20 May, 2024 | Xiaotian Wang†, Jingbo Bai†, Jianhua Wang†, Zhenxiang Cheng*, Shifeng Qian*, Wenhong Wang, Gang Zhang, Zhi-Ming Yu*, Yugui Yao (†These authors contributed equally to this work.)
This study investigates the real topological phononic states in 3D carbon allotropes, focusing on materials with space-time inversion symmetry ($\mathcal{PT}$) and lacking spin-orbit coupling. By analyzing the phonon spectra of 1192 3D carbon allotropes from the Samara Carbon Allotrope Database (SACADA), the authors identify 65 systems with a phononic real Chern insulating (PRCI) state, 2 with a phononic real nodal line (PRNL) state, 10 with a phononic real Dirac point (PRDP) state, and 8 with a phononic real triple-point pair (PRTPP) state. These findings expand the known material candidates for real topology, particularly for gapless topological phonons. The study highlights the potential of 3D carbon allotropes as a valuable platform for exploring phononic hinge modes and real topology, emphasizing the importance of $\mathcal{PT}$-symmetric searches to identify material samples with real topology across the entire phonon spectrum. The research provides a comprehensive classification of real topological phonons and demonstrates the existence of second-order phononic hinge states in 3D systems, with specific examples of 27-SG, 166-pcu-h, 1081-SG, 194-4²T13-CA, 52-SG, 141-gis, and 132-SG. 191-3,4T157 being ideal candidates for these states.This study investigates the real topological phononic states in 3D carbon allotropes, focusing on materials with space-time inversion symmetry ($\mathcal{PT}$) and lacking spin-orbit coupling. By analyzing the phonon spectra of 1192 3D carbon allotropes from the Samara Carbon Allotrope Database (SACADA), the authors identify 65 systems with a phononic real Chern insulating (PRCI) state, 2 with a phononic real nodal line (PRNL) state, 10 with a phononic real Dirac point (PRDP) state, and 8 with a phononic real triple-point pair (PRTPP) state. These findings expand the known material candidates for real topology, particularly for gapless topological phonons. The study highlights the potential of 3D carbon allotropes as a valuable platform for exploring phononic hinge modes and real topology, emphasizing the importance of $\mathcal{PT}$-symmetric searches to identify material samples with real topology across the entire phonon spectrum. The research provides a comprehensive classification of real topological phonons and demonstrates the existence of second-order phononic hinge states in 3D systems, with specific examples of 27-SG, 166-pcu-h, 1081-SG, 194-4²T13-CA, 52-SG, 141-gis, and 132-SG. 191-3,4T157 being ideal candidates for these states.