Orbital Mapping Near Interfaces

According to quantum mechanics, electrons move in so-called orbitals around the atomic nuclei. These orbitals and their interaction with one another give rise to numerous materials properties like, e.g., mechanical stability and adhesion, optical, electrical, and magnetic properties as well as chemical bonding. Therefore, orbitals are of paramount importance for many fields from physics over chemistry and materials science to biology. Despite their central role, it has been difficult to visualize and measure individual orbitals inside of solids so far. In this project, we will combine the two methods of transmission electron microscopy and electron energy loss spectrometry to characterize individual atoms inside selected samples. To that end, the size of the orbitals as well as the required measurement precision pose a significant challenge: they are less than one billionth of a meter in size (about a thousand times smaller than the wavelength of light) and for measuring them, the electron beam has to transfer a very specific amount of energy to the sample. Hence, the measured signal is very weak and noisy. To overcome this challenge, latest-generation instruments will be used to reach ideal imaging conditions. In addition, optimal parameters such as sample thickness, acceleration voltage and energy transfer will be determined both theoretically and experimentally. Moreover, we will investigate the suitability of novel imaging techniques such as wavefunction shaping and differential phase contrast for mapping orbitals. Especially interfaces and defects play an important role for orbital mapping. On the one hand, some conclusions about the direction of orbitals only become possible due to the local changes of the sample in the vicinity of interfaces or defects. On the other hand, they have a huge impact on many practical applications such as the adhesion of protective coatings, the efficiency of electronic devices, or the development of new catalysts. Thus, the novel approaches to orbital mapping that will be developed in this project will not only improve our understanding of orbitals but will also lead to a better applicability of this understanding.

Most physical properties of the world around us are governed by the states and interactions of electrons in atoms. However, due to the electrons' quantum nature and the extremely small size of atoms, most information about the electrons' states so far have been inferred indirectly or calculated but not from directly imaging them. In this project, we further developed a method to directly image the electrons' states by means of a transmission electron microscope. As the signal of individual sample electrons is extremely weak and the samples deteriorate quickly under the necessary imaging conditions, a large aspect of this project was the optimization of the experimental parameters. To this end, several new data processing methods were developed. This allowed us to identify the most promising conditions under which mapping electronic states is possible. Additionally, we improved the theoretical framework underlying our understanding of mapping electron states by incorporating much more sophisticated calculation techniques into our workflow for predicting experimental images. Finally, the methods developed in the project were applied experimentally to several materials. One noteworthy material was graphene, a well-known 2D material consisting of a single sheet of carbon atoms. In a multi-layer graphene sample, we were able to map the differences between electronic states in the plane (which bind the carbon atoms) and those perpendicular to the plane. Another important material analyzed was a special interface at which a so-called 2D electron gas occurs, i.e. electrons can move freely in two dimensions along the interface, but are strongly confined in the third dimension. Such materials play an important role, e.g., in modern semi-conductor devices. The methods and results of this project improve our understanding of the intricate interaction between electrons inside atoms and open up new ways of material characterization on the atomic scale. This will undoubtedly have a large impact on many fields, including chemistry, electronics and material science.