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Recent advancements in time-resolved electron and photon detection enable novel correlative measurements of electrons and their associated cathodoluminescence (CL) photons within a transmission electron microscope. These studies are pivotal for understanding the underlying physics in coherent CL processes. We present experimental investigations of energy-momentum conservation and the corresponding dispersion relation on the single particle level, achieved through coincidence detection of electron-photon pairs. This not only enables unprecedented clarity in detecting weak signals otherwise obscured by non-radiative processes but also provides a new experimental pathway to investigate momentum-position correlations to explore entanglement within electron-photon pairs., Comment: 19 pages, 8 figures including supplementary material

Vanadium dioxide (VO$_2$) has received significant interest in the context of nanophotonic metamaterials and memories owing to its reversible insulator-metal transition associated with significant changes in its optical and electronic properties. While the VO$_2$ transition has been extensively studied for several decades, the hysteresis dynamics of individual single-crystal VO$_2$ nanoparticles (NPs) remains largely unexplored. Here, employing transmission electron microscopy techniques, we investigate phase transitions of single VO$_2$ NPs in real time. Our analysis reveals the statistical distribution of the transition temperature and steepness and how they differ during forward (heating) and backward (cooling) transitions. We assess the stability of coexisting phases in individual NPs and prove the persistent multilevel memory at near-room temperatures using only a few VO$_2$ NPs. Our findings shed new light on the underlying physical mechanisms governing the hysteresis of VO$_2$ and establish VO$_2$ NPs as a promising component of optoelectronic and memory devices with enhanced functionalities.

We present annular dark field scanning transmission electron microscopy (ADF-STEM) as an efficient, fast, and non-destructive nanoscale tool for monitoring solid-state phase transition. Using metal-insulator transition in vanadium dioxide nanoparticles as an example, we characterize lattice and electronic signatures of the phase transition using analytical transmission electron microscopy including diffraction and electron energy-loss spectroscopy. We demonstrate that ADF-STEM shows a clear contrast across the transition, interpreted with the help of convergent electron beam diffraction as stemming from the crystal-lattice modification accompanying the transition. In addition, ADF-STEM utilizes 3--6 orders of magnitude lower electron dose when compared to electron microscopy techniques able to reveal the phase transition with the same spatial resolution and universality. The benefits of ADF-STEM are emphasized by recording a full hysteresis loop for the metal-insulator transition of a single vanadium dioxide nanoparticle. Our study opens the prospect for fast, non-destructive, large-area and nanoscale characterization of solid-state phase transitions.

We explore the inelastic electron scattering in SrTiO3, PbTiO3, and SiC in their phonon energy range, challenging the assumption that phonon polaritons are excluded at large angles in high-resolution transmission electron energy-loss spectroscopy. We demonstrate that through multiple scattering, the electron beam can excite both phonons and phonon polaritons, and the relative proportion of each varies depending on the structure factor and scattering angle. Integrating dielectric theory, density functional theory, and multi-slice simulations, we provide a comprehensive framework for understanding these interactions in materials with polar optical phonons.

Control over the optical properties of atomically thin two-dimensional (2D) layers, including those of transition metal dichalcogenides (TMDs), is needed for future optoelectronic applications. Remarkable advances have been achieved through alloying, chemical and electrical doping, and applied strain. However, the integration of TMDs with other 2D materials in van der Waals heterostructures (vdWHs) to tailor novel functionalities remains largely unexplored. Here, the near-field coupling between TMDs and graphene/graphite is used to engineer the exciton lineshape and charge state. Fano-like asymmetric spectral features are produced in WS$_{2}$, MoSe$_{2}$ and WSe$_{2}$ vdWHs combined with graphene, graphite, or jointly with hexagonal boron nitride (h-BN) as supporting or encapsulating layers. Furthermore, trion emission is suppressed in h-BN encapsulated WSe$_{2}$/graphene with a neutral exciton redshift (44 meV) and binding energy reduction (30 meV). The response of these systems to electron-beam and light probes is well-described in terms of 2D optical conductivities of the involved materials. Beyond fundamental insights into the interaction of TMD excitons with structured environments, this study opens an unexplored avenue toward shaping the spectral profile of narrow optical modes for application in nanophotonic devices.

Vanadium dioxide (VO$_2$) is a strongly-correlated material that exhibits insulator-to-metal transition (IMT) near room temperature, which makes it a promising candidate for applications in nanophotonics or optoelectronics. However, creating VO$_2$ nanostructures with the desired functionality can be challenging due to microscopic inhomogeneities that can significantly impact the local optical and electronic properties. Thin lamellas, produced by focused ion beam milling from a homogeneous layer, provide a useful prototype for studying VO$_2$ at the truly microscopic level using a scanning transmission electron microscope (STEM). High-resolution imaging is used to identify structural inhomogeneities while electron energy-loss spectroscopy (EELS) supported by statistical analysis helps to detect V$_x$O$_y$ stoichiometries with a reduced oxidation number of vanadium at the areas of thickness below 70 nm. On the other hand, the thicker areas are dominated by vanadium dioxide, where the signatures of IMT are detected in both core-loss and low-loss EELS experiments with in-situ heating. The experimental results are interpreted with ab-initio and semi-classical calculations. This work shows that structural inhomogeneities such as pores and cracks present no harm to the desired optical properties of VO$_2$ samples.

Electron energy loss spectroscopy (EELS) is often utilized to characterize localized surface plasmon modes supported by plasmonic antennas. However, the spectral resolution of this technique is only mediocre, and it can be rather difficult to resolve modes close in the energy, such as coupled modes of dimer antennas. Here we address this issue for a case study of the dimer plasmonic antenna composed of two gold discs. We analyze four nearly degenerate coupled plasmon modes of the dimer: longitudinal and transverse bonding and antibonding dipole modes. With a traditional approach, which takes into account the spectral response of the antennas recorded at specific points, the modes cannot be experimentally identified with EELS. Therefore, we employ the spectral and spatial sensitivity of EELS simultaneously. We propose several metrics that can be utilized to resolve the modes. First, we utilize electrodynamic simulations to verify that the metrics indeed represent the spectral positions of the plasmon modes. Next, we apply the metrics to experimental data, demonstrating their ability to resolve three of the above-mentioned modes (with transverse bonding and antibonding modes still unresolved), identify them unequivocally, and determine their energies. In this respect, the spatio-spectral metrics increase the information extracted from electron energy loss spectroscopy applied to plasmonic antennas.

Doping inhomogeneities in solids are not uncommon, but their microscopic observation and understanding are limited due to the lack of bulk-sensitive experimental techniques with high-enough spatial and spectral resolution. Here, we demonstrate nanoscale imaging of both dopants and free charge carriers in La-doped BaSnO3 (BLSO) using high-resolution electron energy-loss spectroscopy (EELS). By analyzing both high- and low-energy excitations in EELS, we reveal chemical and electronic inhomogeneities within a single BLSO nanocrystal. The inhomogeneous doping leads to distinctive localized infrared surface plasmons, including a novel plasmon mode that is highly confined between high- and low-doping regions. We further quantify the carrier density, effective mass, and dopant activation percentage from EELS data and transport measurements on the bulk single crystals of BLSO. These results represent a unique way of studying heterogeneities in solids, understanding structure-property relationships at the nanoscale, and opening the way to leveraging nanoscale doping texture in the design of nanophotonic devices.

Single-pixel imaging, originally developed in light optics, facilitates fast three-dimensional sample reconstruction, as well as probing with light wavelengths undetectable by conventional multi-pixel detectors. However, the spatial resolution of optics-based single-pixel microscopy is limited by diffraction to hundreds of nanometers. Here, we propose an implementation of single-pixel imaging relying on attainable modifications of currently available ultrafast electron microscopes in which optically-modulated electrons are used instead of photons to achieve sub-nanometer spatially- and temporally-resolved single-pixel imaging. We simulate electron beam profiles generated by interaction with the optical field produced by an externally programable spatial light modulator and demonstrate the feasibility of the method by showing that the sample image and its temporal evolution can be reconstructed using realistic imperfect illumination patterns. Electron single-pixel imaging holds strong potential for application in low-dose probing of beam-sensitive biological and molecular samples, including rapid screening during in-situ experiments., Comment: 25 pages, 4 figures, 3 supplementary figures

The inelastic interaction between flying particles and optical nanocavities gives rise to entangled states in which some excitations of the latter are paired with changes in the energy or momentum of the former. In particular, entanglement of free electrons and nanocavity modes opens appealing opportunities associated with the strong interaction capabilities of the electrons. However, the degree of entanglement that is currently achievable by electron interaction with optical cavities is severely limited by the lack of external selectivity over the resulting state mixtures. Here, we propose a scheme to generate pure entanglement between designated optical excitations in a cavity and separable free-electron states. Specifically, we shape the electron wave-function profile to dramatically reduce the number of accessible cavity modes and simultaneously associate them with targeted electron scattering directions. We exemplify this concept through a theoretical description of free-electron entanglement with degenerate and nondegenerate plasmon modes in silver nanoparticles as well as atomic vibrations in an inorganic molecule. The generated entanglement can be further propagated through its electron component to extend quantum interactions beyond currently explored protocols., Comment: 9 pages, 4 figures, 85 references

The ability to control and modify infrared excitations in condensed matter is of both fundamental and application interests. Here we explore a system supporting low-energy excitations, in particular, mid-infrared localized plasmon modes and phonon polaritons that are tuned to be strongly coupled. We study the coupled modes by using far-field infrared spectroscopy, state-of-the-art monochromated electron energy-loss spectroscopy, numerical simulations and analytical modeling. We demonstrate that the electron probe facilitates a precise characterization of polaritons constituting the coupled system, and enables an active control over the coupling and the resulting sample response both in frequency and space. Our work establishes a rigorous description of the spectral features observed in light- and localized electron-based spectroscopies, which can be extended to analogous optical systems with applications in heat management, and electromagnetic field concentration or nanofocusing.

A detailed analysis of the optical response of a system accommodating several coupled modes is needed for the complete understanding of the strong coupling effect. In this paper, we report on the analysis of scattering cross section spectra of Au antennas on a SiO$_{2}$ layer on a Si substrate in the IR region. A classical model of coupled oscillators is used for determining the resonant energies, damping rates and coupling strengths of four phonon polariton modes in the SiO$_{2}$ layer coupled to a localized surface plasmon mode in a Au antenna. The calculated Hopfield mixing coefficients then show the contribution of the individual uncoupled modes to the hybrid modes of the coupled system.

Focused beams of electrons, which act as both sources, and sensors of electric fields, can be used to characterise the electric response of complex photonic systems by locally probing the induced optical near fields. This functionality can be complemented by embracing the recently developed vortex electron beams (VEBs), made up of electrons with orbital angular momentum, which could, in addition, probe induced magnetic near fields. In this work, we revisit the theoretical description of this technique, dubbed vortex Electron Energy-Loss Spectroscopy (v-EELS). We map the fundamental, quantum-mechanical picture of the scattering of the VEB electrons to the intuitive classical models, which treat the electron beams as a superposition of linear electric and magnetic currents. We then apply this formalism to characterise the optical response of dielectric nanoantennas with v-EELS. Our calculations reveal that VEB electrons probe electric or magnetic modes with different efficiency, which can be adjusted by changing either beam vorticity or acceleration voltage to determine the nature of the probed excitations. We also study a chirally-arranged nanostructure, which in the interaction with electron vortices produces dichroism in electron energy loss spectra. Our theoretical work establishes VEBs as versatile probes that could provide information on optical excitations otherwise inaccessible with conventional electron beams.

BaSnO$_3$ exhibits the highest carrier mobility among perovskite oxides, making it ideal for oxide electronics. Collective charge carrier oscillations, plasmons, are expected to arise in this material, thus providing a tool to control the nanoscale optical field for optoelectronics applications. Here, we demonstrate the existence of relatively long-lived plasmons supported by high-mobility charge carriers in La-doped BaSnO$_3$ (BLSO). By exploiting the high spatial and energy resolution of electron energy-loss spectroscopy with a focused beam in a scanning transmission electron microscope, we systematically investigate the dispersion, confinement ratio, and damping of infrared localized surface plasmons (LSP) in BLSO nanoparticles. We find that the LSPs in BLSO are highly spatially confined compared to those sustained by noble metals and have relatively low loss and high quality factor compared to other doped oxides. Further analysis clarifies the relation between plasmon damping and carrier mobility in BLSO. Our results support the use of nanostructured degenerate semiconductors for plasmonic applications in the infrared region and establish a relevant alternative to more traditional plasmonic materials.

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) in 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 sub-tesla 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., Comment: 7 pages, 6 figures, 52 references

Nonlinear light-matter interactions in structured materials are the source of exciting properties and enable vanguard applications in photonics. However, the magnitude of nonlinear effects is generally small, thus requiring high optical intensities for their manifestation at the nanoscale. Here, we reveal a large nonlinear response of monolayer hexagonal boron nitride (hBN) in the mid-infrared phonon-polariton region, triggered by the strongly anharmonic potential associated with atomic vibrations in this material. We present robust first-principles theory predicting a threshold light field $\sim40\,$MV/m to produce order-unity effects in Kerr nonlinearities and harmonic generation, which are made possible by a combination of the long lifetimes exhibited by optical phonons and the strongly asymmetric landscape of the configuration energy in hBN. We further foresee polariton blockade at the few-quanta level in nanometer-sized structures. In addition, by mixing static and optical fields, the strong nonlinear response of monolayer hBN gives rise to substantial frequency shifts of optical phonon modes, exceeding their spectral width for in-plane DC fields that are attainable using lateral gating technology. We therefore predict a practical scheme for electrical tunability of the vibrational modes with potential interest in mid-infrared optoelectronics. The strong nonlinear response, low damping, and robustness of hBN polaritons set the stage for the development of applications in light modulation, sensing, and metrology, while triggering the search for intense vibrational nonlinear response in other ionic materials., Comment: 13 pages, 5 figures, 102 references

Hyperbolic phonon polaritons (HPhPs) in hexagonal boron nitride (hBN) enable the direct manipulation of mid-infrared light at nanometer scales, many orders of magnitude below the free-space light wavelength. High resolution monochromated electron energy-loss spectroscopy (EELS) facilitates measurement of excitations with energies extending into the mid-infrared while maintaining nanoscale spatial resolution, making it ideal for detecting HPhPs. The electron beam is a precise source and probe of HPhPs, that allows us to perform novel experiments to observe nanoscale confinement in HPhP structures and directly extract hBN polariton dispersions for both modes in the bulk of the flake and modes along the edge. Our measurements reveal technologically important non-trivial phenomena, such as localized polaritons induced by environmental heterogeneity, enhanced and suppressed excitation due to two-dimensional interference, and strong modification of high-momenta excitations of edge-confined polaritons by nanoscale heterogeneity on edge boundaries. Our work opens exciting prospects for the design of real-world optical mid-infrared devices based on hyperbolic polaritons.

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, based on 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 dramatic 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 novel materials, including a detailed mapping of isotope distributions., Comment: 16 pages, 11 figures, 55 references

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 phase, which is proportional to the integrated 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., Comment: 10 pages, 4 figures, 67 references

We theoretically describe how fast electrons couple to polaritonic modes in uniaxial materials by analyzing the electron energy loss (EEL) spectra. We show that in the case of an uniaxial medium with hyperbolic dispersion, bulk and surface modes can be excited by a fast electron traveling through the volume or along an infinite interface between the material and vacuum. Interestingly, and in contrast to the excitations in isotropic materials, bulk modes can be excited by fast electrons traveling outside the uniaxial medium. We demonstrate our findings with the representative uniaxial material hexagonal boron nitride. We show that the excitation of bulk and surface phonon polariton modes is strongly related to the electron velocity and highly dependent on the angle between the electron beam trajectory and the optical axis of the material. Our work provides a systematic study for understanding bulk and surface polaritons excited by a fast electron beam in hyperbolic materials and sets a way to steer and control the propagation of the polaritonic waves by changing the electron velocity and its direction.

The interaction between free electrons and optical near fields is attracting increasing attention as a way to manipulate the electron wave function in space, time, and energy. Relying on currently attainable experimental capabilities, we design optical near-field plates to imprint a lateral phase on the electron wave function that can largely correct spherical aberration without the involvement of electric or magnetic lenses in the electron optics, and further generate on-demand lateral focal spot profiles. Our work introduces a disruptive and powerful approach toward aberration correction based on light-electron interactions that could lead to compact and versatile time-resolved free-electron microscopy and spectroscopy., Comment: 8 pages, 6 figures, 53 references

We theoretically demonstrate the ability of electron beams to probe the nonlinear photonic response with nanometer spatial resolution, well beyond the capabilities of existing optical techniques. Although the interaction of electron beams with photonic modes is generally weak, the use of optical pumping produces stimulated electron-light interactions that can reach order-unity probabilities in photon-induded near field electron microscopy (PINEM). Here, we demonstrate that PINEM can locally and quantitatively probe the nonlinear optical response. Specifically, we predict a dependence of PINEM electron spectra on the sample nonlinearity that can reveal the second-harmonic (SH) response of optical materials with nanometer resolution, observed through asymmetries between electron energy losses and gains. We illustrate this concept by showing that PINEM spectra are sensitive to the SH near field of centrosymmetric structures and by finding substantial spectral asymmetries in geometries for which the linear interaction is reduced., Comment: 11 pages, 5 figures, 66 references

We revisit plasmonic modes in nanoparticle dimers with conductive or insulating junction resulting in conductive or capacitive coupling. In our study which combines electron energy loss spectroscopy, optical spectroscopy, and numerical simulations, we show coexistence of strongly and weakly hybridized modes. While the properties of the former ones strongly depend on the nature of the junction, the properties of the latter ones are nearly unaffected. This opens up a prospect for independent engineering of different plasmonic modes in a single plasmonic antenna. In addition, we show that Babinet's principle allows to engineer the near field of plasmonic modes independent of their energy. Finally, we demonstrate that combined electron energy loss imaging of a plasmonic antenna and its Babinet-complementary counterpart allows to reconstruct the distribution of both electric and magnetic near fields of localised plasmonic resonances supported by the antenna as well as charge and current antinodes of related charge oscillations.

We theoretically study plasmonic antennas featuring areas of extremely concentrated electric or magnetic field, known as hot spots. We combine two types of electric-magnetic complementarity to increase the degree of freedom for the design of the antennas: bow-tie and diabolo duality and Babinet's principle. We evaluate the figures of merit for different plasmon-enhanced optical spectroscopy methods: field enhancement, decay rate enhancement, and quality factor of the plasmon resonances. The role of Babinet's principle in interchanging electric and magnetic field hot spots and its consequences for practical antenna design are discussed. In particular, diabolo antennas exhibit slightly better performance than bow-ties in terms of larger field enhancement and larger Q factor. For specific resonance frequency, diabolo antennas are considerably smaller than bow-ties which makes them favourable for the integration into more complex devices but also makes their fabrication more demanding in terms of spatial resolution. Finally, we propose Babinet-type dimer antenna featuring electromagnetic hot spot with both the electric and magnetic field components treated on equal footing.

Van der Waals (vdW) materials exhibit intriguing structural, electronic and photonic properties. Electron Energy Loss Spectroscopy (EELS) within Scanning Transmission Electron Microscope (STEM) allows for nanoscale mapping of such properties. However, typical STEM-EELS detection is limited to energy losses in the eV range, which are too large for probing important low-energy excitation such as phonons or mid-IR plasmons. Here we adapt a conventional STEM-EELS system to probe energy loss down to 100 meV, and apply it to map phononic states in h-BN, a representative van der Waals (vdW) material. The h-BN EELS spectra, surprisingly, depend on the h-BN thickness and the distance of the electron beam to h-BN flake edges. To explain this observation, we developed a classical response theory describing the interaction of fast electrons with (anisotropic) slabs of vdW materials. Theoretical and numerical calculations perfectly match the experimental h-BN spectra, and reveal that the electron loss is dominated by the excitation of hyperbolic phonon polaritons, and not of bulk phonons as often reported. Thus, STEM-EELS offers the possibility to probe low-energy polaritons in vdW materials, with our theory being of fundamental importance for interpreting future experiments.