Phonon Self-Energy Corrections: To Screen, or Not to Screen

First-principles calculations of phonons are often based on the adiabatic approximation and on Brillouin-zone samplings that might not always be sufficient to capture the subtleties of Kohn anomalies. These shortcomings can be addressed through corrections to the phonon self-energy arising from the low-energy

electrons.

The exact phonon self-energy involves a product of a bare and a screened electron-phonon vertex [1] but is inaccessible for practical calculations. In most cases, the exact electron-phonon vertex is approximated by a static mean-field one. Within this approximation, we find that using two screened electron-phonon vertices yields more accurate results than using one bare and one screened vertex due to designed error cancellation to first order [2], but there is no clear path for improvements.

We therefore propose a holistic strategy based on downfolding to partially screened phonons and interactions [3], opening the way to strongly correlated materials and the frequency dependence of the electron-phonon vertex.

[1] F. Giustino, Rev. Mod. Phys. 89, 015003 (2017)

[2] M. Calandra, G. Profeta, and F. Mauri, Phys. Rev. B 82, 165111 (2010)

[3] Y. Nomura and R. Arita, Phys. Rev. B 92, 245108 (2015)