Three-Dimensional Dirac Phonons with Inversion Symmetry

Dirac semimetals associated with bulk fermions are well-known in topological electronic systems. In sharp contrast, three-dimensional (3D) phonons crystalline solids still unavailable. Here we perform symmetry arguments and first-principles calculations to systematically investigate 3D all space groups inversion symmetry. The results show that there two categories of depending on their protection mechanisms positions momentum space. first category originates from the four-dimensional irreducible representations at high points. second arises phonon branch inversion, guarantees points be located along lines. Furthermore, reveal non-symmorphic symmetries combination time-reversal play essential roles emergence phonons. Our work not only offers a comprehensive understanding but also provides significant guidance for exploring bosons both phononic photonic