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 ($\cal T$) 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 \emph{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 $\Gamma$ and \emph{P}, respectively, and exhibit exotic quadruple surface states. More than these, the topological phononic nodal links also appear around the point $\Gamma$, 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.

The type-I, III nodal ring, type-I, III quadratic nodal point, and Dirac valley phonons in 2D kagome lattices M2C3 (M = As, Bi, Cd, Hg, P, Sb, Zn)

“…To date, different Chern numbers of Weyl phonons have been predicted in the phononic systems, including single Weyl phonons with the topological charges C = ±1 [22,26], charge-two Weyl phonons with C = ±2 [27], chargethree Weyl phonons with C = ±3 [28,29] and charge-four Weyl phonons with C = ±4 [23]. In addition, the nodal lines phonons are also predicted in realistic materials, such as the nodal rings phonons [22,30], nodal net phonons [31], and nodal links phonons [32]. The nodal surface phonons are also studied in the phononic systems, such as the one-nodal surface phonons [33], the two-nodal surface phonons [34], and the three-nodal surface phonons [35].…”