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Author: Lubk, Axel × End date: 2022 × Start date: 2014 × Publisher: Amsterdam : SciPost Foundation ×

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    Bridging nano-optics and condensed matter formalisms in a unified description of inelastic scattering of relativistic electron beams
    (Amsterdam : SciPost Foundation, 2021) Lourenço-Martins, Hugo; Lubk, Axel; Kociak, Mathieu
    In the last decades, the blossoming of experimental breakthroughs in the domain of electron energy loss spectroscopy (EELS) has triggered a variety of theoretical developments. Those have to deal with completely different situations, from atomically resolved phonon mapping to electron circular dichroism passing by surface plasmon mapping. All of them rely on very different physical approximations and have not yet been reconciled, despite early attempts to do so. As an effort in that direction, we report on the development of a scalar relativistic quantum electrodynamic (QED) approach of the inelastic scattering of fast electrons. This theory can be adapted to describe all modern EELS experiments, and under the relevant approximations, can be reduced to any of the last EELS theories. In that aim, we present in this paper the state of the art and the basics of scalar relativistic QED relevant to the electron inelastic scattering. We then give a clear relation between the two once antagonist descriptions of the EELS, the retarded green Dyadic, usually applied to describe photonic excitations and the quasi-static mixed dynamic form factor (MDFF), more adapted to describe core electronic excitations of material. We then use this theory to establish two important EELS-related equations. The first one relates the spatially resolved EELS to the imaginary part of the photon propagator and the incoming and outgoing electron beam wavefunction, synthesizing the most common theories developed for analyzing spatially resolved EELS experiments. The second one shows that the evolution of the electron beam density matrix is proportional to the mutual coherence tensor, proving that quite universally, the electromagnetic correlations in the target are imprinted in the coherence properties of the probing electron beam.
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    Axion Mie theory of electron energy loss spectroscopy in topological insulators
    (Amsterdam : SciPost Foundation, 2021) Schultz, Johannes; Nogueira, Flavio S.; Büchner, Bernd; van den Brink, Jeroen; Lubk, Axel
    Electronic topological states of matter exhibit novel types of responses to electromagnetic fields. The response of strong topological insulators, for instance, is characterized by a so-called axion term in the electromagnetic Lagrangian which is ultimately due to the presence of topological surface states. Here we develop the axion Mie theory for the electromagnetic response of spherical particles including arbitrary sources of fields, i.e., charge and current distributions. We derive an axion induced mixing of transverse magnetic and transverse electric modes which are experimentally detectable through small induced rotations of the field vectors. Our results extend upon previous analyses of the problem. Our main focus is on the experimentally relevant problem of electron energy loss spectroscopy in topological insulators, a technique that has so far not yet been used to detect the axion electromagnetic response in these materials.