Unified ab initio quantum-electrodynamical density-functional theory for cavity-modified electron-phonon-photon coupling in solids

Abstract

Quantum-electrodynamical density-functional theory (QEDFT) provides a first-principles framework for describing materials coupled to quantized electromagnetic fields. While QEDFT has successfully captured cavity-induced modifications of electronic structures in atoms and molecules, a fully self-consistent and accurate framework to simulate and predict the structural, phonon-related, polarization and optical response of periodic solids in optical cavities has remained elusive. Here, we introduce a unified QEDFT approach that combines collective light-matter coupling parameter in the electronic ground state, density functional perturbation theory for phonons, and real-time time-dependent QEDFT for optical excitations. This framework enables ab initio calculations of cavity-modified electronic and phononic dispersions, Born effective charges, dielectric tensors, and both resonant and non-resonant optical absorption spectra. Using wurtzite gallium nitride (GaN) in an optical cavity as a case study, we demonstrate that the quantized vacuum field reshapes electronic, phononic and polarization properties, producing experimentally accessible signatures in the dielectric function and absorption spectra. These results establish QEDFT as a general first-principles platform for predicting and exploring cavity-modified quantum materials.