Electron-Phonon Coupling using Many-Body Perturbation Theory: Implementation in the Questaal Electronic Structure Suite

The ability to calculate the electron-phonon coupling (e-ph) from first principles is of tremendous interest in materials science, as it provides a non-empirical approach to understand and predict a wide range of phenomena. While this has largely been accomplished in the Kohn-Sham framework of density functional theory (KS-DFT), it is becoming more apparent that standard approximations in KS-DFT can be inaccurate. These discrepancies are often attributed to a non-local potential where more advanced approaches to DFT or many-body perturbation theory have been used. However, a highly reliable and efficient first-principles approach to compute these quantities is still missing. With the goal of realizing a high-fidelity description of e-ph, we present a new field-theoretical methodology, incorporating the seminal work of Baym and Hedin within the quasiparticle self-consistent GW (QSGW) approximation, and the Questaal electronic structure package. We show within the response function framework employed here, that no Pulay corrections are needed to account for a change in the basis functions.