Real Topological Phonons in 3D Carbon Allotropes

There has been a significant focus on real topological systems that enjoy space-time inversion symmetry and lack spin-orbit coupling. While the theoretical classification of the real topology has been established, more progress has yet to be made in the materials realization of real topological phononic states in 3D. To address this crucial issue, high-throughput computing is performed to inspect the real topology in the phonon spectrums of the 3D carbon allotropes. Among 1661 carbon allotropes listed in the Samara Carbon Allotrope Database (SACADA), 79 candidates host a phononic real Chern insulating (PRCI) state, 2 candidates host a phononic real nodal line (PRNL) state, 12 candidates host a phononic real Dirac point (PRDP) state, and 10 candidates host a phononic real triple-point pair (PRTPP) state. The PRCI, PRNL, PRTPP, and PRDP states of 27-SG. 166-pcu-h, 1081-SG. 194-4²T13-CA, 52-SG. 141-gis, and 132-SG. 191-3,4T157 are exhibited as illustrative examples, and the second-order phononic hinge modes are explored. This study broadens the understanding of 3D topological phonons and expands the material candidates with phononic hinge modes and phononic real topology.