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