Public thesis defense Thomas Van Waas - IMCN
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Numerical extraction of the electron self-energy and Eliashberg function from ARPES
Friday August 21st, 2026 - 4pm - Auditorium CYCL01 - Chemin du Cyclotron, 2 - 1348 Louvain-la-Neuve
Many-body interactions are a central topic in condensed-matter physics. Here, angle-resolved photoemission spectroscopy (ARPES) is an experimental method for simultaneously probing the energy and momentum degrees of freedom of electrons. The electron self-energy is the central quantity encoding these many-body interactions, often decomposed into contributions coming from phonons, impurities, and other electrons. Together with the bare band, the self-energy constitutes the electron spectral function underlying the ARPES photointensity. From the phonon contribution, the Eliashberg spectral function can be extracted, as a measure of the electron-phonon coupling strength across the phonon energy spectrum. However, it is often unclear how to disentangle the contributions from the bare band and the self-energy, while the bare band is often linearised during the analysis for simplicity. These challenges are further complicated by the modulation of the ARPES intensity by photoemission matrix elements. Furthermore, little evidence exists for the numerical stability of the inversion problem in which the Eliashberg function is extracted.
The aim of this PhD thesis is to address these challenges. An expression for the ARPES photointensity is derived to show that the photoemission matrix elements and the spectral function can be decoupled for 2-dimensional systems and surface states. Subsequently, methods are introduced for extracting the self-energy and bare-band quantities. The invertibility of the Eliashberg function is tested against the signal-to-noise ratio and the energy resolution. Furthermore, a Bayesian inference loop is wrapped around the extraction procedure to obtain the most probable parameters describing the bare band and the self-energy. After verifying these methods on an artificial example, they are applied to the 2-dimensional electron liquid on the surface of Nb-doped SrTiO$_3$. These methodologies are implemented in the Python package \textsc{xARPES}.
Jury members
Prof. Samuel Poncé (UCLouvain), Supervisor
Prof. Xavier Gonze (UCLouvain), Chairperson
Prof. Gian-Marco Rignanese (UCLouvain), Secretary
Prof. Benoît Hackens (UCLouvain)
Prof. J. Hugo Dil (EPFL, Switzerland)
Prof. Michael Schüler (University of Fribourg, Switzerland)