GPAW: An open Python package for electronic structure calculations.

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for the implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE), providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe-Salpeter Equation, variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn-Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support for graphics processing unit (GPU) acceleration has been achieved with minor modifications to the GPAW code thanks to the CuPy library. We end the review with an outlook, describing some future plans for GPAW.

Creation of Single Vacancies in hBN with Electron Irradiation.

Understanding electron irradiation effects is vital not only for reliable transmission electron microscopy characterization, but increasingly also for the controlled manipulation of 2D materials. The displacement cross sections of monolayer hexagonal boron nitride (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 dominate. Notably, it 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 the vibrations of the atoms. A theoretical description is developed to account for the lowering of the displacement threshold due to valence ionization resulting from inelastic scattering of probe electrons, modeled 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.

Ion-Induced Surface Charge Dynamics in Freestanding Monolayers of Graphene and MoS_{2} Probed by the Emission of Electrons.

We compare the ion-induced electron emission from freestanding monolayers of graphene and MoS_{2} to find a sixfold higher number of emitted electrons for graphene even though both materials have similar work functions. An effective single-band Hubbard model explains this finding by a charge-up in MoS_{2} that prevents low energy electrons from escaping the surface within a period of a few femtoseconds after ion impact. We support these results by measuring the electron energy distribution for correlated pairs of electrons and transmitted ions. The majority of emitted primary electrons have an energy below 10 eV and are therefore subject to the dynamic charge-up effects at surfaces.

Computationally Efficient Handling of Partially Coherent Electron Sources in (S)TEM Image Simulations via Matrix Diagonalization.

We introduce a novel method to improve the computational efficiency for (S)TEM image simulation by employing matrix diagonalization of the mixed envelope function (MEF). The MEF is derived by taking the finite size and the energy spread of the effective electron source into account, and is a component of the transmission cross-coefficient that accounts for the correlation between partially coherent waves. Since the MEF is a four-dimensional array and its application in image calculations is time-consuming, we reduce the computation time by using its eigenvectors. By incorporating the aperture function into the matrix diagonalization, only a small number of eigenvectors are required to approximate the original matrix with high accuracy. The diagonalization enables for each eigenvector the calculation of the corresponding image by employing the coherent model. The individual images are weighted by the corresponding eigenvalues and then summed up, resulting in the total partially coherent image.

Atomic-Level Structural Engineering of Graphene on a Mesoscopic Scale.

Structural engineering is the first step toward changing properties of materials. While this can be at relative ease done for bulk materials, for example, using ion irradiation, similar engineering of 2D materials and other low-dimensional structures remains a challenge. The difficulties range from the preparation of clean and uniform samples to the sensitivity of these structures to the overwhelming task of sample-wide characterization of the subjected modifications at the atomic scale. Here, we overcome these issues using a near ultrahigh vacuum system comprised of an aberration-corrected scanning transmission electron microscope and setups for sample cleaning and manipulation, which are combined with automated atomic-resolution imaging of large sample areas and a convolutional neural network approach for image analysis. This allows us to create and fully characterize atomically clean free-standing graphene with a controlled defect distribution, thus providing the important first step toward atomically tailored two-dimensional materials.

Interferometric 4D-STEM for Lattice Distortion and Interlayer Spacing Measurements of Bilayer and Trilayer 2D Materials.

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, e.g., 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 3D information about the relative positions of atoms in the corresponding layers. Here, an interferometric 4D scanning transmission electron microscopy technique is described that utilizes this phenomenon to extract precise structural information from few-layer materials with nm-scale resolution. It is demonstrated 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.

Electron-Beam Manipulation of Silicon Dopants in Graphene.

The direct manipulation of individual atoms in materials using scanning probe microscopy has been a seminal achievement of nanotechnology. Recent advances in imaging resolution and sample stability have made scanning transmission electron microscopy a promising alternative for single-atom manipulation of covalently bound materials. Pioneering experiments using an atomically focused electron beam have demonstrated the directed movement of silicon atoms over a handful of sites within the graphene lattice. Here, we achieve a much greater degree of control, allowing us to precisely move silicon impurities along an extended path, circulating a single hexagon, or back and forth between the two graphene sublattices. Even with manual operation, our manipulation rate is already comparable to the state-of-the-art in any atomically precise technique. We further explore the influence of electron energy on the manipulation rate, supported by improved theoretical modeling taking into account the vibrations of atoms near the impurities, and implement feedback to detect manipulation events in real time. In addition to atomic-level engineering of its structure and properties, graphene also provides an excellent platform for refining the accuracy of quantitative models and for the development of automated manipulation.

Structure and electronic states of a graphene double vacancy with an embedded Si dopant.

Silicon represents a common intrinsic impurity in graphene, bonding to either three or four carbon neighbors, respectively, in a single or double carbon vacancy. We investigate the effect of the latter defect (Si-C4) on the structural and electronic properties of graphene using density functional theory. Calculations based both on molecular models and with periodic boundary conditions have been performed. The two-carbon vacancy was constructed from pyrene (pyrene-2C) which was then expanded to circumpyrene-2C. The structural characterization of these cases revealed that the ground state is slightly non-planar, with the bonding carbons displaced from the plane by up to ±0.2 Å. This non-planar structure was confirmed by embedding the defect into a 10 × 8 supercell of graphene, resulting in 0.22 eV lower energy than the previously considered planar structure. Natural bond orbital analysis showed sp3 hybridization at the silicon atom for the non-planar structure and sp2d hybridization for the planar structure. Atomically resolved electron energy loss spectroscopy and corresponding spectrum simulations provide a mixed picture: a flat structure provides a slightly better overall spectrum match, but a small observed pre-peak is only present in the corrugated simulation. Considering the small energy barrier between the two equivalent corrugated conformations, both structures could plausibly exist as a superposition over the experimental time scale of seconds.

Silicon-carbon bond inversions driven by 60-keV electrons in graphene.

We demonstrate that 60-keV electron irradiation drives the diffusion of threefold-coordinated Si dopants in graphene by one lattice site at a time. First principles simulations reveal that each step is caused by an electron impact on a C atom next to the dopant. Although the atomic motion happens below our experimental time resolution, stochastic analysis of 38 such lattice jumps reveals a probability for their occurrence in a good agreement with the simulations. Conversions from three- to fourfold coordinated dopant structures and the subsequent reverse process are significantly less likely than the direct bond inversion. Our results thus provide a model of nondestructive and atomically precise structural modification and detection for two-dimensional materials.

Single atoms and metal nanoclusters anchored to graphene vacancies.

Fabricating dispersed single atoms and size-controlled metal nanoclusters remains a difficult challenge due to sintering. Here, we demonstrate that atoms and clusters can be immobilized using atomically clean defect-engineered graphene as the matrix. The graphene is first cleaned of surface contamination with laser heating, after which low-energy Ar irradiation is used to create spatially well-separated vacancies into it. Metal atoms are then evaporated either via thermal or ebeam evaporation onto graphene, where they diffuse until being trapped into a vacancy. The density of embedded structures can be controlled through irradiation dose, and the size of the structures through evaporation time. The resulting structures are confirmed through atomic-resolution scanning transmission electron microscopy and electron energy loss spectroscopy. We demonstrate here incorporation of Al, Ti, Fe, Ag and Au single atoms or nanoclusters, but the method should work equally well for other elements.

Deep reinforcement learning for data-driven adaptive scanning in ptychography.

We present a method that lowers the dose required for an electron ptychographic reconstruction by adaptively scanning the specimen, thereby providing the required spatial information redundancy in the regions of highest importance. The proposed method is built upon a deep learning model that is trained by reinforcement learning, using prior knowledge of the specimen structure from training data sets. We show that using adaptive scanning for electron ptychography outperforms alternative low-dose ptychography experiments in terms of reconstruction resolution and quality.

Replacing academic journals.

Replacing traditional journals with a more modern solution is not a new idea. Here, we propose ways to overcome the social dilemma underlying the decades of inaction. Any solution needs to not only resolve the current problems but also be capable of preventing takeover by corporations: it needs to replace traditional journals with a decentralized, resilient, evolvable network that is interconnected by open standards and open-source norms under the governance of the scholarly community. It needs to replace the monopolies connected to journals with a genuine, functioning and well-regulated market. In this new market, substitutable service providers compete and innovate according to the conditions of the scholarly community, avoiding sustained vendor lock-in. Therefore, a standards body needs to form under the governance of the scholarly community to allow the development of open scholarly infrastructures servicing the entire research workflow. We propose a redirection of money from legacy publishers to the new network by funding bodies broadening their minimal infrastructure requirements at recipient institutions to include modern infrastructure components replacing and complementing journal functionalities. Such updated eligibility criteria by funding agencies would help realign the financial incentives for recipient institutions with public and scholarly interest.

Linear indium atom chains at graphene edges.

The presence of metal atoms at the edges of graphene nanoribbons (GNRs) opens new possibilities toward tailoring their physical properties. We present here formation and high-resolution characterization of indium (In) chains on the edges of graphene-supported GNRs. The GNRs are formed when adsorbed hydrocarbon contamination crystallizes via laser heating into small ribbon-like patches of a second graphitic layer on a continuous graphene monolayer and onto which In is subsequently physical vapor deposited. Using aberration-corrected scanning transmission electron microscopy (STEM), we find that this leads to the preferential decoration of the edges of the overlying GNRs with multiple In atoms along their graphitic edges. Electron-beam irradiation during STEM induces migration of In atoms along the edges of the GNRs and triggers the formation of longer In atom chains during imaging. Density functional theory (DFT) calculations of GNRs similar to our experimentally observed structures indicate that both bare zigzag (ZZ) GNRs as well as In-terminated ZZ-GNRs have metallic character, whereas in contrast, In termination induces metallicity for otherwise semiconducting armchair (AC) GNRs. Our findings provide insights into the creation and properties of long linear metal atom chains at graphitic edges.

Identifying and manipulating single atoms with scanning transmission electron microscopy.

The manipulation of individual atoms has developed from visionary speculation into an established experimental science. Using focused electron irradiation in a scanning transmission electron microscope instead of a physical tip in a scanning probe microscope confers several benefits, including thermal stability of the manipulated structures, the ability to reach into bulk crystals, and the chemical identification of single atoms. However, energetic electron irradiation also presents unique challenges, with an inevitable possibility of irradiation damage. Understanding the underlying mechanisms will undoubtedly continue to play an important role to guide experiments. Great progress has been made in several materials including graphene, carbon nanotubes, and crystalline silicon in the eight years since the discovery of electron-beam manipulation, but the important challenges that remain will determine how far we can expect to progress in the near future.

Accurate Computational Prediction of Core-Electron Binding Energies in Carbon-Based Materials: A Machine-Learning Model Combining Density-Functional Theory and GW.

We present a quantitatively accurate machine-learning (ML) model for the computational prediction of core-electron binding energies, from which X-ray photoelectron spectroscopy (XPS) spectra can be readily obtained. Our model combines density functional theory (DFT) with GW and uses kernel ridge regression for the ML predictions. We apply the new approach to disordered materials and small molecules containing carbon, hydrogen, and oxygen and obtain qualitative and quantitative agreement with experiment, resolving spectral features within 0.1 eV of reference experimental spectra. The method only requires the user to provide a structural model for the material under study to obtain an XPS prediction within seconds. Our new tool is freely available online through the XPS Prediction Server.

Toward Exotic Layered Materials: 2D Cuprous Iodide.

Heterostructures composed of 2D materials are already opening many new possibilities in such fields of technology as electronics and magnonics, but far more could be achieved if the number and diversity of 2D materials were increased. So far, only a few dozen 2D crystals have been extracted from materials that exhibit a layered phase in ambient conditions, omitting entirely the large number of layered materials that may exist at other temperatures and pressures. This work demonstrates how such structures can be stabilized in 2D van der Waals (vdw) stacks under room temperature via growing them directly in graphene encapsulation by using graphene oxide as the template material. Specifically, an ambient stable 2D structure of copper and iodine, a material that normally only occurs in layered form at elevated temperatures between 645 and 675 K, is produced. The results establish a simple route to the production of more exotic phases of materials that would otherwise be difficult or impossible to stabilize for experiments in ambient.

Beam-driven Dynamics of Aluminium Dopants in Graphene.

Substituting heteroatoms into graphene can tune its properties for applications ranging from catalysis to spintronics. The further recent discovery that covalent impurities in graphene can be manipulated at atomic precision using a focused electron beam may open avenues towards sub-nanometer device architectures. However, the preparation of clean samples with a high density of dopants is still very challenging. Here, we report vacancy-mediated substitution of aluminium into laser-cleaned graphene, and without removal from our ultra-high vacuum apparatus, study their dynamics under 60 keV electron irradiation using aberration-corrected scanning transmission electron microscopy and spectroscopy. Three- and four-coordinated Al sites are identified, showing excellent agreement with ab initio predictions including binding energies and electron energy-loss spectrum simulations. We show that the direct exchange of carbon and aluminium atoms predicted earlier occurs under electron irradiation, although unexpectedly it is less probable than the same process for silicon. We also observe a previously unknown nitrogen-aluminium exchange that occurs at Al─N double-dopant sites at graphene divacancies created by our plasma treatment.