Ideal nodal-net, nodal-chain, and nodal-cage phonons in some realistic materials.

The topological interpretation of phonons provides a new platform for new concepts in phonon physics. While reports on topological electronic excitations are plenty, the number of reports on phonons is extremely limited. In this paper, we present some realistic materials as examples and demonstrate the appearance of ideal nodal-net, nodal-chain, and nodal-cage phonons in these materials based on first-principle calculations; 2 LiAlSe has a nodal-net phonon, which is composed of two nodal-chain phonons along the - and - directions; NaMgH has a nodal-chain phonon in the extended Brillouin zone (BZ), which comprises two Weyl nodal-ring phonons in the - and - planes. Moreover, 4/ AuBr has a nodal-cage phonon, which is composed of nodal-line phonons in the = 0, = π, = 0, and = 0 planes. Because the presented phonon bands and phonon surface states in these materials are quite clean, they can be easily detected in experiments. Our research results provide an ideal platform for realising complex geometric shapes (formed by nodal lines) in the momentum space of phonons.