Topological phonons in allotropes of carbon

Carbon, as one of the earliest light elements ingrained and used by humans, constructs abundant varieties of allotropic phases to exhibit rich physical features. To explore further their inspiring physical properties, in this work, by using symmetry analyses and first-principles calculations, we uncover that no less than eighteen allotropic phases of carbon can exhibit topologically nontrivial phonons, which include zero-dimensional types (i.e., single Weyl, spin-1 Weyl, and charge-2 Weyl phonons, WPs), one-dimensional types (i.e., nodal-link, nodal-chain, and various open straight nodal-line phonons) and two-dimensional types (one-nodal surface phonons). More importantly, several novel topological features are revealed in them: (i) the spin-1 WPs are compensated by the monopole single WPs in K6-Carbon, and the induced double-helicoid surface arcs appear clearly; (ii) the nodal-link or -chain phonons induced drumhead-like surface states are observed in some carbon allotropes and (iii), carbon allotropes provide us the first realistic material sample, i.e., Superprismane-Carbon, to realize the coexistence of one-nodal surface phonons and nearly perfect straight nodal-lines phonons. Our theoretical results not only propose various carbon allotropes exhibiting novel topological phonons, but also provide many ideal material samples to study topological phonons in light-element systems.