Fully dynamically screened treatment of nonlinear phonon renormalization

Develop a fully dynamically screened treatment of the linear and nonlinear electron–phonon vertices, including screening corrections and explicit dynamical screening and plasmon–phonon hybridization when the electronic plasma frequency is comparable to the relevant phonon frequencies.

Background

The paper analyzes phonon renormalization using unscreened long-range one-electron-one-phonon and one-electron-two-phonon vertices. At sufficiently large carrier densities, however, screening can modify these polar interactions. In particular, when the electronic plasma frequency approaches the phonon-frequency scale, dynamical screening and plasmon–phonon hybridization may become important.

The calculations deliberately omit these screening corrections in order to isolate the renormalization generated by the two electron–phonon interaction channels. A complete extension would therefore need to calculate the vertices and phonon self-energy within a fully dynamically screened framework, especially for highly doped or photoexcited materials.

References

In the present work, we do not include screening corrections to the electron-phonon vertices, to focus on the phonon renormalization arising from the linear and nonlinear electron–phonon vertices considered here. We expect this approximation to capture the leading qualitative trends, while a full dynamically screened treatment is left for future work.

— First-principles theory of phonon renormalization from nonlinear electron-phonon interactions  (2609.20639 - Kluibenschedl et al., 17 Sep 2026) in Section 2, paragraph beginning “In materials with large charge carrier densities”