Breakdown of the dipole approximation in core losses

Current opinion on the prospect of mapping electronic orbitals in the transmission electron microscope: State of the art, challenges and perspectives

The concept of electronic orbitals has enabled the understanding of a wide range of physical and chemical properties of solids through the definition of, for example, chemical bonding between atoms. In the transmission electron microscope, which is one of the most used and powerful analytical tools for high-spatial-resolution analysis of solids, the accessible quantity is the local distribution of electronic states. However, the interpretation of electronic state maps at atomic resolution in terms of electronic orbitals is far from obvious, not always possible, and often remains a major hurdle preventing a better understanding of the properties of the system of interest. In this review, the current state of the art of the experimental aspects for electronic state mapping and its interpretation as electronic orbitals is presented, considering approaches that rely on elastic and inelastic scattering, in real and reciprocal spaces. This work goes beyond resolving spectral variations between adjacent atomic columns, as it aims at providing deeper information about, for example, the spatial or momentum distributions of the states involved. The advantages and disadvantages of existing experimental approaches are discussed, while the challenges to overcome and future perspectives are explored in an effort to establish the current state of knowledge in this field. The aims of this review are also to foster the interest of the scientific community and to trigger a global effort to further enhance the current analytical capabilities of transmission electron microscopy for chemical bonding and electronic structure analysis.

Entanglement and decoherence in electron microscopy

Interaction of the probe with the specimen in an electron microscope inevitably leads to entanglement between the probe and the scatterer. In spite of the importance of entanglement in many areas of modern physics, this subject has not been touched in the literature. Here, we develop some ideas about entanglement in electron microscopy for a number of scattering mechanisms. The relationship between entropy, density matrices, and coherence is discussed. In addition, we explore the questions "Why is Bragg scattering coherent and energy loss incoherent?" and "When does decoherence play a role?" It seems to be possible to measure decoherence on extremely short timescales of ∼10^-8s. This is especially important in view of recent developments in ultrafast electron microscopy.

Exploring possibilities of band gap measurement with off-axis EELS in TEM

A technique to measure the band gap of dielectric materials with high refractive index by means of energy electron loss spectroscopy (EELS) is presented. The technique relies on the use of a circular (Bessel) aperture and suppresses Cherenkov losses and surface-guided light modes by enforcing a momentum transfer selection. The technique also strongly suppresses the elastic zero loss peak, making the acquisition, interpretation and signal to noise ratio of low loss spectra considerably better, especially for excitations in the first few eV of the EELS spectrum. Simulations of the low loss inelastic electron scattering probabilities demonstrate the beneficial influence of the Bessel aperture in this setup even for high accelerating voltages. The importance of selecting the optimal experimental convergence and collection angles is highlighted. The effect of the created off-axis acquisition conditions on the selection of the transitions from valence to conduction bands is discussed in detail on a simplified isotropic two band model. This opens the opportunity for deliberately selecting certain transitions by carefully tuning the microscope parameters. The suggested approach is experimentally demonstrated and provides good signal to noise ratio and interpretable band gap signals on reference samples of diamond, GaN and AlN while offering spatial resolution in the nm range.

Real-space mapping of electronic orbitals

Electronic states are responsible for most material properties, including chemical bonds, electrical and thermal conductivity, as well as optical and magnetic properties. Experimentally, however, they remain mostly elusive. Here, we report the real-space mapping of selected transitions between p and d states on the Ångström scale in bulk rutile (TiO2) using electron energy-loss spectrometry (EELS), revealing information on individual bonds between atoms. On the one hand, this enables the experimental verification of theoretical predictions about electronic states. On the other hand, it paves the way for directly investigating electronic states under conditions that are at the limit of the current capabilities of numerical simulations such as, e.g., the electronic states at defects, interfaces, and quantum dots.

EMCD with an electron vortex filter: Limitations and possibilities

We discuss the feasibility of detecting spin polarized electronic transitions with a vortex filter. This approach does not rely on the principal condition of the standard electron energy-loss magnetic chiral dichroism (EMCD) technique, the precise alignment of the crystal in order to use it as a beam splitter, and thus would pave the way for the application of EMCD to new classes of materials and problems, like amorphous magnetic alloys and interface magnetism. The dichroic signal strength at the L_{2, 3}-edge of ferromagnetic Cobalt (Co) is estimated on theoretical grounds using a single atom scattering approach. To justify this approach, multi-slice simulations were carried out in order to confirm that orbital angular momentum (OAM) is conserved in amorphous materials over an extended range of sample thickness and also in very thin crystalline specimen, which is necessary for the detection of EMCD. Also artefact sources like spot size, mask tilt and astigmatism are discussed. In addition, the achievable SNR under typical experimental conditions is assessed.

Site-specific ionisation edge fine-structure of Rutile in the electron microscope

Combined Bloch-wave and density functional theory simulations are performed to investigate the effects of different channelling conditions on the fine-structure of electron energy-loss spectra. The simulated spectra compare well with experiments. Furthermore, we demonstrate that using this technique, the site-specific investigation of atomic orbitals is possible. This opens new possibilities for chemical analyses.

Is magnetic chiral dichroism feasible with electron vortices?

We discuss the feasibility of detecting magnetic transitions with focused electron vortex probes, suggested by selection rules for the magnetic quantum number. We theoretically estimate the dichroic signal strength in the L₂,₃ edge of ferromagnetic d metals. It is shown that under realistic conditions, the dichroic signal is undetectable for nanoparticles larger than ∼1 nm. This is confirmed by a key experiment with nanometer-sized vortices.

Simulation of spatially resolved electron energy loss near-edge structure for scanning transmission electron microscopy

Aberration-corrected scanning transmission electron microscopy yields probe-position-dependent energy-loss near-edge structure (ELNES) measurements, potentially providing spatial mapping of the underlying electronic states. ELNES calculations, however, typically describe excitations by a plane wave traveling in vacuum, neglecting the interaction of the electron probe with the local electronic environment as it propagates through the specimen. Here, we report a methodology that combines a full electronic-structure calculation with propagation of a focused beam in a thin film. The results demonstrate that only a detailed calculation using this approach can provide quantitative agreement with observed variations in probe-position-dependent ELNES.

Transition probability functions for applications of inelastic electron scattering

In this work, the transition matrix elements for inelastic electron scattering are investigated which are the central quantity for interpreting experiments. The angular part is given by spherical harmonics. For the weighted radial wave function overlap, analytic expressions are derived in the Slater-type and the hydrogen-like orbital models. These expressions are shown to be composed of a finite sum of polynomials and elementary trigonometric functions. Hence, they are easy to use, require little computation time, and are significantly more accurate than commonly used approximations.