Straight and twisted open nodal-line phonon states in the CaI 2 family of materials.

Based on first-principles calculations and symmetry analysis, we propose that trigonal CaI 2 with the space group P 3̄ m 1 possesses straight and twisted open nodal-line phonon states with linear dispersion. The symmetry analysis indicates that joint symmetry PT and rotational symmetry C 3z protect the straight nodal lines along Γ - A and K - H while PT and mirror symmetry M 010 ( M 110 ) maintain the twisted nodal lines that traverse Γ - M ( Γ - K ) and A - L ( A - H ). 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 2 and MgI 2 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.