Dynamical and anharmonic effects on the electron-phonon coupling and the zero-point renormalization of the electronic structure

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 nonperturbative 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.