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We measure the two-dimensional elastic modulus $E^\text{2D}$ of atomically clean defect-engineered graphene with a known defect distribution and density in correlated ultra-high vacuum experiments. The vacancies are introduced via low-energy (< 200 eV) Ar ion irradiation and the atomic structure is obtained via semi-autonomous scanning transmission electron microscopy and image analysis. Based on atomic force microscopy nanoindentation measurements, a decrease of $E^\text{2D}$ from 286 to 158 N/m is observed when measuring the same graphene membrane before and after an ion irradiation-induced vacancy density of $1.0\times 10^{13}$ cm$^{-2}$. This decrease is significantly greater than what is predicted by most theoretical studies and in stark contrast to some measurements presented in the literature. With the assistance of atomistic simulations, we show that this softening is mostly due to corrugations caused by local strain at vacancies with two or more missing atoms, while the influence of single vacancies is negligible. We further demonstrate that the opposite effect can be measured when surface contamination is not removed before defect engineering, Comment: 16 pages, 10 figures

Monolayer hexagonal boron nitride (hBN) has recently become the focus of intense research as a material to host quantum emitters. Although it is well known that such emission is associated with point defects, so far no conclusive correlation between the spectra and specific defects has been demonstrated. Here, we prepare atomically clean suspended hBN samples and subject them to low-energy ion irradiation. The samples are characterized before and after irradiation via automated scanning transmission electron microscopy imaging to assess the defect concentrations and distributions. We find an intrinsic defect concentration of ca. 0.03/nm2 (with ca. 55% boron and 8% nitrogen single vacancies, 20% double vacancies and 16% more complex vacancy structures). To be able to differentiate between these and irradiation-induced defects, we create a significantly higher (but still moderate) concentration of defects with the ions (0.30/nm2), and now find ca. 55% boron and 12% nitrogen single vacancies, 14% double vacancies, and 18% more complex vacancy structures. The results demonstrate that already the simplest irradiation provides selectivity for the defect types, and open the way for future experiments to explore changing the selectivity by modifying the irradiation parameters., Comment: 7 pages, 4 figures

Understanding electron irradiation effects is vital not only for reliable transmission electron microscopy characterization, but increasingly also for the controlled manipulation of two-dimensional materials. The displacement cross sections of monolayer hBN are measured using aberration-corrected scanning transmission electron microscopy in near ultra-high vacuum at primary beam energies between 50 and 90 keV. Damage rates below 80 keV are up to three orders of magnitude lower than previously measured at edges under poorer residual vacuum conditions where chemical etching appears to have been dominant. Notably, is possible to create single vacancies in hBN using electron irradiation, with boron almost twice as likely as nitrogen to be ejected below 80 keV. Moreover, any damage at such low energies cannot be explained by elastic knock-on, even when accounting for vibrations of the atoms. A theoretical description is developed to account for lowering of the displacement threshold due to valence ionization resulting from inelastic scattering of probe electrons, modelled using charge-constrained density functional theory molecular dynamics. Although significant reductions are found depending on the constrained charge, quantitative predictions for realistic ionization states are currently not possible. Nonetheless, there is potential for defect-engineering of hBN at the level of single vacancies using electron irradiation., Comment: 38 pages, 15 figures

Electron irradiation-induced damage is often the limiting factor in imaging materials prone to ionization or electronic excitations due to inelastic electron scattering. Quantifying the related processes at the atomic scale has only become possible with the advent of aberration-corrected (scanning) transmission electron microscopes and two-dimensional materials that allow imaging each lattice atom. While it has been shown for graphene that pure knock-on damage arising from elastic scattering is sufficient to describe the observed damage, the situation is more complicated with two-dimensional semiconducting materials such as MoS2. Here, we measure the displacement cross section for sulfur atoms in MoS2 with primary beam energies between 55 and 90 keV, and correlate the results with existing measurements and theoretical models. Our experimental data suggests that the displacement process can occur from the ground state, or with single or multiple excitations, all caused by the same impinging electron. The results bring light to reports in the recent literature, and add necessary experimental data for a comprehensive description of electron irradiation damage in a two-dimensional semiconducting material. Specifically, the results agree with a combined inelastic and elastic damage mechanism at intermediate energies, in addition to a pure elastic mechanism that dominates above 80 keV. When the inelastic contribution is assumed to arise through impact ionization, the associated excitation lifetime is on the order of picoseconds, on par with expected excitation lifetimes in MoS2, whereas it drops to some tens of femtoseconds when direct valence excitation is considered., Comment: 19 pages, 4 figures, 1 table

Charge transfer between atoms is fundamental to chemical bonding but has remained very challenging to detect directly in real space. Atomic-resolution imaging of charge density is not sufficient by itself, as the change in the density due to bonding is very subtle compared to the total local charge density. Sufficiently high sensitivity, precision and accuracy are required, which we demonstrate here for the detection of charge transfer at defects in two-dimensional WS\textsubscript{2} via high-speed electron ptychography and its ability to correct errors due to residual lens aberrations.

Although surface diffusion is critical for many physical and chemical processes, including the epitaxial growth of crystals and heterogeneous catalysis, it is particularly challenging to directly study. Here, we estimate the carbon adatom migration barrier on freestanding monolayer graphene by quantifying its temperature-dependent electron knock-on damage. Due to the fast healing of vacancies by diffusing adatoms, the damage rate decreases with increasing temperature. By analyzing the observed damage rates at 300-1073 K using a model describing our finite scanning probe, we find a barrier of (0.33 \pm 0.03) eV., Comment: 6 pages, 3 figures. Additionally, some supplemental material has been uploaded: 1 PDF, 1 Jupyter Notebook, 1 Python module, 3 data files in tabular form)

The precise positioning of dopant atoms within bulk crystal lattices could enable novel applications in areas including solid-state sensing and quantum computation. Established scanning probe techniques are capable tools for the manipulation of surface atoms, but at a disadvantage due to their need to bring a physical tip into contact with the sample. This has prompted interest in electron-beam techniques, followed by the first proof-of-principle experiment of bismuth dopant manipulation in crystalline silicon. Here, we use first principles modeling to discover a novel indirect exchange mechanism that allows electron impacts to non-destructively move dopants with atomic precision within the silicon lattice. However, this mechanism only works for the two heaviest group V donors with split-vacancy configurations, Bi and Sb. We verify our model by directly imaging these configurations for Bi, and by demonstrating that the promising nuclear spin qubit Sb can be manipulated using a focused electron beam., Comment: 23 pages, 4 figures, 1 table

Van der Waals materials composed of stacks of individual atomic layers have attracted considerable attention due to their exotic electronic properties that can be altered by, for example, manipulating the twist angle of bilayer materials or the stacking sequence of trilayer materials. To fully understand and control the unique properties of these few-layer materials, a technique that can provide information about their local in-plane structural deformations, twist direction, and out-of-plane structure is needed. In principle, interference in overlap regions of Bragg disks originating from separate layers of a material encodes three-dimensional information about the relative positions of atoms in the corresponding layers. Here, we describe an interferometric four-dimensional scanning transmission electron microscopy technique that utilizes this phenomenon to extract precise structural information from few-layer materials with nm-scale resolution. We demonstrate how this technique enables measurement of local pm-scale in-plane lattice distortions as well as twist direction and average interlayer spacings in bilayer and trilayer graphene, and therefore provides a means to better understand the interplay between electronic properties and precise structural arrangements of few-layer 2D materials.

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 $\textit{ab initio}$ 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., Comment: 41 pages, 5 figures, 3 tables, 137 references

Electron microscopy is a powerful tool for studying the properties of materials down to their atomic structure. In many cases, the quantitative interpretation of images requires simulations based on atomistic structure models. These typically use the independent atom approximation that neglects bonding effects, which may, however, be measurable and of physical interest. Since all electrons and the nuclear cores contribute to the scattering potential, simulations that go beyond this approximation have relied on computationally highly demanding all-electron calculations. Here, we describe a new method to generate ab initio electrostatic potentials when describing the core electrons by projector functions. Combined with an interface to quantitative image simulations, this implementation enables an easy and fast means to model electron microscopy images. We compare simulated transmission electron microscopy images and diffraction patterns to experimental data, showing an accuracy equivalent to earlier all-electron calculations at a much lower computational cost., Comment: 10 pages, 5 figures, 2 tables

Recording atomic-resolution transmission electron microscopy (TEM) images is becoming increasingly routine. A new bottleneck is then analyzing this information, which often involves time-consuming manual structural identification. We have developed a deep learning-based algorithm for recognition of the local structure in TEM images, which is stable to microscope parameters and noise. The neural network is trained entirely from simulation but is capable of making reliable predictions on experimental images. We apply the method to single sheets of defected graphene, and to metallic nanoparticles on an oxide support., Comment: v2: Typo in author list corrected

In a paper from 2006, Couder and Fort [1] describe a version of the famous double slit experiment performed with drops bouncing on a vibrated fluid surface, where interference in the particle statistics is found even though it is possible to determine unambiguously which slit the "walking" drop passes. It is one of the first papers in an impressive series, showing that such walking drops closely resemble de Broglie waves and can reproduce typical quantum phenomena like tunneling and quantized states [2-13]. The double slit experiment is, however, a more stringent test of quantum mechanics, because it relies upon superposition and phase coherence. In the present comment we first point out that the experimental data presented in [1] are not convincing, and secondly we argue that it is not possible in general to capture quantum mechanical results in a system, where the trajectory of the particle is well-defined., Comment: 4 pages, 1 figure