First-principles equation for coherent phonons: Dynamics and polaron distortions

This paper addresses the first-principles description of coherent phonons in systems subjected to optical excitations and/or doping. We reformulate the first-principles Ehrenfest equation (fpEE) [Phys. Rev. X 13, 031026 (2023)2160-330810.1103/PhysRevX.13.031026] in terms of Born-Oppenheimer phonon frequencies and dynamical Born effective charges. We demonstrate that nonadiabatic effects renormalize the Born-Oppenheimer frequencies and introduce a damping term responsible for the finite lifetime of coherent phonons. Notably, both the frequency renormalization and the lifetime are identical to those of quantum phonons. Furthermore, we show that electrons exert a force driven by an unconventional dynamically screened electron-phonon coupling. This coupling is smaller than the bare one even in the adiabatic limit, highlighting the need to revise current models. The fpEE is also used to develop a first-principles polaron theory that describes lattice distortions induced by doping.