Extraction of the self energy and Eliashberg function from angle resolved photoemission spectroscopy using the xARPES code
(2026) npj Computational Materials — Vol. 12, n° 1, p. 172 (2026)
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- (en) Angle-resolved photoemission spectroscopy is a powerful experimental technique for studying anisotropic many-body interactions through the electron spectral function. Existing attempts to decompose the spectral function into non-interacting dispersions and electron-phonon, electron-electron, and electron-impurity self-energies rely on linearization of the bands and manual assignment of self-energy magnitudes. Here, we show how self-energies can be extracted consistently for curved dispersions. We extend the maximum-entropy method to Eliashberg-function extraction with Bayesian inference, optimizing the parameters describing the dispersions and the magnitudes of electron-electron and electron-impurity interactions. We compare these novel methodologies with state-of-the-art approaches on model data, then demonstrate their applicability with two high-quality experimental data sets. With the first set, we identify the phonon modes of a two-dimensional electron liquid on TiO 2-terminated SrTiO 3. With the second set, we obtain unprecedented agreement between two Eliashberg functions of Li-doped graphene extracted from separate dispersions. We release these functionalities in the novel Python code XARPES. The coupling of electrons with bosons is a central subject in condensed matter physics 1 , governing many experimental phenomena 1-6. In solids, a commonly encountered boson is the phonon, where lattice vibrations affect electronic properties such as the resistivity in metals 7 , Cooper pairing in conventional superconductors 8 , lifetimes of electron spins 9 , and the formation of polarons 10. Depending on the material, the coupling of electrons with other types of bosons such as magnons 11,12 and plasmons 13 may also show pronounced effects. In this work, we focus on systems where electron-phonon coupling (EPC) is the predominant type of electron-boson coupling , as it is intrinsic to all materials. In metals, EPC typically appears as a photoemission kink in the spectral function near the chemical potential 14 , which can be quantified in terms of the Eliashberg function 15. The Eliash-berg function directly affects the effective mass of the charge carriers in the metallic state, reveals the frequencies and coupling strength of the relevant phonons 16 , and enters into the Migdal-Eliashberg theory of superconductivity 17. In general, the Eliashberg function is an anisotropic function of the electron momentum 18 ; for example, MgB 2 is an anisotropic superconductor with one of the highest ambient-pressure phonon-mediated critical temperatures of T c = 39 K 19. Its two superconducting gaps originate from the out-of-plane σ-state Fermi sheets and the two in-plane tubular structures arising from the π states 7,20. The Eliashberg function is accessible through experimental techniques, including optical-conductivity experiments 21 , electron tunneling 22 , Landau level spectroscopy 23 , and angle-resolved photoemission spectroscopy (ARPES) 24. However, optical-conductivity experiments and electron tun-neling only provide access to the isotropic Eliashberg function, making
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van Waas, T., Berthod, C., Berges, J., Marzari, N., Dil, J., & Poncé, S. (2026). Extraction of the self energy and Eliashberg function from angle resolved photoemission spectroscopy using the xARPES code. npj Computational Materials, 12(1), 172. https://doi.org/10.1038/s41524-026-02026-9 (Original work published 2026)