  We investigate the spectroscopic fingerprints of electron-plasmon coupling in
integrated (PES) and angle-resolved photoemission spectroscopy (ARPES). To
account for electron-plasmon interactions at a reduced computational cost, we
derived the plasmonic polaron model, an approach based on the cumulant
expansion of many-body perturbation theory that circumvents the calculation of
the GW self-energy. Through the plasmonic polaron model, we predict the
complete spectral functions and the effects of electron-plasmon coupling for
Si, Ge, GaAs, and diamond. Si, Ge, and GaAs exhibit well-defined plasmonic
polaron band structures, i.e., broadened replica of the valence bands
redshifted by the plasmon energy. Based on these results, (i) we assign the
structures of the plasmon satellite of silicon (as revealed by PES experiments)
to plasmonic Van Hove singularities occurring at the L, $\Omega$, and X
high-symmetry points and (ii) we predict the ARPES signatures of
electron-plasmon coupling for Si, Ge, GaAs, and diamond. Overall, the concept
of plasmonic polaron bands emerges as a new paradigm for the interpretation of
electronic processes in condensed matter, and the theoretical approach
presented here provides a computationally affordable tool to explore its effect
in a broad set of materials.
