Abstract Recent progress in electron and photon spectroscopy now provides resolution down to the milli-eV, both in large scale infrastructures and tabletop experiments. Phonon, magnon, and other low energy excitations have become accessible to measurements, and even essential to the interpretation of full spectra. This is an especially exciting era given the central role of electron-boson coupling in solid state physics, whether in superconductivity, thermoelectricity, or photovoltaics. Further, the coupling quantifies thermal shifts and broadenings in the scattering energies of electrons, neutrons, muons or photons. In this talk I review our first principles calculations of the spectroscopic signatures and the consequences of phonon coupling, focusing on Angle-Resolved Photo-Emission Spectra (exemplified in LaB6 and diamond), photoluminescence and absorption (at defects in 2D materials). Employing the tools of many bodies perturbation theory as well as model Hamiltonians we can now predict finite temperature and polaronic properties, satellites and sideband features, both in pristine bulk systems and defected or nanostructured ones. References [1]A. Rattanachata, L. Nicolaï, H. Martins, G. Conti, M. Verstraete, M. Gehlmann, S. Ueda, K. Kobayashi, I. Vishik, C. Schneider, C. Fadley, A. Gray, J. Minár, S. Nemšák, Phys. Rev. Materials, 5, 055002 (2021) [2]J. de Abreu, J. Nery, M. Giantomassi, X. Gonze, M. Verstraete, Phys. Chem. Chem. Phys., 24, 12580-12591 (2022) [3]P. de Melo, J. de Abreu, B. Guster, M. Giantomassi, Z. Zanolli, X. Gonze, M. Verstraete, npj. Comput. Mater., 9, 147 (2023) [4]P. M. C. de Melo, Z. Zanolli, M. Verstraete, Adv. Quantum. Tech., 4, (2021) [5]F. Libbi, P. de Melo, Z. Zanolli, M. Verstraete, N. Marzari, Phys. Rev. Lett., 128, 167401 (2022)
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