The renormalization of the band structure at zero temperature due to electron-phonon coupling is explored in diamond, BN, LiF and MgO crystals. We implement a dynamical scheme to compute the frequency-dependent self-energy and the resulting quasiparticle electronic structure. Our calculations reveal the presence of a satellite band below the Fermi level of LiF and MgO. We show that the renormalization factor (Z), which is neglected in the adiabatic approximation, can reduce the zero-point renormalization (ZPR) by as much as 40%. Anharmonic effects in the renormalized eigenvalues at finite atomic displacements are explored with the frozen-phonon method. We use a non-perturbative expression for the ZPR, going beyond the Allen-Heine-Cardona theory. Our results indicate that high-order electron-phonon coupling terms contribute significantly to the zero-point renormalization for certain materials.
Antonius, G., Poncé, S., Lantagne-Hurtubise, E., Auclair, G., Gonze, X., & Côté, M. (2015). Dynamical and anharmonic effects on the electron-phonon coupling and the zero-point renormalization of the electronic structure. Physical review. B, Condensed matter and materials physics, 92(8), 85137. https://doi.org/10.1103/PhysRevB.92.085137 (Original work published 2015)