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

Conventional ab initio approaches are unable to describe phonon time-reversal symmetry ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="script">T</mml:mi> </mml:mrow> </mml:math> ) 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="script">T</mml:mi> </mml:mrow> </mml:math> and mirror symmetries, quantitatively reproduce the observed phonon splittings observed in experiments, and reveal distinct microscopic origins for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>E</mml:mi> <mml:mi>g</mml:mi> </mml:msub> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>E</mml:mi> <mml:mi>u</mml:mi> </mml:msub> </mml:mrow> </mml:math> modes: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>E</mml:mi> <mml:mi>g</mml:mi> </mml:msub> </mml:mrow> </mml:math> splitting is governed by MBC and is accurately captured by our algorithm, whereas <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>E</mml:mi> <mml:mi>u</mml:mi> </mml:msub> </mml:mrow> </mml:math> 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.