Searching for topological carbon allotropes and the possible nontrivial quasi-particle states in them

Abstract

Carbon, as one of the most abundant elements on earth, possesses numerous allotropes that display a diverse range of physical properties. In this study, we utilized ab initio calculations and symmetry analyses to investigate 703 carbon allotropes, leading to the discovery of 315 (32) topological phononic (electronic) materials with ideal nontrivial characteristics. The topological phonons encompass single, charge-two, three, and four Weyl phonons, as well as Dirac (Weyl) node-lines phonons. Topological electronic states include topological insulators, Dirac points (Type-II), triple nodal points, and more. To verify this significant discovery, we adopt several real carbon allotropes with $uni$ ($pbg$) structure within space group (SG) No 178 (230) to showcase their topological characteristics. The $uni$ structure exhibits a combination of single-pair Weyl phonons and one-nodal surface phonons, resulting in a single surface arc in the (100) surface Brillouin zone (BZ) and isolated double-helix surface states in the (110) surface BZ. In the topological semimetal $pbg$, perfect triple degenerate nodal points near the Fermi level are found, resulting in distinct surface states in the (001) and (110) surfaces BZ. This research not only significantly broadens our understanding of topological quasi-particle states in carbon allotropes, but also offer a valuable material platform for further exploration of topological electrons and phonons in light element materials.