Adiabatic and nonadiabatic phonon dispersion in a Wannier function approach

We develop a first-principles scheme to calculate adiabatic and nonadiabatic phonon frequencies in the full Brillouin zone. The method relies on the stationary properties of a force-constant functional with respect to the first-order perturbation of the electronic charge density and on the localization of the deformation potential in the Wannier function basis. This allows for calculation of phonon-dispersion curves free from convergence issues related to Brillouin-zone sampling. In addition our approach justifies the use of the static screened potential in the calculation of the phonon linewidth due to decay in electron-hole pairs. We apply the method to the calculation of the phonon dispersion and electron-phonon coupling in MgB2 and CaC6. In both compounds we demonstrate the occurrence of several Kohn anomalies, absent in previous calculations, that are manifest only after careful electron- and phonon-momentum integration. In MgB2, the presence of Kohn anomalies on the E-2g branches improves the agreement with measured phonon spectra and affects the position of the main peak in the Eliashberg function. In CaC6 we show that the nonadiabatic effects on in-plane carbon vibrations are not localized at zone center but are sizable throughout the full Brillouin zone. Our method opens perspectives in large-scale first-principles calculations of dynamical properties and electron-phonon interaction.