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 nonsymmorphic 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.

中文翻译：

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具有反对称性的三维狄拉克声子

与体狄拉克费米子有关的狄拉克半金属在拓扑电子系统中是众所周知的。与之形成鲜明对比的是，晶体固体中的三维（3D）Dirac声子仍然不可用。在这里，我们执行对称性参数和第一性原理计算，以系统地研究具有反对称性的所有空间组中的3D Dirac声子。结果表明，根据3D Dirac声子的保护机制和在动量空间中的位置，存在两种类型的3D Dirac声子。第一类源于高对称点处的不可简化的四维表示。第二类来自声子支路反演，对称性确保狄拉克点位于高对称线上。此外，我们揭示了非对称的对称性以及反转和时间反转对称性的组合在3D Dirac声子的出现中起着至关重要的作用。我们的工作不仅提供对3D Dirac声子的全面理解，而且为探索声子和光子系统中的Dirac玻色子提供重要指导。