Symmetry-enforced straight nodal-line phonons

Based on first-principles calculations and effective model analysis, all possible straight nodal-line (NL) phonons in symmorphic and nonsymmorphic space groups are uncovered. A classification of two-band k . p models at an arbitrary point on the NLs is carried out, and these NL phonons are found to locate along the high-symmetry lines of the Brillouin zone. According to our classification, there are two types of NL phonons. The first type is topologically nontrivial with a linear dispersion, while the second type is topologically trivial, exhibiting a quadratic dispersion. The second type hosts the highest order of NLs in phonon systems, and it is a promising platform for investigating topological phase transitions. All the minimum symmetries that guarantee the existence of straight NL phonons are uncovered, which can be used to distinguish the types of straight NLs. This paper not only classifies NL phonons but also provides guidance to search for topological NLs in bosonic systems.