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arXiv · 2512.12479

Many-Body Correlation Effects in Fr\"ohlich Electron-Phonon Coupling

Zien Zhu·Chih-En Hsu·Benran Zhang·Zhenfa Zheng·Mauro Del Ben·Antonios M. Alvertis·Hung-Chung Hsueh·Zhenglu Li
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Abstract

In compound semiconductors and insulators, the polar electron-phonon coupling diverges at long range, known as the Fr\"ohlich interaction. Modern first-principles electron-phonon calculations treat the Fr\"ohlich interaction in a semiclassical electrostatic formalism based on density-functional perturbation theory. Here, using many-body $GW$ perturbation theory, we reveal important electron correlation effects in the Fr\"ohlich-type electron-phonon coupling, which are missed by the prevailing approaches and rooted in the fundamentally distinct behavior between quasiparticle self-energy and semi-local exchange-correlation functionals in the long-range limit. Going beyond the electrostatic treatment, we derive and implement the $GW$ self-energy contribution to the long-range polar electron-phonon coupling, and demonstrate its critical role and nontrivial behaviors in properties such as electron linewidth and polaron formation in several prototype semiconductors. Remarkably, calculations on photoemission kink in electron-doped TiO$_2$ achieve excellent agreement with experiment. Our work establishes the many-body generalization of the Fr\"ohlich interaction that is essential for accurate electron-phonon calculations at the full $GW$ level combined with Wannier interpolation techniques.

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Zien Zhu, Chih-En Hsu, Benran Zhang, Zhenfa Zheng, Mauro Del Ben, Antonios M. Alvertis, Hung-Chung Hsueh, Zhenglu Li. 2025-12-13. Many-Body Correlation Effects in Fr\"ohlich Electron-Phonon Coupling. https://arxiv.org/abs/2512.12479

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