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

Conventional ab initio approaches are unable to describe phonon time-reversal symmetry ( T ) 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 Co 3 Sn 2 S 2 as a model system, our ab initio framework yields phonon spectra that break both T and mirror symmetries, quantitatively reproduce the observed phonon splittings observed in experiments, and reveal distinct microscopic origins for the E g and E u modes: E g splitting is governed by MBC and is accurately captured by our algorithm, whereas E u 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.