Inclusion of infrared dielectric screening in the GW method from polaron energies to charge mobilities

We introduce in the many-body GW scheme the modulation of the screened Coulomb interaction W arising from the macroscopic dielectric response in the infrared. We derive expressions for the polaron binding energies, the renormalization of the effective masses and for the electron and hole relaxation times. Electron and hole mobilities are then obtained from the incorporation of appropriate scattering rules. Zinc-blende GaN and orthorhombic MAPbI(3) are used as test beds finding fair agreement with results from rigorous electron-phonon coupling approaches. Although limited to polar phonons, our method has a negligible computational cost.