Straight and twisted open nodal-line phonon states in the CaI family of materials.

Based on first-principles calculations and symmetry analysis, we propose that trigonal CaI with the space group 3̄1 possesses straight and twisted open nodal-line phonon states with linear dispersion. The symmetry analysis indicates that joint symmetry and rotational symmetry protect the straight nodal lines along - and - while and mirror symmetry () maintain the twisted nodal lines that traverse - (-) and - (-). The calculated π Berry phase suggests that all the nodal lines are nontrivial and the corresponding drumhead-like surface states are clearly visible in the observation window, which is less than 6 THz, suggesting a significant chance for them to be measured using meV-resolution inelastic X-ray scattering. The distribution of the nodal lines in the Brillouin zone is also confirmed by the phononic tight-binding model. Furthermore, the isostructural compounds MgBr and MgI show similar phonon spectra and topological nontrivial surface states. This work provides promising candidates for investigating straight and twisted open nodal-line phonon states in a single material, which will facilitate future experimental observation.