Hourglass Weyl and Dirac nodal line phonons, and drumhead-like and torus phonon surface states in orthorhombic-type KCuS

Symmetry-enforced fourfold degenerate phonons in noncentrosymmetric space groups

Multifold degenerate phonons have received much attention due to their nontrivial monopole topological charge and fascinating boundary states. Although Yuet alrecently provides a comprehensive list of all potential nodal points for systems with specific space groups (SGs) (2022Sci. Bull.67375). However, our understanding of the fundamental mechanisms that give rise to the formation of fourfold-degenerate (FD) phonons is still limited. In this paper, we have directed our research towards investigating the generation mechanism of these FD phonons in noncentrosymmetric SGs. Using symmetry arguments andk⋅pmodel analysis, we have classified them into two categories: the first origins from the commutation/anticommutation relation of the little cogroup operations, and the second associates to the combination of threefold rotation, mirror and time-reversal symmetries. Moreover, the band dispersions of the FD phonons in the first group are required to be linear, whereas the band dispersions of the FD phonons in the second category may be quadratic. On the basis of first-principles calculations, we propose that K2Mg2O3and Na4SnSe4are representative candidates for the two categories, respectively. Furthermore, for each SG with fourfold degenerate phonons, we propose corresponding materials that must host the FD points. Our work not only deepens our understanding of the mechanisms underlying the formation of these FD phonons, but it also proposes practical materials for observing FD phonons in crystalline systems without inversion symmetry.

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; Pna2₁ LiAlSe₂ has a nodal-net phonon, which is composed of two nodal-chain phonons along the U-R and U-Z directions; Pnma NaMgH₃ has a nodal-chain phonon in the extended Brillouin zone (BZ), which comprises two Weyl nodal-ring phonons in the k_x-k_z and k_x-k_y planes. Moreover, P4₂/ncm AuBr has a nodal-cage phonon, which is composed of nodal-line phonons in the k_z = 0, k_z = π, k_x = 0, and k_y = 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.

Complex nodal structure phonons formed by open and closed nodal lines in CoAsS and Na2CuP solids

Topological phononic states with nodal lines have not only updated our knowledge of the phases of matter in a fundamental way, they have also become a major frontier research direction...