PH-NODE: A DFPT and finite displacement supercell based python code for searching nodes in topological phononic materials

Exploring the topological physics of phonons is fundamentally important for understanding various practical applications. Here, we present a density-functional perturbation theory and finite displacement supercell based Python 3 software package called PH-NODE for efficiently computing phonon nodes present in real material through a first-principle approach. The present version of the code is interfaced with the WIEN2k, Elk, and ABINIT packages. In order to benchmark the code, four different types of materials are considered, which include (i) FeSi, a well-known double-Weyl point; (ii) LiCaAs, a half-Heusler single-type-I Weyl topological phonon (TP); and (iii) ScZn, coexisting nodal-line and nodal-ring TPs; (iv) TiS, six pairs of bulk Weyl nodes. In FeSi, the node points are found at Γ(0, 0, 0) and R(0.5, 0.5, 0.5) high symmetric points. Also, there are 21 energy values at which the node points are situated, corresponding to the full Brillouin Zone. For LiCaAs, the previously reported literature claims that there is a node point along the W-X high symmetry direction between the highest longitudinal acoustic and the lowest transverse optical branch, while in our DFT calculations, a gap of 0.17 meV is found. Furthermore, ScZn hosts six nodal-ring TPs phonons at the boundary planes of the Brillouin Zone in the vicinity of the M high-symmetric point. In addition to this, straight-line TPs are also found along the Γ-X and Γ-R high symmetric directions. Moreover, for TiS, six weyl node points (WP1, WP2, WP3, WP4, WP5 and WP6) are found along H-K high-symmetric direction. The results obtained from the PH-NODE code are in good agreement with the experimentally and theoretically reported data for each material.