Ab initio downfolding for nonadiabatic phonons and dynamical electron-phonon coupling

First-principle calculations of phonons and electron-phonon coupling typically rely on the adiabatic Born-Oppenheimer approximation, which assumes that the electrons remain in their ground state for each instantaneous atomic configuration. However, this assumption fails whenever there is a low-energy electronic excitation [1, 2]. In this talk, I will present an ab initio framework for studying phonons in the nonadiabatic regime. By downfolding the electronic Hamiltonian to a low-dimensional subspace, one can efficiently and accurately compute the phonon spectral function and the frequency-dependent electron-phonon coupling. I will show applications of this approach to real materials, highlighting how nonadiabatic effects influence the doping and temperature dependence of the phonons. This method also provides a benchmark for testing commonly used approximations.

[1] S. Pisana et al., Nature Materials 6, 198 (2007) [2] J. Berges et al., Physical Review X 13, 041009 (2023)