Observing the Quantum Wave Nature of Free Electrons through Spontaneous Emission.

We investigate, both experimentally and theoretically, the interpretation of the free-electron wave function using spontaneous emission. We use a transversely wide single-electron wave function to describe the spatial extent of transverse coherence of an electron beam in a standard transmission electron microscope. When the electron beam passes next to a metallic grating, spontaneous Smith-Purcell radiation is emitted. We then examine the effect of the electron wave function transversal size on the emitted radiation. Two interpretations widely used in the literature are considered: (1) radiation by a continuous current density attributed to the quantum probability current, equivalent to the spreading of the electron charge continuously over space; and (2) interpreting the square modulus of the wave function as a probability distribution of finding a point particle at a certain location, wherein the electron charge is always localized in space. We discuss how these two interpretations give contradictory predictions for the radiation pattern in our experiment, comparing the emission from narrow and wide wave functions with respect to the emitted radiation's wavelength. Matching our experiment with a new quantum-electrodynamics derivation, we conclude that the measurements can be explained by the probability distribution approach wherein the electron interacts with the grating as a classical point charge. Our findings clarify the transition between the classical and quantum regimes and shed light on the mechanisms that take part in general light-matter interactions.

Spherical aberration correction in a scanning transmission electron microscope using a sculpted thin film.

Nearly eighty years ago, Scherzer showed that rotationally symmetric, charge-free, static electron lenses are limited by an unavoidable, positive spherical aberration. Following a long struggle, a major breakthrough in the spatial resolution of electron microscopes was reached two decades ago by abandoning the first of these conditions, with the successful development of multipole aberration correctors. Here, we use a refractive silicon nitride thin film to tackle the second of Scherzer's constraints and demonstrate an alternative method for correcting spherical aberration in a scanning transmission electron microscope. We reveal features in Si and Cu samples that cannot be resolved in an uncorrected microscope. Our thin film corrector can be implemented as an immediate low cost upgrade to existing electron microscopes without re-engineering of the electron column or complicated operation protocols and can be extended to the correction of additional aberrations.

Unveiling the orbital angular momentum and acceleration of electron beams.

New forms of electron beams have been intensively investigated recently, including vortex beams carrying orbital angular momentum, as well as Airy beams propagating along a parabolic trajectory. Their traits may be harnessed for applications in materials science, electron microscopy, and interferometry, and so it is important to measure their properties with ease. Here, we show how one may immediately quantify these beams' parameters without need for additional fabrication or nonstandard microscopic tools. Our experimental results are backed by numerical simulations and analytic derivation.

Sculpturing the electron wave function using nanoscale phase masks.

Electron beams are extensively used in lithography, microscopy, material studies and electronic chip inspection. Today, beams are mainly shaped using magnetic or electric forces, enabling only simple shaping tasks such as focusing or scanning. Recently, binary amplitude gratings achieved complex shapes. These, however, generate multiple diffraction orders, hence the desired shape, appearing only in one order, retains little of the beam energy. Here we demonstrate a method in electron-optics for arbitrarily shaping electron beams into a single desired shape, by precise patterning of a thin-membrane. It is conceptually similar to shaping light beams using refractive or diffractive glass elements such as lenses or holograms - rather than applying electromagnetic forces, the beam is controlled by spatially modulating its wavefront. Our method allows for nearly-maximal energy transference to the designed shape, and may avoid physical damage and charging effects that are the scorn of commonly-used (e.g. Zernike and Hilbert) phase-plates. The experimental demonstrations presented here - on-axis Hermite-Gauss and Laguerre-Gauss (vortex) beams, and computer-generated holograms - are a first example of nearly-arbitrary manipulation of electron beams. Our results herald exciting prospects for microscopic material studies, enables electron lithography with fixed sample and beam and high resolution electronic chip inspection by structured electron illumination.

The stabilization of a single domain in free-standing ferroelectric nanocrystals.

High resolution electron microscopy, electron diffraction and electron holography were used to study individual free-standing ∼ 30 nm barium titanate nanocrystals. Large unidirectional variations in the tetragonal distortion were mapped across the smaller nanocrystals, peaking to anomalously large values of up to 4% at the centers of the nanocrystals. This indicated that the nanocrystals consist of highly strained single ferroelectric domains. Simulations using an effective Hamiltonian for modeling a nanocrystal under a small depolarizing field and negative pressure qualitatively confirm this picture. These simulations, along with the development of a phenomenological model, show that the tetragonal distortion variation is a combined effect of: (i) electrostrictive coupling between the spontaneous polarization and strain inside the nanocrystal, and (ii) a surface-induced effective stress existing inside the nanodot. As a result, a 'strain skin layer', having a smaller tetragonal distortion relative to the core of the nanocrystal, is created.

Generation of electron Airy beams.

Within the framework of quantum mechanics, a unique particle wave packet exists in the form of the Airy function. Its counterintuitive properties are revealed as it propagates in time or space: the quantum probability wave packet preserves its shape despite dispersion or diffraction and propagates along a parabolic caustic trajectory, even though no force is applied. This does not contradict Newton's laws of motion, because the wave packet centroid propagates along a straight line. Nearly 30 years later, this wave packet, known as an accelerating Airy beam, was realized in the optical domain; later it was generalized to an orthogonal and complete family of beams that propagate along parabolic trajectories, as well as to beams that propagate along arbitrary convex trajectories. Here we report the experimental generation and observation of the Airy beams of free electrons. These electron Airy beams were generated by diffraction of electrons through a nanoscale hologram, which imprinted on the electrons' wavefunction a cubic phase modulation in the transverse plane. The highest-intensity lobes of the generated beams indeed followed parabolic trajectories. We directly observed a non-spreading electron wavefunction that self-heals, restoring its original shape after passing an obstacle. This holographic generation of electron Airy beams opens up new avenues for steering electronic wave packets like their photonic counterparts, because the wave packets can be imprinted with arbitrary shapes or trajectories.

Large anisotropic conductance and band gap fluctuations in nearly round-shape bismuth nanoparticles.

Unlike their bulk counterpart, nanoparticles often show spontaneous fluctuations in their crystal structure at constant temperature [Iijima, S.; Ichihashi T. Phys. Rev. Lett.1985, 56, 616; Ajayan, P. M.; Marks L. D. Phys. Rev. Lett.1988, 60, 585; Ben-David, T.; Lereah, Y.; Deutscher, G.; Penisson, J. M.; Bourret, A.; Korman, R.; Cheyssac, P. Phys. Rev. Lett.1997, 78, 2585]. This phenomenon takes place whenever the net gain in the surface energy of the particles outweighs the energy cost of internal strain. The configurational space is then densely populated due to shallow free-energy barriers between structural local minima. Here we report that in the case of bismuth (Bi) nanoparticles (BiNPs), given the high anisotropy of the mass tensor of their charge carriers, structural fluctuations result in substantial dynamic changes in their electronic and conductance properties. Transmission electron microscopy is used to probe the stochastic dynamic structural fluctuations of selected BiNPs. The related fluctuations in the electronic band structure and conductance properties are studied by scanning tunneling spectroscopy and are shown to be temperature dependent. Continuous probing of the conductance of individual BiNPs reveals corresponding dynamic fluctuations (as high as 1 eV) in their apparent band gap. At 80 K, upon freezing of structural fluctuations, conductance anisotropy in BiNPs is detected as band gap variations as a function of tip position above individual particles. BiNPs offer a unique system to explore anisotropy in zero-dimension conductors as well as the dynamic nature of nanoparticles.

Spreading of mercury droplets on thin silver films at room temperature.

We study the spreading characteristics of a reactive-wetting system of mercury (Hg) droplets on silver (Ag) films in room temperature. This is done using our recently developed method for reconstructing the dynamical three-dimensional shape of spreading droplets from two-dimensional microscope images [A. Be'er and Y. Lereah, J. Microsc. 208, 148 (2002)]. We study the time evolution of the droplet radius and its contact angle, and find that the spreading process consists of two stages: (i) the "bulk propagation" regime, controlled by chemical reaction on the surface, and (ii) the "fast-flow" regime, which occurs within the metal film as well as on the surface and consists of both reactive and diffusive propagation. We show that the transition time between the two main time regimes depends solely on the thickness of the Ag film. We also discuss the chemical structure of the intermetallic compound formed in this process.

Growth of Au/Ag nanowires in thin surfactant solution films: an electron microscopy study.

The surfactant templated gold-silver nanowire growth process in a thin solution film was probed by cryo-transmission electron microscopy (cryo-TEM). The increasing surfactant concentration upon film drying appears to induce phase transformations in the film and form a liquid crystalline template for the nanowires growth. High-resolution transmission electron microscopy (HRTEM) and electron holography revealed that the nanowires were polycrystalline with some preferred crystallite orientations and had a roughly cylindrical cross-section. Further improvement of the technique may lead to highly ordered metal nanowire arrays within the surfactant matrix similar to the closely related mesoporous materials.