Topological nodal-link phonons, three-fold, Dirac and six-fold nodal-point phonons in the insulator SiO₂

Abstract By using first-principles calculations and symmetry analysis, we study the topologically nontrivial features of sextuple nodal-point phonons together with other kinds of topological phonons in realistic materials. The sextuple nodal-point phonons in all 230 space groups, enumerated in this paper, are localized at the boundaries of the three-dimensional Brillouin zone (BZ), and protected both by time-reversal symmetry ( ) and little-group symmetries. Moreover, in a realistic material sample of insulator SiO 2 , we find that the sextuple nodal-point phonons exist at the high-symmetry point H of the first BZ, and generate four-fold surface states. Interestingly, owing to the special crystal symmetries in SiO 2 , triple nodal-point phonons and Dirac phonons exist at the point Γ and P , respectively, and exhibit exotic quadruple surface states. More than these, the topological phononic nodal links also appear around the point Γ, and exhibit drumhead like surface states in this material. Our theoretical work not only proposes an effective way to search for multi-fold topological phonons including Dirac phonons and sextuple nodal-point phonons, but also presents a realistic material sample to realize the coexistence of multiple nodal-point and nodal-link phonons.