Electron-Beam Mapping of Vibrational Modes with Nanometer Spatial Resolution

Probing the Polarization of Low-Energy Excitations in 2D Materials from Atomic Crystals to Nanophotonic Arrays Using Momentum-Resolved Electron Energy Loss Spectroscopy

Spectroscopies utilizing free electron beams as probes offer detailed information on the reciprocal-space excitations of 2D materials such as graphene and transition metal dichalcogenide monolayers. Yet, despite the attention paid to such quantum materials, less consideration has been given to the electron-beam characterization of 2D periodic nanostructures such as photonic crystals, metasurfaces, and plasmon arrays, which can exhibit the same lattice and excitation symmetries as their atomic analogues albeit at drastically different length, momentum, and energy scales. Because of their lack of covalent bonding and influence of retarded electromagnetic interactions, important physical distinctions arise that complicate interpretation of scattering signals. Here we present a fully-retarded theoretical framework for describing the inelastic scattering of wide-field electron beams from 2D materials and apply it to investigate the complementarity in sample excitation information gained in the measurement of a honeycomb plasmon array versus angle-resolved optical spectroscopy in comparison to single monolayer graphene.

Nonequivalent Atomic Vibrations at Interfaces in a Polar Superlattice

In heterostructures made from polar materials, e.g., AlN-GaN-AlN, the nonequivalence of the two interfaces is long recognized as a critical aspect of their electronic properties; in that, they host different 2D carrier gases. Interfaces play an important role in the vibrational properties of materials, where interface states enhance thermal conductivity and can generate unique infrared-optical activity. The nonequivalence of the corresponding interface atomic vibrations, however, is not investigated so far due to a lack of experimental techniques with both high spatial and high spectral resolution. Herein, the nonequivalence of AlN-(Al0.65Ga0.35)N and (Al0.65Ga0.35)N-AlN interface vibrations is experimentally demonstrated using monochromated electron energy-loss spectroscopy in the scanning transmission electron microscope (STEM-EELS) and density-functional-theory (DFT) calculations are employed to gain insights in the physical origins of observations. It is demonstrated that STEM-EELS possesses sensitivity to the displacement vector of the vibrational modes as well as the frequency, which is as critical to understanding vibrations as polarization in optical spectroscopies. The combination enables direct mapping of the nonequivalent interface phonons between materials with different phonon polarizations. The results demonstrate the capacity to carefully assess the vibrational properties of complex heterostructures where interface states dominate the functional properties.

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.

Four-dimensional electron energy-loss spectroscopy

Recent advances in scanning transmission electron microscopy have enabled atomic-scale focused, coherent, and monochromatic electron probes, achieving nanoscale spatial resolution, meV energy resolution, sufficient momentum resolution, and a wide energy detection range in electron energy-loss spectroscopy (EELS). A four-dimensional EELS (4D-EELS) dataset can be recorded with a slot aperture selecting the specific momentum direction in the diffraction plane and the beam scanning in two spatial dimensions. In this paper, the basic principle of the 4D-EELS technique and a few examples of its application are presented. In addition to parallelly acquired dispersion with energy down to a lattice vibration scale, it can map the real space variation of any EELS spectrum features with a specific momentum transfer and energy loss to study various locally inhomogeneous scattering processes. Furthermore, simple mathematical combinations associating the spectra at different momenta are feasible from the 4D dataset, e.g., the efficient acquisition of a reliable electron magnetic circular dichroism (EMCD) signal is demonstrated. This 4D-EELS technique provides new opportunities to probe the local dispersion and related physical properties at the nanoscale.

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.

Automatic and Quantitative Measurement of Spectrometer Aberrations

The performance of electron energy loss spectrometers can often be limited by their electron optical aberrations. Due to recent developments in high energy resolution and momentum-resolved electron energy loss spectroscopy (EELS), there is renewed interest in optimizing the performance of such spectrometers. For example, the "ω - q" mode of momentum-resolved EELS, which uses a small convergence angle and requires aligning diffraction spots with the slot aperture, presents a challenge in the realignments of the spectrometer required by the adjustment of the projection lenses. Automated and robust alignment can greatly benefit such a process. The first step toward this goal is automatic and quantitative measurement of spectrometer aberrations. We demonstrate the measurement of geometric aberrations and distortions in EELS within a monochromated scanning transmission electron microscope (STEM). To better understand the results, we present a wave mechanical simulation of the experiment. Using the measured aberration and distortion coefficients as inputs to the simulation, we find a good match between the simulation and experiment, verifying formulae used in the simulation. From verified simulations with known aberration coefficients, we can assess the accuracy of measurements. Understanding the errors and inaccuracies in the procedure can guide further progress in aberration measurement and correction for new spectrometer developments.

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.

A brief peek at the cyclotron in our microscope

The influence of low energy bremsstrahlung emission on the performance of electron spectrometers and monochromators is investigated. Despite the occurrence of multi-photon events, the effect of the main azimuthal (organ pipe) mode is likely to be negligible. Potentially more serious is a new radial mode not considered in the classical theory but revealed in the quantum mechanics picture. The progress of the finely focused wave at the spectrometer entrance slit is described by a coherent wave packet of many oscillator states. It is shielded from disruption by a relatively much longer half-life. Cavity effects causing additional suppression of bremsstrahlung emission are briefly discussed.

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.

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.

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.

SnSe, the rising star thermoelectric material: a new paradigm in atomic blocks, building intriguing physical properties

Thermoelectric (TE) materials, which enable direct energy conversion between waste heat and electricity, have witnessed enormous and exciting developments over last several decades due to innovative breakthroughs both in materials and the synergistic optimization of structures and properties. Among the promising state-of-the-art materials for next-generation thermoelectrics, tin selenide (SnSe) has attracted rapidly growing research interest for its high TE performance and the intrinsic layered structure that leads to strong anisotropy. Moreover, complex interactions between lattice, charge, and orbital degrees of freedom in SnSe make up a large phase space for the optimization of its TE properties via the simultaneous tuning of structural and chemical features. Various techniques, especially advanced electron microscopy (AEM), have been devoted to exploring these critical multidiscipline correlations between TE properties and microstructures. In this review, we first focus on the intrinsic layered structure as well as the extrinsic structural "imperfectness" of various dimensions in SnSe as studied by AEM. Based on these characterization results, we give a comprehensive discussion on the current understanding of the structure-property relationship. We then point out the challenges and opportunities as provided by modern AEM techniques toward a deeper knowledge of SnSe based on electronic structures and lattice dynamics at the nanometer or even atomic scale, for example, the measurements of local charge and electric field distribution, phonon vibrations, bandgap, valence state, temperature, and resultant TE effects.

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.

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.

Direct observation of highly confined phonon polaritons in suspended monolayer hexagonal boron nitride

Phonon polaritons enable light confinement at deep subwavelength scales, with potential technological applications, such as subdiffraction imaging, sensing and engineering of spontaneous emission. However, the trade-off between the degree of confinement and the excitation efficiency of phonon polaritons prevents direct observation of these modes in monolayer hexagonal boron nitride (h-BN), where they are expected to reach ultrahigh confinement. Here, we use monochromatic electron energy-loss spectroscopy (about 7.5 meV energy resolution) in a scanning transmission electron microscope to measure phonon polaritons in monolayer h-BN, directly demonstrating the existence of these modes as the phonon Reststrahlen band (RS) disappears. We find phonon polaritons in monolayer h-BN to exhibit high confinement (>487 times smaller wavelength than that of light in free space) and ultraslow group velocity down to about 10^-5c. The large momentum compensation provided by electron beams additionally allows us to excite phonon polaritons over nearly the entire RS band of multilayer h-BN. These results open up a broad range of opportunities for the engineering of metasurfaces and strongly enhanced light-matter interactions.

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.

Single-atom vibrational spectroscopy in the scanning transmission electron microscope

Single-atom impurities and other atomic-scale defects can notably alter the local vibrational responses of solids and, ultimately, their macroscopic properties. Using high-resolution electron energy-loss spectroscopy in the electron microscope, we show that a single substitutional silicon impurity in graphene induces a characteristic, localized modification of the vibrational response. Extensive ab initio calculations reveal that the measured spectroscopic signature arises from defect-induced pseudo-localized phonon modes-that is, resonant states resulting from the hybridization of the defect modes and the bulk continuum-with energies that can be directly matched to the experiments. This finding realizes the promise of vibrational spectroscopy in the electron microscope with single-atom sensitivity and has broad implications across the fields of physics, chemistry, and materials science.

Efficient and Versatile Model for Vibrational STEM-EELS

We introduce a novel method for the simulation of the impact scattering in vibrational scanning transmission electron microscopy electron energy loss spectroscopy simulations. The phonon-loss process is modeled by a combination of molecular dynamics and elastic multislice calculations within a modified frozen phonon approximation. The key idea is thereby to use a so-called δ thermostat in the classical molecular dynamics simulation to generate frequency dependent configurations of the vibrating specimen's atomic structure. The method includes correlated motion of atoms and provides vibrational spectrum images at a cost comparable to standard frozen phonon calculations. We demonstrate good agreement of our method with simulations and experiments for a 15 nm flake of hexagonal boron nitride.

Emerging Electron Microscopy Techniques for Probing Functional Interfaces in Energy Materials

Interfaces play a fundamental role in many areas of chemistry. However, their localized nature requires characterization techniques with high spatial resolution in order to fully understand their structure and properties. State-of-the-art atomic resolution or in situ scanning transmission electron microscopy and electron energy-loss spectroscopy are indispensable tools for characterizing the local structure and chemistry of materials with single-atom resolution, but they are not able to measure many properties that dictate function, such as vibrational modes or charge transfer, and are limited to room-temperature samples containing no liquids. Here, we outline emerging electron microscopy techniques that are allowing these limitations to be overcome and highlight several recent studies that were enabled by these techniques. We then provide a vision for how these techniques can be paired with each other and with in situ methods to deliver new insights into the static and dynamic behavior of functional interfaces.

Unexpected Strong Thermally Induced Phonon Energy Shift for Mapping Local Temperature

Measuring temperature in nanoscale is crucial for the research and development of microelectronic devices. Plasmon resonance has been utilized to map local temperature gradient in metallic materials (Al) due to their large coefficients of thermal expansion. However, most semiconductors (including Si and SiC) possess much smaller coefficients of thermal expansion due to their strong covalent bonding in crystal structure, for which the plasmon-based temperature measurement becomes unreliable. Here, we report an unexpected strong, thermally induced phonon energy shift in SiC by spatially resolved vibrational spectroscopy in transmission electron microscopy with in situ heating, demonstrating that this shift can be applied as a useful tool for measuring nanoscale temperature. When a bulk phonon spectrum is used, the spatial resolution of vibrational spectroscopy can be as high as one nanometer. Molecular dynamics simulations reveal that lattice expansion only contributes a small fraction of phonon energy shift and that vibrant motions away from the bonds are predominate factors. This study gains deeper insight into the understanding of dynamic behaviors of the phonon and provides a new avenue to measure local temperature in nanodevices.

Position and momentum mapping of vibrations in graphene nanostructures

Propagating atomic vibrational waves-phonons-determine important thermal, mechanical, optoelectronic and transport characteristics of materials. Thus a knowledge of phonon dispersion (that is, the dependence of vibrational energy on momentum) is a key part of our understanding and optimization of a material's behaviour. However, the phonon dispersion of a free-standing monolayer of a two-dimensional material such as graphene, and its local variations, have remained elusive for the past decade because of the experimental limitations of vibrational spectroscopy. Even though electron energy loss spectroscopy (EELS) in transmission has recently been shown to probe local vibrational charge responses^1-4, such studies are still limited by momentum space integration due to the focused beam geometry; they are also restricted to polar materials such as boron nitride or oxides^1-4, in which huge signals induced by strong dipole moments are present. On the other hand, measurements on graphene performed by inelastic X-ray (neutron) scattering spectroscopy^5-7 or EELS in reflection^8,9 do not have any spatial resolution and require large microcrystals. Here we provide a new pathway to determine phonon dispersions down to the scale of an individual free-standing graphene monolayer by mapping the distinct vibrational modes for a large momentum transfer. The measured scattering intensities are accurately reproduced and interpreted with density functional perturbation theory¹⁰. Additionally, a nanometre-scale mapping of selected momentum-resolved vibrational modes using graphene nanoribbon structures has enabled us to spatially disentangle bulk, edge and surface vibrations. Our results are a proof-of-principle demonstration of the feasibility of studying local vibrational modes in two-dimensional monolayer materials at the nanometre scale.

Identification of site-specific isotopic labels by vibrational spectroscopy in the electron microscope

The identification of isotopic labels by conventional macroscopic techniques lacks spatial resolution and requires relatively large quantities of material for measurements. We recorded the vibrational spectra of an α amino acid, l-alanine, with damage-free “aloof” electron energy-loss spectroscopy in a scanning transmission electron microscope to directly resolve carbon-site–specific isotopic labels in real space with nanoscale spatial resolution. An isotopic red shift of 4.8 ± 0.4 milli–electron volts in C–O asymmetric stretching modes was observed for 13C-labeled l-alanine at the carboxylate carbon site, which was confirmed by macroscopic infrared spectroscopy and theoretical calculations. The accurate measurement of this shift opens the door to nondestructive, site-specific, spatially resolved identification of isotopically labeled molecules with the electron microscope.

Phonon Spectroscopy at Atomic Resolution

Advances in source monochromation in transmission electron microscopy have opened up new possibilities for investigations of condensed matter using the phonon-loss sector of the energy-loss spectrum. Here, we explore the spatial variations of the spectrum as an atomic-sized probe is scanned across a thin flake of hexagonal boron nitride. We demonstrate that phonon spectral mapping of atomic structure is possible. These results are consistent with a model for the quantum excitation of phonons and confirm that Z-contrast imaging is based on inelastic scattering associated with phonon excitation.

Vibrational Spectroscopy of Water with High Spatial Resolution

The ability to examine the vibrational spectra of liquids with nanometer spatial resolution will greatly expand the potential to study liquids and liquid interfaces. In fact, the fundamental properties of water, including complexities in its phase diagram, electrochemistry, and bonding due to nanoscale confinement are current research topics. For any liquid, direct investigation of ordered liquid structures, interfacial double layers, and adsorbed species at liquid-solid interfaces are of interest. Here, a novel way of characterizing the vibrational properties of liquid water with high spatial resolution using transmission electron microscopy is reported. By encapsulating water between two sheets of boron nitride, the ability to capture vibrational spectra to quantify the structure of the liquid, its interaction with the liquid-cell surfaces, and the ability to identify isotopes including H2 O and D2 O using electron energy-loss spectroscopy is demonstrated. The electron microscope used here, equipped with a high-energy-resolution monochromator, is able to record vibrational spectra of liquids and molecules and is sensitive to surface and bulk morphological properties both at the nano- and micrometer scales. These results represent an important milestone for liquid and isotope-labeled materials characterization with high spatial resolution, combining nanoscale imaging with vibrational spectroscopy.

Nanoscale momentum-resolved vibrational spectroscopy

Vibrational modes affect fundamental physical properties such as the conduction of sound and heat and can be sensitive to nano- and atomic-scale structure. Probing the momentum transfer dependence of vibrational modes provides a wealth of information about a materials system; however, experimental work has been limited to essentially bulk and averaged surface approaches or to small wave vectors. We demonstrate a combined experimental and theoretical methodology for nanoscale mapping of optical and acoustic phonons across the first Brillouin zone, in the electron microscope, probing a volume ~10¹⁰ to 10²⁰ times smaller than that of comparable bulk and surface techniques. In combination with more conventional electron microscopy techniques, the presented methodology should allow for direct correlation of nanoscale vibrational mode dispersions with atomic-scale structure and chemistry.

Exploring the capabilities of monochromated electron energy loss spectroscopy in the infrared regime

Monochromated electron energy loss spectroscopy (EELS) is one of the leading techniques to study materials properties that correspond to low (<5 eV) energy losses (i.e. band-gaps, plasmons, and excitons) with nanoscale spatial resolution. Recently a new generation of monochromators have become available, opening regimes and unlocking excitations that were previously unobservable in the electron microscope. The capabilities of these new instruments are still being explored, and here we study the effect of monochromation on various aspects of EELS analysis in the infrared (<1 eV) regime. We investigate the effect of varying levels of monochromation on energy resolution, zero-loss peak (ZLP) tail reduction, ZLP tail shape, signal-to-noise-ratio, and spatial resolution. From these experiments, the new capabilities of monochromated EELS are shown to be highly promising for the future of localized spectroscopic analysis.

Temperature Measurement by a Nanoscale Electron Probe Using Energy Gain and Loss Spectroscopy

Heat dissipation in integrated nanoscale devices is a major issue that requires the development of nanoscale temperature probes. Here, we report the implementation of a method that combines electron energy gain and loss spectroscopy to provide a direct measurement of the local temperature in the nanoenvironment. Loss and gain peaks corresponding to an optical-phonon mode in boron nitride were measured from room temperature to ∼1600  K. Both loss and gain peaks exhibit a shift towards lower energies as the sample is heated up. First-principles calculations of the temperature-induced phonon frequency shifts provide insights into the origin of this effect and confirm the experimental data. The experiments and theory presented here open the doors to the study of anharmonic effects in materials by directly probing phonons in the electron microscope.

First-Principles Vibrational Electron Energy Loss Spectroscopy of β-Guanine

A general approach to model vibrational electron energy loss spectra obtained using an electron beam positioned away from the specimen is presented. The energy-loss probability of the fast electron is evaluated using first-principles quantum mechanical calculations (density functional theory) of the dielectric response of the specimen. The validity of the method is assessed using recently measured anhydrous β-guanine, an important molecular solid used by animals to produce structural colors. The good agreement between theory and experiments lays the basis for a quantitative interpretation of this spectroscopy in complex systems.

New instrumentation and cutting edge research

Stimulated by Ondrej Krivanek's contributions, the complex interaction between research and innovations in the instrumentation for electron microscopy is discussed. Specific attention is given to aberration correction and to spectroscopy in both the valence region and at the energies of localised phonons or bond vibrations. Current thinking about projection imaging and dielectric excitation theory may be challenged. More significantly in the new fields of investigation opened up to them, electron microscopists will need to build closer relations, particularly with the photonics and scanning tunnelling microscopy communities. Further improvements in instrumentation could usefully be directed towards imaging and spectroscopy at higher scattering angles as well as the incorporation of other facilities such as photon stimulation and secondary electron imaging.

Ondrej Krivanek: A pioneering visionary in electron microscopy

This article is a short biographical sketch of the life and times of Ondrej Krivanek. The story starts with his early days in Prague, Czechia, and briefly outlines various events from a PhD in Cambridge to post-docs in Kyoto, Bell Labs, and building his first spectrometer at UC Berkeley. Ondrej's pioneering contributions to electron microscopy as Assistant Professor at Arizona State University and later as Director of R&D at Gatan are covered, as well as his return to academia and focusing on aberration correction. The story wraps up with the founding of Nion, the early success of the Nion aberration correctors, and subsequent progress such as building a complete cutting-edge electron microscope and later a record-breaking monochromator. Ondrej continues to be actively involved in design and in running Nion, and while this article ends at the present, further breakthroughs can be expected from him.