Symmetry-enforced straight nodal-line phonons

Based on first-principles calculations and effective model analysis, all possible straight nodal-line phonons in symmorphic space groups are uncovered. A classification of two-band ${\textbf{k}}\cdot {\textbf{p}}$ models at an arbitrary point the nodal lines is carried out, these found to locate along high symmetry Brillouin zone. According our classification, there two types groups. The first type possesses a linear dispersion perpendicular lines, while second exhibits quadratic dispersion. underlying mechanisms revealed by can be distinguished through little group lines. Our work not only classifies but also provides guidance search for topological bosonic systems.