General ab initio framework for electronic-order-induced lattice-dynamics symmetry breaking

Conventional ab initio approaches are unable to describe phonon time-reversal symmetry ([Formula: see text]) breaking. Here, we develop an ab initio framework, grounded in molecular Berry curvature (MBC) theory, which captures electronic-order-driven symmetry breaking in lattice dynamics. Using Co₃Sn₂S₂ as a model system, our ab initio framework yields phonon spectra that break both [Formula: see text] and mirror symmetries, quantitatively reproduce the observed phonon splittings observed in experiments, and reveal distinct microscopic origins for the [Formula: see text] and [Formula: see text] modes: [Formula: see text] splitting is governed by MBC and is accurately captured by our algorithm, whereas [Formula: see text] splitting is enhanced by the Fano resonance and matches the experimental data once the Fano-factor correction is included. Leveraging this algorithm, we predict several candidate materials with nonzero electronic-order-driven symmetry breaking in lattice dynamics, establishing a first-principles route to understand electron-phonon coupling, phonon magnetism, and related Hall-type lattice responses.