We present a comprehensive theoretical investigation of the electron-phonon contribution to the lifetime broadening of the surface states on Cu(111) and Ag(111), in comparison with high-resolution photoemission results. The calculations, including electron and phonon states of the bulk and the surface, resolve the relative importance of the Rayleigh mode, being dominant for the lifetime at small hole binding energies. Including the electron-electron interaction, the theoretical results are in excellent agreement with the measured binding energy and temperature dependent lifetime broadening.

We present an efficient scheme for calculating phonon-induced potentials with high precision. The method exploits the idea of Wannier functions applied to the change of the electron potentials, allowing for an accurate evaluation of coupling constants for arbitrary wave vectors. In order to demonstrate the capability of the method, we include three examples: bulk ${\text{MgB}}_2$, bcc tungsten, and the hydrogen covered $1\times 1$ W(110) surface. For these cases we calculate the momentum resolved ($\mathbf{k}$ dependent) Eliashberg function for a selected set of $\mathbf{k}$ points and the electron-phonon mass enhancement parameter ${\lambda }_{\mathbf{k}}$.

Ab initio calculations of the phonon-induced band structure renormalization are currently based on the perturbative Allen-Heine theory and its many-body generalizations. These approaches are unsuitable to describe materials where electrons form localized polarons. Here, we develop a self-consistent, many-body Green’s function theory of band structure renormalization that incorporates localization and self-trapping. We show that the present approach reduces to the Allen-Heine theory in the weak-coupling limit, and to total energy calculations of self-trapped polarons in the strong-coupling limit. To demonstrate this methodology, we reproduce the path-integral results of Feynman and diagrammatic Monte Carlo calculations for the Fröhlich model at all couplings, and we calculate the zero point renormalization of the band gap of an ionic insulator including polaronic effects.

We present results of a theoretical investigation of the phonon-mediated decay of metal surface states. The calculated energy- and temperature-dependent lifetime broadening of a hole as well as the electron-phonon coupling parameter for the surface-state band on Al(100), Ag(111), Cu(111) and Au(111) are given. A detailed analysis of the Eliashberg spectral function shows that the intraband scattering is of minor importance for these systems. The surface Rayleigh phonon mode is shown to be crucial for the surface-state decay on the noble metal surfaces, in particular for energies close to the Fermi level where the Rayleigh mode is responsible for the major part of the phonon induced lifetime broadening.

An efficient scheme is presented to compute the transverse magnetic susceptibility within time-dependent density functional theory from which magnon dispersions can be extracted. The scheme makes use of maximally localized Wannier functions in order to interpolate the band structure onto a fine k mesh in order to converge sums on the first Brillouin zone. The gap error in the magnon dispersion at $\Gamma${}, numerically violating Goldstone's theorem, is analyzed and a correction scheme is devised that can be generalized to systems where Goldstone's theorem does not apply. The method is applied to the computation of the magnon dispersion of bulk bcc iron and fcc nickel.

We present a theoretical framework to describe polarons from first principles within a many-body Green's function formalism. Starting from a general electron-phonon Hamiltonian, we derive a self-consistent Dyson equation in which the phonon-mediated self-energy is composed by two distinct terms. One term is the Fan-Migdal self-energy and describes dynamic electron-phonon processes, the other term is a contribution to the self-energy originating from the static displacements of the atomic nuclei in the polaronic ground state. The lowest-order approximation to the present theory yields the standard many-body perturbation theory approach to electron-phonon interactions in the limit of large polarons, and the ab initio polaron equations introduced [Sio et al., Phys. Rev. B 99, 235139 (2019); Phys. Rev. Lett. 122, 246403 (2019)] in the limit of small polarons. A practical recipe to implement the present unifying formalism in first-principles calculations is outlined. We apply our method to the Fröhlich model, and obtain remarkably accurate polaron energies at all couplings, in line with Feynman's polaron theory and diagrammatic Monte Carlo calculations. We also recover the well-known results of Fröhlich and Pekar at weak and strong coupling, respectively. The present approach enables predictive many-body calculations of polarons in real materials at all couplings.