emergence of local phonon modes. This research provides insights into the phonon-defect relation and would be of importance in the design and application of polycrystalline materials.

Accelerating Quantum Materials Development with Advances in Transmission Electron Microscopy

Quantum materials are driving a technology revolution in sensing, communication, and computing, while simultaneously testing many core theories of the past century. Materials such as topological insulators, complex oxides, superconductors, quantum dots, color center-hosting semiconductors, and other types of strongly correlated materials can exhibit exotic properties such as edge conductivity, multiferroicity, magnetoresistance, superconductivity, single photon emission, and optical-spin locking. These emergent properties arise and depend strongly on the material's detailed atomic-scale structure, including atomic defects, dopants, and lattice stacking. In this review, we describe how progress in the field of electron microscopy (EM), including in situ and in operando EM, can accelerate advances in quantum materials and quantum excitations. We begin by describing fundamental EM principles and operation modes. We then discuss various EM methods such as (i) EM spectroscopies, including electron energy loss spectroscopy (EELS), cathodoluminescence (CL), and electron energy gain spectroscopy (EEGS); (ii) four-dimensional scanning transmission electron microscopy (4D-STEM); (iii) dynamic and ultrafast EM (UEM); (iv) complementary ultrafast spectroscopies (UED, XFEL); and (v) atomic electron tomography (AET). We describe how these methods could inform structure-function relations in quantum materials down to the picometer scale and femtosecond time resolution, and how they enable precision positioning of atomic defects and high-resolution manipulation of quantum materials. For each method, we also describe existing limitations to solve open quantum mechanical questions, and how they might be addressed to accelerate progress. Among numerous notable results, our review highlights how EM is enabling identification of the 3D structure of quantum defects; measuring reversible and metastable dynamics of quantum excitations; mapping exciton states and single photon emission; measuring nanoscale thermal transport and coupled excitation dynamics; and measuring the internal electric field and charge density distribution of quantum heterointerfaces- all at the quantum materials' intrinsic atomic and near atomic-length scale. We conclude by describing open challenges for the future, including achieving stable sample holders for ultralow temperature (below 10K) atomic-scale spatial resolution, stable spectrometers that enable meV energy resolution, and high-resolution, dynamic mapping of magnetic and spin fields. With atomic manipulation and ultrafast characterization enabled by EM, quantum materials will be poised to integrate into many of the sustainable and energy-efficient technologies needed for the 21st century.

Lossless Monochromator in an Ultrafast Electron Microscope Using Near-Field THz Radiation

The ability to form monoenergetic electron beams is vital for high-resolution electron spectroscopy and imaging. Such capabilities are commonly achieved using an electron monochromator, which energy filters a dispersed electron beam, thus reducing the electron flux to yield down to meV energy resolution. This reduction in flux hinders the use of monochromators in many applications, such as ultrafast transmission electron microscopes (UTEMs). Here, we develop and demonstrate a mechanism for electron energy monochromation that does not reduce the flux-a lossless monochromator. The mechanism is based on the interaction of free-electron pulses with single-cycle THz near fields, created by nonlinear conversion of an optical laser pulse near the electron beam path inside a UTEM. Our experiment reduces the electron energy spread by a factor of up to 2.9 without compromising the beam flux. Moreover, as the electron-THz interaction takes place over an extended region of many tens of microns in free space, the realized technique is highly robust-granting uniform monochromation over a wide area, larger than the electron beam diameter. We further demonstrate the wide tunability of our method by monochromating the electron beam at multiple primary electron energies from 60 to 200 keV, studying the effect of various electron and THz parameters on its performance. Our findings have direct applications in the fast-growing field of ultrafast electron microscopy, allowing time- and energy-resolved studies of exciton physics, phononic vibrational resonances, charge transport effects, and optical excitations in the mid IR to the far IR.

Spectroscopic Observation and Modeling of Photonic Modes in CeO2 Nanostructures

Photonic modes in dielectric nanostructures, e.g., wide gap semiconductor like CeO2 (ceria), have the potential for various applications such as information transmission and sensing technology. To fully understand the properties of such phenomenon at the nanoscale, electron energy-loss spectroscopy (EELS) in a scanning transmission electron microscope was employed to detect and explore photonic modes in well-defined ceria nanocubes. To facilitate the interpretation of the observations, EELS simulations were performed with finite-element methods. The simulations allow the electric and magnetic field distributions associated with different modes to be determined. A simple analytical eigenfunction model was also used to estimate the energy of the photonic modes. In addition, by comparing various spectra taken at different location relative to the cube, the effect of the surrounding environment on the modes could be sensed. This work gives a high-resolution description of the photonic modes' properties in nanostructures, while demonstrating the advantage of EELS in characterizing optical phenomena locally.

In Situ and Emerging Transmission Electron Microscopy for Catalysis Research

Catalysts are the primary facilitator in many dynamic processes. Therefore, a thorough understanding of these processes has vast implications for a myriad of energy systems. The scanning/transmission electron microscope (S/TEM) is a powerful tool not only for atomic-scale characterization but also in situ catalytic experimentation. Techniques such as liquid and gas phase electron microscopy allow the observation of catalysts in an environment conducive to catalytic reactions. Correlated algorithms can greatly improve microscopy data processing and expand multidimensional data handling. Furthermore, new techniques including 4D-STEM, atomic electron tomography, cryogenic electron microscopy, and monochromated electron energy loss spectroscopy (EELS) push the boundaries of our comprehension of catalyst behavior. In this review, we discuss the existing and emergent techniques for observing catalysts using S/TEM. Challenges and opportunities highlighted aim to inspire and accelerate the use of electron microscopy to further investigate the complex interplay of catalytic systems.

Single-atom vibrational spectroscopy with chemical-bonding sensitivity

Correlation of lattice vibrational properties with local atomic configurations in materials is essential for elucidating functionalities that involve phonon transport in solids. Recent developments in vibrational spectroscopy in a scanning transmission electron microscope have enabled direct measurements of local phonon modes at defects and interfaces by combining high spatial and energy resolution. However, pushing the ultimate limit of vibrational spectroscopy in a scanning transmission electron microscope to reveal the impact of chemical bonding on local phonon modes requires extreme sensitivity of the experiment at the chemical-bond level. Here we demonstrate that, with improved instrument stability and sensitivity, the specific vibrational signals of the same substitutional impurity and the neighbouring carbon atoms in monolayer graphene with different chemical-bonding configurations are clearly resolved, complementary with density functional theory calculations. The present work opens the door to the direct observation of local phonon modes with chemical-bonding sensitivity, and provides more insights into the defect-induced physics in graphene.

Phonon transition across an isotopic interface

Isotopic mixtures result in distinct properties of materials such as thermal conductivity and nuclear process. However, the knowledge of isotopic interface remains largely unexplored mainly due to the challenges in atomic-scale isotopic identification. Here, using electron energy-loss spectroscopy in a scanning transmission electron microscope, we reveal momentum-transfer-dependent phonon behavior at the h-¹⁰BN/h-¹¹BN isotope heterostructure with sub-unit-cell resolution. We find the phonons' energy changes gradually across the interface, featuring a wide transition regime. Phonons near the Brillouin zone center have a transition regime of ~3.34 nm, whereas phonons at the Brillouin zone boundary have a transition regime of ~1.66 nm. We propose that the isotope-induced charge effect at the interface accounts for the distinct delocalization behavior. Moreover, the variation of phonon energy between atom layers near the interface depends on both of momentum transfer and mass change. This study provides new insights into the isotopic effects in natural materials.

Imaging of Antiferroelectric Dark Modes in an Inverted Plasmonic Lattice

Plasmonic lattice nanostructures are of technological interest because of their capacity to manipulate light below the diffraction limit. Here, we present a detailed study of dark and bright modes in the visible and near-infrared energy regime of an inverted plasmonic honeycomb lattice by a combination of Au⁺ focused ion beam lithography with nanometric resolution, optical and electron spectroscopy, and finite-difference time-domain simulations. The lattice consists of slits carved in a gold thin film, exhibiting hotspots and a set of bright and dark modes. We proposed that some of the dark modes detected by electron energy-loss spectroscopy are caused by antiferroelectric arrangements of the slit polarizations with two times the size of the hexagonal unit cell. The plasmonic resonances take place within the 0.5-2 eV energy range, indicating that they could be suitable for a synergistic coupling with excitons in two-dimensional transition metal dichalcogenides materials or for designing nanoscale sensing platforms based on near-field enhancement over a metallic surface.

Atomic-scale origin of the low grain-boundary resistance in perovskite solid electrolyte Li0.375Sr0.4375Ta0.75Zr0.25O3

Oxide solid electrolytes (OSEs) have the potential to achieve improved safety and energy density for lithium-ion batteries, but their high grain-boundary (GB) resistance generally is a bottleneck. In the well-studied perovskite oxide solid electrolyte, Li_3xLa_2/3-xTiO₃ (LLTO), the ionic conductivity of grain boundaries is about three orders of magnitude lower than that of the bulk. In contrast, the related Li_0.375Sr_0.4375Ta_0.75Zr_0.25O₃ (LSTZ0.75) perovskite exhibits low grain boundary resistance for reasons yet unknown. Here, we use aberration-corrected scanning transmission electron microscopy and spectroscopy, along with an active learning moment tensor potential, to reveal the atomic scale structure and composition of LSTZ0.75 grain boundaries. Vibrational electron energy loss spectroscopy is applied for the first time to reveal atomically resolved vibrations at grain boundaries of LSTZ0.75 and to characterize the otherwise unmeasurable Li distribution therein. We find that Li depletion, which is a major reason for the low grain boundary ionic conductivity of LLTO, is absent for the grain boundaries of LSTZ0.75. Instead, the low grain boundary resistivity of LSTZ0.75 is attributed to the formation of a nanoscale defective cubic perovskite interfacial structure that contained abundant vacancies. Our study provides new insights into the atomic scale mechanisms of low grain boundary resistivity.

Probing the Boundary between Classical and Quantum Mechanics by Analyzing the Energy Dependence of Single-Electron Scattering Events at the Nanoscale

The relation between the energy-dependent particle and wave descriptions of electron-matter interactions on the nanoscale was analyzed by measuring the delocalization of an evanescent field from energy-filtered amplitude images of sample/vacuum interfaces with a special aberration-corrected electron microscope. The spatial field extension coincided with the energy-dependent self-coherence length of propagating wave packets that obeyed the time-dependent Schrödinger equation, and underwent a Goos-Hänchen shift. The findings support the view that wave packets are created by self-interferences during coherent-inelastic Coulomb interactions with a decoherence phase close to Δφ = 0.5 rad. Due to a strictly reciprocal dependence on energy, the wave packets shrink below atomic dimensions for electron energy losses beyond 1000 eV, and thus appear particle-like. Consequently, our observations inevitably include pulse-like wave propagations that stimulate structural dynamics in nanomaterials at any electron energy loss, which can be exploited to unravel time-dependent structure-function relationships on the nanoscale.

Electron Microscopy Probing Electron-Photon Interactions in SiC Nanowires with Ultrawide Energy and Momentum Match

Light-matter interactions are commonly probed by optical spectroscopy, which, however, has some fundamental limitations such as diffraction-limited spatial resolution, tiny momentum transfer, and noncontinuous excitation/detection. In this work, through the use of scanning transmission electron microscopy-electron energy loss spectroscopy (STEM-EELS) with ultrawide energy and momentum match and subnanometer spatial resolution, the longitudinal Fabry-Perot (FP) resonating modes and the transverse whispering-gallery modes (WGMs) in individual SiC nanowires are simultaneously excited and detected, which span from near-infrared (∼1.2 μm) to ultraviolet (∼0.2 μm) spectral regime, and the momentum transfer can range up to 10⁸ cm^-1. The size effects on the resonant spectra of nanowires are also revealed. This work provides an alternative technique to optical resonating spectroscopy and light-matter interactions in dielectric nanostructures, which is promising for modulating free electrons via photonic structures.

Sub-nanometer mapping of strain-induced band structure variations in planar nanowire core-shell heterostructures

Strain relaxation mechanisms during epitaxial growth of core-shell nanostructures play a key role in determining their morphologies, crystal structure and properties. To unveil those mechanisms, we perform atomic-scale aberration-corrected scanning transmission electron microscopy studies on planar core-shell ZnSe@ZnTe nanowires on α-Al₂O₃ substrates. The core morphology affects the shell structure involving plane bending and the formation of low-angle polar boundaries. The origin of this phenomenon and its consequences on the electronic band structure are discussed. We further use monochromated valence electron energy-loss spectroscopy to obtain spatially resolved band-gap maps of the heterostructure with sub-nanometer spatial resolution. A decrease in band-gap energy at highly strained core-shell interfacial regions is found, along with a switch from direct to indirect band-gap. These findings represent an advance in the sub-nanometer-scale understanding of the interplay between structure and electronic properties associated with highly mismatched semiconductor heterostructures, especially with those related to the planar growth of heterostructured nanowire networks.

Planar growth of nanowire arrays involves interactions between materials that affect the electronic behavior of the effective heterojunction. Here, authors show how core curvature and cross-section morphology affect shell growth, demonstrating how strain at the core-shell interface induces electronic band modulations in ZnSe@ZnTe nanowires.

Nanoscale imaging of phonon dynamics by electron microscopy

Spatially resolved vibrational mapping of nanostructures is indispensable to the development and understanding of thermal nanodevices1, modulation of thermal transport2 and novel nanostructured thermoelectric materials3-5. Through the engineering of complex structures, such as alloys, nanostructures and superlattice interfaces, one can significantly alter the propagation of phonons and suppress material thermal conductivity while maintaining electrical conductivity2. There have been no correlative experiments that spatially track the modulation of phonon properties in and around nanostructures due to spatial resolution limitations of conventional optical phonon detection techniques. Here we demonstrate two-dimensional spatial mapping of phonons in a single silicon-germanium (SiGe) quantum dot (QD) using monochromated electron energy loss spectroscopy in the transmission electron microscope. Tracking the variation of the Si optical mode in and around the QD, we observe the nanoscale modification of the composition-induced red shift. We observe non-equilibrium phonons that only exist near the interface and, furthermore, develop a novel technique to differentially map phonon momenta, providing direct evidence that the interplay between diffuse and specular reflection largely depends on the detailed atomistic structure: a major advancement in the field. Our work unveils the non-equilibrium phonon dynamics at nanoscale interfaces and can be used to study actual nanodevices and aid in the understanding of heat dissipation near nanoscale hotspots, which is crucial for future high-performance nanoelectronics.

Localized Phonon Densities of States at Grain Boundaries in Silicon

Since it is now possible to record vibrational spectra at nanometer scales in the electron microscope, it is of interest to explore whether extended defects in crystals such as dislocations or grain boundaries will result in measurable changes of the phonon densities of states (dos) that are reflected in the spectra. Phonon densities of states were calculated for a set of high angle grain boundaries in silicon. The boundaries are modeled by supercells with up to 160 atoms, and the vibrational densities of states were calculated by taking the Fourier transform of the velocity–velocity autocorrelation function from molecular dynamics simulations with larger supercells doubled in all three directions. In selected cases, the results were checked on the original supercells by comparison with the densities of states obtained by diagonalizing the dynamical matrix calculated using density functional theory. Near the core of the grain boundary, the height of the optic phonon peak in the dos at 60 meV was suppressed relative to features due to acoustic phonons that are largely unchanged relative to their bulk values. This can be attributed to the variation in the strength of bonds in grain boundary core regions where there is a range of bond lengths.

Atomic-scale probing of heterointerface phonon bridges in nitride semiconductor

Interface phonon modes that are generated by several atomic layers at the heterointerface play a major role in the interface thermal conductance for nanoscale high-power devices such as nitride-based high-electron-mobility transistors and light-emitting diodes. Here we measure the local phonon spectra across AlN/Si and AlN/Al interfaces using atomically resolved vibrational electron energy-loss spectroscopy in a scanning transmission electron microscope. At the AlN/Si interface, we observe various interface phonon modes, of which the extended and localized modes act as bridges to connect the bulk AlN modes and bulk Si modes and are expected to boost the phonon transport, thus substantially contributing to interface thermal conductance. In comparison, no such phonon bridge is observed at the AlN/Al interface, for which partially extended modes dominate the interface thermal conductivity. This work provides valuable insights into understanding the interfacial thermal transport in nitride semiconductors and useful guidance for thermal management via interface engineering.

Understanding Heterogeneities in Quantum Materials

Quantum materials are usually heterogeneous, with structural defects, impurities, surfaces, edges, interfaces, and disorder. These heterogeneities are sometimes viewed as liabilities within conventional systems; however, their electronic and magnetic structures often define and affect the quantum phenomena such as coherence, interaction, entanglement, and topological effects in the host system. Therefore, a critical need is to understand the roles of heterogeneities in order to endow materials with new quantum functions for energy and quantum information science applications. In this article, several representative examples are reviewed on the recent progress in connecting the heterogeneities to the quantum behaviors of real materials. Specifically, three intertwined topic areas are assessed: i) Reveal the structural, electronic, magnetic, vibrational, and optical degrees of freedom of heterogeneities. ii) Understand the effect of heterogeneities on the behaviors of quantum states in host material systems. iii) Control heterogeneities for new quantum functions. This progress is achieved by establishing the atomistic-level structure-property relationships associated with heterogeneities in quantum materials. The understanding of the interactions between electronic, magnetic, photonic, and vibrational states of heterogeneities enables the design of new quantum materials, including topological matter and quantum light emitters based on heterogenous 2D materials.

Emergent interface vibrational structure of oxide superlattices

As the length scales of materials decrease, the heterogeneities associated with interfaces become almost as important as the surrounding materials. This has led to extensive studies of emergent electronic and magnetic interface properties in superlattices^1–9. However, the interfacial vibrations that affect the phonon-mediated properties, such as thermal conductivity^10,11, are measured using macroscopic techniques that lack spatial resolution. Although it is accepted that intrinsic phonons change near boundaries^12,13, the physical mechanisms and length scales through which interfacial effects influence materials remain unclear. Here we demonstrate the localized vibrational response of interfaces in strontium titanate–calcium titanate superlattices by combining advanced scanning transmission electron microscopy imaging and spectroscopy, density functional theory calculations and ultrafast optical spectroscopy. Structurally diffuse interfaces that bridge the bounding materials are observed and this local structure creates phonon modes that determine the global response of the superlattice once the spacing of the interfaces approaches the phonon spatial extent. Our results provide direct visualization of the progression of the local atomic structure and interface vibrations as they come to determine the vibrational response of an entire superlattice. Direct observation of such local atomic and vibrational phenomena demonstrates that their spatial extent needs to be quantified to understand macroscopic behaviour. Tailoring interfaces, and knowing their local vibrational response, provides a means of pursuing designer solids with emergent infrared and thermal responses.

The vibrational states emerging at the interface in oxide superlattices are characterized theoretically and at atomic resolution, showing the impact of material length scales on structure and vibrational response.

Measuring phonon dispersion at an interface

The breakdown of translational symmetry at heterointerfaces leads to the emergence of new phonon modes localized at the interface¹. These modes have an essential role in thermal and electrical transport properties in devices, especially in miniature ones wherein the interface may dominate the entire response of the device². Although related theoretical work began decades ago^1,3-5, experimental research is totally absent owing to challenges in achieving the combined spatial, momentum and spectral resolutions required to probe localized modes. Here, using the four-dimensional electron energy-loss spectroscopy technique, we directly measure both the local vibrational spectra and the interface phonon dispersion relation for an epitaxial cubic boron nitride/diamond heterointerface. In addition to bulk phonon modes, we observe modes localized at the interface and modes isolated from the interface. These features appear only within approximately one nanometre around the interface. The localized modes observed here are predicted to substantially affect the interface thermal conductance and electron mobility. Our findings provide insights into lattice dynamics at heterointerfaces, and the demonstrated experimental technique should be useful in thermal management, electrical engineering and topological phononics.

Robotic fabrication of high-quality lamellae for aberration-corrected transmission electron microscopy

Aberration-corrected scanning transmission electron microscopy (STEM) is widely used for atomic-level imaging of materials but severely requires damage-free and thin samples (lamellae). So far, the preparation of the high-quality lamella from a bulk largely depends on manual processes by a skilled operator. This limits the throughput and repeatability of aberration-corrected STEM experiments. Here, inspired by the recent successes of "robot scientists", we demonstrate robotic fabrication of high-quality lamellae by focused-ion-beam (FIB) with automation software. First, we show that the robotic FIB can prepare lamellae with a high success rate, where the FIB system automatically controls rough-milling, lift-out, and final-thinning processes. Then, we systematically optimized the FIB parameters of the final-thinning process for single crystal Si. The optimized Si lamellae were evaluated by aberration-corrected STEM, showing atomic-level images with 55 pm resolution and quantitative repeatability of the spatial resolution and lamella thickness. We also demonstrate robotic fabrication of high-quality lamellae of SrTiO3 and sapphire, suggesting that the robotic FIB system may be applicable for a wide range of materials. The throughput of the robotic fabrication was typically an hour per lamella. Our robotic FIB will pave the way for the operator-free, high-throughput, and repeatable fabrication of the high-quality lamellae for aberration-corrected STEM.

Making the Most of your Electrons: Challenges and Opportunities in Characterizing Hybrid Interfaces with STEM

Inspired by the unique architectures composed of hard and soft materials in natural and biological systems, synthetic hybrid structures and associated soft-hard interfaces have recently evoked significant interest. Soft matter is typically dominated by fluctuations even at room temperature, while hard matter (which often serves as the substrate or anchor for the soft component) is governed by rigid mechanical behavior. This dichotomy offers considerable opportunities to leverage the disparate properties offered by these components across a wide spectrum spanning from basic science to engineering insights with significant technological overtones. Such hybrid structures, which include polymer nanocomposites, DNA functionalized nanoparticle superlattices and metal organic frameworks to name a few, have delivered promising insights into the areas of catalysis, environmental remediation, optoelectronics, medicine, and beyond. The interfacial structure between these hard and soft phases exists across a variety of length scales and often strongly influence the functionality of hybrid systems. While scanning/transmission electron microscopy (S/TEM) has proven to be a valuable tool for acquiring intricate molecular and nanoscale details of these interfaces, the unusual nature of hybrid composites presents a suite of challenges that make assessing or establishing the classical structure-property relationships especially difficult. These include challenges associated with preparing electron-transparent samples and obtaining sufficient contrast to resolve the interface between dissimilar materials given the dose sensitivity of soft materials. We discuss each of these challenges and supplement a review of recent developments in the field with additional experimental investigations and simulations to present solutions for attaining a nano or atomic-level understanding of these interfaces. These solutions present a host of opportunities for investigating and understanding the role interfaces play in this unique class of functional materials.

Inelastic Scattering of Electron Beams by Nonreciprocal Nanotructures

Probing optical excitations with high resolution is important for understanding their dynamics and controlling their interaction with other photonic elements. This can be done using state-of-the-art electron microscopes, which provide the means to sample optical excitations with combined meV-sub-nm energy-space resolution. For reciprocal photonic systems, electrons traveling in opposite directions produce identical signals, while this symmetry is broken in nonreciprocal structures. Here, we theoretically investigate this phenomenon by analyzing electron energy-loss spectroscopy (EELS) and cathodoluminescence (CL) for structures consisting of magnetically biased InAs as an instance of gyrotropic nonreciprocal material. We find that the spectral features associated with excitations of InAs films depend on the electron propagation direction in both EELS and CL, and can be tuned by varying the applied magnetic field within a relatively modest subtesla regime. The magnetic field modifies the optical field distribution of the sampled resonances, and this in turn produces a direction-dependent coupling to the electron. The present results pave the way to the use of electron microscope spectroscopies to explore the near-field characteristics of nonreciprocal systems with high spatial resolution.

A semi-classical theory of magnetic inelastic scattering in transmission electron energy loss spectroscopy

The feasibility of detecting magnetic excitations using monochromated electron energy loss spectroscopy in the transmission electron microscope is examined. Inelastic scattering cross-sections are derived using a semi-classical electrodynamic model, and applied to AC magnetic susceptibility measurements and magnon characterization. Consideration is given to electron probes with a magnetic moment, such as vortex beams, where additional inelastic scattering can take place due to the change in magnetic potential energy of the incident electron in a non-uniform magnetic field. This so-called 'Stern-Gerlach' energy loss can be used to enhance the strength of the scattering by increasing the orbital angular momentum of the vortex beam, and enables separation of magnetic from non-magnetic (i.e. dielectric) energy losses, thus providing a promising experimental route for detecting magnons. AC magnetic susceptibility measurements are however not feasible using Stern-Gerlach energy losses for a vortex beam.

Advances and Applications of Atomic-Resolution Scanning Transmission Electron Microscopy

Although scanning transmission electron microscopy (STEM) images of individual heavy atoms were reported 50 years ago, the applications of atomic-resolution STEM imaging became wide spread only after the practical realization of aberration correctors on field-emission STEM/TEM instruments to form sub-Ångstrom electron probes. The innovative designs and advances of electron optical systems, the fundamental understanding of electron–specimen interaction processes, and the advances in detector technology all played a major role in achieving the goal of atomic-resolution STEM imaging of practical materials. It is clear that tremendous advances in computer technology and electronics, image acquisition and processing algorithms, image simulations, and precision machining synergistically made atomic-resolution STEM imaging routinely accessible. It is anticipated that further hardware/software development is needed to achieve three-dimensional atomic-resolution STEM imaging with single-atom chemical sensitivity, even for electron-beam-sensitive materials. Artificial intelligence, machine learning, and big-data science are expected to significantly enhance the impact of STEM and associated techniques on many research fields such as materials science and engineering, quantum and nanoscale science, physics and chemistry, and biology and medicine. This review focuses on advances of STEM imaging from the invention of the field-emission electron gun to the realization of aberration-corrected and monochromated atomic-resolution STEM and its broad applications.

Role of Convergence and Collection Angles in the Excitation of Long- and Short-Wavelength Phonons with Vibrational Electron Energy-Loss Spectroscopy

Current generation electron monochromators employed as attachments to scanning transmission electron microscopes (STEM) offer the ability to obtain vibrational information from materials using electron energy-loss spectroscopy (EELS). We show here that in crystals, long- and short-wavelength phonon modes can be probed simultaneously with on-axis vibrational STEM EELS. The long-wavelength phonons are probed via dipole scattering, while the short-wavelength modes are probed via impact scattering of the incident electrons. The localized character of the short-wavelength modes is demonstrated by scanning the electron beam across the edge of a hexagonal boron nitride nanoparticle. It is found that employing convergence angles that encompass multiple Brillouin zone boundaries enhances the short-wavelength phonon contribution to the vibrational energy-loss spectrum much more than that achieved by employing collection angles that encompass multiple Brillouin zone boundaries. Probing short-wavelength phonons at high spatial resolution with on-axis vibrational STEM EELS will help develop a fundamental connection between vibrational excitations and bonding arrangements at atomic-scale heterogeneities in materials.

Theory of Atomic-Scale Vibrational Mapping and Isotope Identification with Electron Beams

Transmission electron microscopy and spectroscopy currently enable the acquisition of spatially resolved spectral information from a specimen by focusing electron beams down to a sub-angstrom spot and then analyzing the energy of the inelastically scattered electrons with few-meV energy resolution. This technique has recently been used to experimentally resolve vibrational modes in 2D materials emerging at mid-infrared frequencies. Here, on the basis of first-principles theory, we demonstrate the possibility of identifying single isotope atom impurities in a nanostructure through the trace that they leave in the spectral and spatial characteristics of the vibrational modes. Specifically, we examine a hexagonal boron nitride molecule as an example of application, in which the presence of a single isotope impurity is revealed through changes in the electron spectra, as well as in the space-, energy-, and momentum-resolved inelastic electron signal. We compare these results with conventional far-field spectroscopy, showing that electron beams offer superior spatial resolution combined with the ability to probe the complete set of vibrational modes, including those that are optically dark. Our study is relevant for the atomic-scale characterization of vibrational modes in materials of interest, including a detailed mapping of isotope distributions.

The abTEM code: transmission electron microscopy from first principles

Simulation of transmission electron microscopy (TEM) images or diffraction patterns is often required to interpret experimental data. Since nuclear cores dominate electron scattering, the scattering potential is typically described using the independent atom model, which completely neglects valence bonding and its effect on the transmitting electrons. As instrumentation has advanced, new measurements have revealed subtle details of the scattering potential that were previously not accessible to experiment. We have created an open-source simulation code designed to meet these demands by integrating the ability to calculate the potential via density functional theory (DFT) with a flexible modular software design. abTEM can simulate most standard imaging modes and incorporates the latest algorithmic developments. The development of new techniques requires a program that is accessible to domain experts without extensive programming experience. abTEM is written purely in Python and designed for easy modification and extension. The effective use of modern open-source libraries makes the performance of abTEM highly competitive with existing optimized codes on both CPUs and GPUs and allows us to leverage an extensive ecosystem of libraries, such as the Atomic Simulation Environment and the DFT code GPAW. abTEM is designed to work in an interactive Python notebook, creating a seamless and reproducible workflow from defining an atomic structure, calculating molecular dynamics (MD) and electrostatic potentials, to the analysis of results, all in a single, easy-to-read document.  This article provides ongoing documentation of abTEM development. In this first version, we show use cases for hexagonal boron nitride, where valence bonding can be detected, a 4D-STEM simulation of molybdenum disulfide including ptychographic phase reconstruction, a comparison of MD and frozen phonon modeling for convergent-beam electron diffraction of a 2.6-million-atom silicon system, and a performance comparison of our fast implementation of the PRISM algorithm for a decahedral 20000-atom gold nanoparticle.

The abTEM code: transmission electron microscopy from first principles

Simulation of transmission electron microscopy (TEM) images or diffraction patterns is often required to interpret experimental data. Since nuclear cores dominate electron scattering, the scattering potential is typically described using the independent atom model, which completely neglects valence bonding and its effect on the transmitting electrons. As instrumentation has advanced, new measurements have revealed subtle details of the scattering potential that were previously not accessible to experiment. We have created an open-source simulation code designed to meet these demands by integrating the ability to calculate the potential via density functional theory (DFT) with a flexible modular software design. abTEM can simulate most standard imaging modes and incorporates the latest algorithmic developments. The development of new techniques requires a program that is accessible to domain experts without extensive programming experience. abTEM is written purely in Python and designed for easy modification and extension. The effective use of modern open-source libraries makes the performance of abTEM highly competitive with existing optimized codes on both CPUs and GPUs and allows us to leverage an extensive ecosystem of libraries, such as the Atomic Simulation Environment and the DFT code GPAW. abTEM is designed to work in an interactive Python notebook, creating a seamless and reproducible workflow from defining an atomic structure, calculating molecular dynamics (MD) and electrostatic potentials, to the analysis of results, all in a single, easy-to-read document.  This article provides ongoing documentation of abTEM development. In this first version, we show use cases for hexagonal boron nitride, where valence bonding can be detected, a 4D-STEM simulation of molybdenum disulfide including ptychographic phase reconstruction, a comparison of MD and frozen phonon modeling for convergent-beam electron diffraction of a 2.6-million-atom silicon system, and a performance comparison of our fast implementation of the PRISM algorithm for a decahedral 20000-atom gold nanoparticle.

Optical Excitations with Electron Beams: Challenges and Opportunities

Free electron beams such as those employed in electron microscopes have evolved into powerful tools to investigate photonic nanostructures with an unrivaled combination of spatial and spectral precision through the analysis of electron energy losses and cathodoluminescence light emission. In combination with ultrafast optics, the emerging field of ultrafast electron microscopy utilizes synchronized femtosecond electron and light pulses that are aimed at the sampled structures, holding the promise to bring simultaneous sub-Å-sub-fs-sub-meV space-time-energy resolution to the study of material and optical-field dynamics. In addition, these advances enable the manipulation of the wave function of individual free electrons in unprecedented ways, opening sound prospects to probe and control quantum excitations at the nanoscale. Here, we provide an overview of photonics research based on free electrons, supplemented by original theoretical insights and discussion of several stimulating challenges and opportunities. In particular, we show that the excitation probability by a single electron is independent of its wave function, apart from a classical average over the transverse beam density profile, whereas the probability for two or more modulated electrons depends on their relative spatial arrangement, thus reflecting the quantum nature of their interactions. We derive first-principles analytical expressions that embody these results and have general validity for arbitrarily shaped electrons and any type of electron-sample interaction. We conclude with some perspectives on various exciting directions that include disruptive approaches to noninvasive spectroscopy and microscopy, the possibility of sampling the nonlinear optical response at the nanoscale, the manipulation of the density matrices associated with free electrons and optical sample modes, and appealing applications in optical modulation of electron beams, all of which could potentially revolutionize the use of free electrons in photonics.

Imaging Secondary Electron Emission from a Single Atomic Layer

Graphene-based devices hold promise for a wide range of technological applications. Yet characterizing the structure and the electrical properties of a material that is only one atomic layer thick still poses technical challenges. Recent investigations indicate that secondary-electron electron-beam-induced current (SE-EBIC) imaging can reveal subtle details regarding electrical conductivity and electron transport with high spatial resolution. Here, it is shown that the SEEBIC imaging mode can be used to detect suspended single layers of graphene and distinguish between different numbers of layers. Pristine and contaminated areas of graphene are also compared to show that pristine graphene exhibits a substantially lower SE yield than contaminated regions. This SEEBIC imaging mode may provide valuable information for the engineering of surface coatings where SE yield is a priority.

ab initio description of bonding for transmission electron microscopy

The simulation of transmission electron microscopy (TEM) images or diffraction patterns is often required to interpret their contrast and extract specimen features. This is especially true for high-resolution phase-contrast imaging of materials, but electron scattering simulations based on atomistic models are widely used in materials science and structural biology. Since electron scattering is dominated by the nuclear cores, the scattering potential is typically described by the widely applied independent atom model. This approximation is fast and fairly accurate, especially for scanning TEM (STEM) annular dark-field contrast, but it completely neglects valence bonding and its effect on the transmitting electrons. However, an emerging trend in electron microscopy is to use new instrumentation and methods to extract the maximum amount of information from each electron. This is evident in the increasing popularity of techniques such as 4D-STEM combined with ptychography in materials science, and cryogenic microcrystal electron diffraction in structural biology, where subtle differences in the scattering potential may be both measurable and contain additional insights. Thus, there is increasing interest in electron scattering simulations based on electrostatic potentials obtained from first principles, mainly via density functional theory, which was previously mainly required for holography. In this Review, we discuss the motivation and basis for these developments, survey the pioneering work that has been published thus far, and give our outlook for the future. We argue that a physically better justified ab initio description of the scattering potential is both useful and viable for an increasing number of systems, and we expect such simulations to steadily gain in popularity and importance.

Optical Modulation of Electron Beams in Free Space

We exploit free-space interactions between electron beams and tailored light fields to imprint on-demand phase profiles on the electron wave functions. Through rigorous semiclassical theory involving a quantum description of the electrons, we show that monochromatic optical fields focused in vacuum can be used to correct electron beam aberrations and produce selected focal shapes. Stimulated elastic Compton scattering is exploited to imprint the required electron phase, which is proportional to the integral of the optical field intensity along the electron path and depends on the transverse beam position. The required light intensities are attainable in currently available ultrafast electron microscope setups, thus opening the field of free-space optical manipulation of electron beams.

Can Copper Nanostructures Sustain High-Quality Plasmons?

Silver, king among plasmonic materials, features low inelastic absorption in the visible-infrared (vis-IR) spectral region compared to other metals. In contrast, copper is commonly regarded as too lossy for actual applications. Here, we demonstrate vis-IR plasmons with quality factors >60 in long copper nanowires (NWs), as determined by electron energy-loss spectroscopy. We explain this result by noticing that most of the electromagnetic energy in these plasmons lies outside the metal, thus becoming less sensitive to inelastic absorption. Measurements for silver and copper NWs of different diameters allow us to elucidate the relative importance of radiative and nonradiative losses in plasmons spanning a wide spectral range down to <20 meV. Thermal population of such low-energy modes becomes significant and generates electron energy gains associated with plasmon absorption, rendering an experimental determination of the NW temperature. Copper is therefore emerging as an attractive, cheap, abundant material platform for high-quality plasmonics in elongated nanostructures.

Computation and data driven discovery of topological phononic materials

The discovery of topological quantum states marks a new chapter in both condensed matter physics and materials sciences. By analogy to spin electronic system, topological concepts have been extended into phonons, boosting the birth of topological phononics (TPs). Here, we present a high-throughput screening and data-driven approach to compute and evaluate TPs among over 10,000 real materials. We have discovered 5014 TP materials and grouped them into two main classes of Weyl and nodal-line (ring) TPs. We have clarified the physical mechanism for the occurrence of single Weyl, high degenerate Weyl, individual nodal-line (ring), nodal-link, nodal-chain, and nodal-net TPs in various materials and their mutual correlations. Among the phononic systems, we have predicted the hourglass nodal net TPs in TeO₃, as well as the clean and single type-I Weyl TPs between the acoustic and optical branches in half-Heusler LiCaAs. In addition, we found that different types of TPs can coexist in many materials (such as ScZn). Their potential applications and experimental detections have been discussed. This work substantially increases the amount of TP materials, which enables an in-depth investigation of their structure-property relations and opens new avenues for future device design related to TPs.

Topological phononic (TP) materials are attracting wide attentions and it is more difficult to seek TP materials compared to electronic materials. Here, the authors present a high-throughput screening and data-driven approach to discover 5014 TP materials and further clarify the mechanism for the occurrence of various TPs.

Four-dimensional vibrational spectroscopy for nanoscale mapping of phonon dispersion in BN nanotubes

Directly mapping local phonon dispersion in individual nanostructures can advance our understanding of their thermal, optical, and mechanical properties. However, this requires high detection sensitivity and combined spatial, energy and momentum resolutions, thus has been elusive. Here, we demonstrate a four-dimensional electron energy loss spectroscopy technique, and present position-dependent phonon dispersion measurements in individual boron nitride nanotubes. By scanning the electron beam in real space while monitoring both the energy loss and the momentum transfer, we are able to reveal position- and momentum-dependent lattice vibrations at nanometer scale. Our measurements show that the phonon dispersion of multi-walled nanotubes is locally close to hexagonal-boron nitride crystals. Interestingly, acoustic phonons are sensitive to defect scattering, while optical modes are insensitive to small voids. This work not only provides insights into vibrational properties of boron nitride nanotubes, but also demonstrates potential of the developed technique in nanoscale phonon dispersion measurements.

Topology of transition metal dichalcogenides: the case of the core-shell architecture

Non-planar architectures of the traditionally flat 2D materials are emerging as an intriguing paradigm to realize nascent properties within the family of transition metal dichalcogenides (TMDs). These non-planar forms encompass a diversity of curvatures, morphologies, and overall 3D architectures that exhibit unusual characteristics across the hierarchy of length-scales. Topology offers an integrated and unified approach to describe, harness, and eventually tailor non-planar architectures through both local and higher order geometry. Topological design of layered materials intrinsically invokes elements highly relevant to property manipulation in TMDs, such as the origin of strain and its accommodation by defects and interfaces, which have broad implications for improved material design. In this review, we discuss the importance and impact of geometry on the structure and properties of TMDs. We present a generalized geometric framework to classify and relate the diversity of possible non-planar TMD forms. We then examine the nature of curvature in the emerging core-shell architecture, which has attracted high interest due to its versatility and design potential. We consider the local structure of curved TMDs, including defect formation, strain, and crystal growth dynamics, and factors affecting the morphology of core-shell structures, such as synthesis conditions and substrate morphology. We conclude by discussing unique aspects of TMD architectures that can be leveraged to engineer targeted, exotic properties and detail how advanced characterization tools enable detection of these features. Varying the topology of nanomaterials has long served as a potent methodology to engineer unusual and exotic properties, and the time is ripe to apply topological design principles to TMDs to drive future nanotechnology innovation.

Properties of Dipole-Mode Vibrational Energy Losses Recorded From a TEM Specimen

The authors discuss the dipole vibrational modes that predominate in the energy-loss spectra of ionic materials below 1 eV, concentrating on thin-film specimens of typical transmission electron microscopy (TEM) thickness. The thickness dependence of the intensity is shown to be a useful guide to the bulk or surface character of vibrational peaks. The lateral and depth resolution of the energy-loss signal is investigated with the aid of finite-element calculations.

Lattice resolution of vibrational modes in the electron microscope

The combination of aberration correction and ultra high energy resolution with monochromators has made it possible to record images showing lattice resolution in phonon modes, both with a displaced collection aperture and more recently with an on -axis collection aperture. In practice the objective aperture has to include Bragg reflections that correspond to the observed lattice image spacings, and the specimen has to be sufficiently thick for adequate phonon scattered intensity. There has been controversy as to whether the images with the on axis detector are really a consequence of lattice resolution in a phonon mode or just a transfer of information from an image that was formed by elastically scattered electrons. We present results of calculations based on a theory that includes the possibility of dynamical electron diffraction for both incident and scattered electrons and the full phonon dispersion relation. We show that Umklapp scattering from the second Brillouin Zone back to the first Brillouin Zone is necessary for lattice resolution with the on axis detector and that it is therefore reasonable to attribute the lattice resolution to the phonon scattering.

Manipulation of surface phonon polaritons in SiC nanorods

Surface phonon polaritons (SPhPs) are potentially very attractive for subwavelength control and manipulation of light at the infrared to terahertz wavelengths. Probing their propagation behavior in nanostructures is crucial to guide rational device design. Here, aided by monochromatic scanning transmission electron microscopy-electron energy loss spectroscopy technique, we measure the dispersion relation of SPhPs in individual SiC nanorods and reveal the effects of size and shape. We find that the SPhPs can be modulated by the geometric shape and size of SiC nanorods. The energy of SPhPs shows red-shift with decreasing radius and the surface optical phonon is mainly concentrated on the surface with large radius. Therefore, the fields can be precisely confined in specific positions by varying the size of the nanorod, allowing effective tuning at nanometer scale. The findings of this work are in agreement with dielectric response theory and numerical simulation, and provide novel strategies for manipulating light in polar dielectrics through shape and size control, enabling the design of novel nanoscale phonon-photonic devices.