First-principles theory of phonon renormalization from nonlinear electron-phonon interactions
Abstract
Electron-phonon interactions renormalize phonon frequencies and lifetimes and are central to the dynamical properties of solids. While these effects are usually described within linear electron-phonon coupling, the role of nonlinear electron-phonon interactions for phonon properties remains largely unexplored. In this work, we study phonon renormalization arising from the long-range linear one-electron-one-phonon and the nonlinear one-electron-two-phonon interactions within a diagrammatic framework. We derive the corresponding self-energy diagrams, which depend on the chemical potential and temperature, and evaluate them from first principles for the two polar semiconductors LiF and KTaO3. In both materials, the two interaction channels renormalize the phonon spectrum in qualitatively distinct ways. The linear contribution is sharply localized near the Brillouin-zone center, whereas the nonlinear process couples an incoming phonon to other branches throughout the spectrum. As a result, it renormalizes phonons across the entire Brillouin-zone, with a pronounced temperature dependence governed by the thermal occupation of those branches. This behavior provides a clean experimental signature of the one-electron-two-phonon coupling. While the nonlinear phonon renormalization is small in LiF, it is somewhat larger in KTaO3, which we attribute to its greater number of thermally populated phonon branches at room temperature. Our results establish a general framework to assess nonlinear electron-phonon effects on the phonon properties in materials with stronger lattice fluctuations, including soft semiconductors such as lead-halide perovskites.
Related
- Nonlinear electron-phonon interactions from first principles
- Unifying dynamical electron-electron and electron-phonon interactions from first principles
- Predictive Renormalization-Group Theory of Universality Classes in Nonlinear Systems
- Strong coupling polarons in cavity quantum materials: limits of cavity-induced electron mass renormalization
- Contact Renormalization of One-Mode Electron Correlation: Validation in Four- and Ten-Electron Systems
BibTeX
@misc{kluibenschedl2026firstprinciples,
title = {{First-principles theory of phonon renormalization from nonlinear electron-phonon interactions}},
author = {Florian Kluibenschedl and Matthew Houtput and Jacques Tempere and Cesare Franchini and Mikhail Lemeshko and Ragheed Alhyder},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.20639},
eprint = {2609.20639},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20639},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - First-principles theory of phonon renormalization from nonlinear electron-phonon interactions
AU - Florian Kluibenschedl
AU - Matthew Houtput
AU - Jacques Tempere
AU - Cesare Franchini
AU - Mikhail Lemeshko
AU - Ragheed Alhyder
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2609.20639
UR - https://arxiv.org/abs/2609.20639
AB - Electron-phonon interactions renormalize phonon frequencies and lifetimes and are central to the dynamical properties of solids. While these effects are usually described within linear electron-phonon coupling, the role of nonlinear electron-phonon interactions for phonon properties remains largely unexplored. In this work, we study phonon renormalization arising from the long-range linear one-electron-one-phonon and the nonlinear one-electron-two-phonon interactions within a diagrammatic framework. We derive the corresponding self-energy diagrams, which depend on the chemical potential and temperature, and evaluate them from first principles for the two polar semiconductors LiF and KTaO_3. In both materials, the two interaction channels renormalize the phonon spectrum in qualitatively distinct ways. The linear contribution is sharply localized near the Brillouin-zone center, whereas the nonlinear process couples an incoming phonon to other branches throughout the spectrum. As a result, it renormalizes phonons across the entire Brillouin-zone, with a pronounced temperature dependence governed by the thermal occupation of those branches. This behavior provides a clean experimental signature of the one-electron-two-phonon coupling. While the nonlinear phonon renormalization is small in LiF, it is somewhat larger in KTaO_3, which we attribute to its greater number of thermally populated phonon branches at room temperature. Our results establish a general framework to assess nonlinear electron-phonon effects on the phonon properties in materials with stronger lattice fluctuations, including soft semiconductors such as lead-halide perovskites.
ER -