Dirac nodal line phonons: Theoretical recipe and material realization

Dirac nodal lines (DNLs), whose fourfold degenerate nodes with linear dispersion form a continuous line in reciprocal space, have been extensively investigated in the condensed matter community due to their intriguing topological and transport properties. However, a uniform approach to efficiently and expediently exploring the symmetry-enforced DNLs is quite lacking in bosonic systems, especially for the recently proposed topological phonons. Here, based on the group representation theory analysis, we present a recipe for discovering the DNL phonons along high symmetry lines (HSLs) in all space groups. The results show that only five space groups with inversion symmetry are identified to host the DNL phonons along seven HSLs. Furthermore, using first-principles calculations, we screen out a set of realistic materials as the ideal candidates to realize the DNL phonons along HSLs. The Zintl phase ${\mathrm{K}}_{2}{\mathrm{BaSi}}_{4}$ and pyrite-type ${\mathrm{PdAs}}_{2}$ are selected as examples to elaborate the DNLs and their related topological features. Our work not only paves the way to explore the novel DNL phonons, but also provides realistic material candidates to facilitate the possible experimental observation of DNLs in phonon systems.