3D 3,4⁴T19 Type Carbon Allotrope (3,4⁴T19‐CA): An Ideal Candidate with Phononic Stiefel–Whitney Topology and Multi–Dimensional Boundary Vibrational Modes

The Stiefel–Whitney (SW) insulator, which lacks spin‐orbit coupling and has space–time inversion () symmetry, has attracted significant interest due to its fragile topological state and unconventional bulk‐boundary correspondence. Previously, the identification of SW insulators has been widely proposed for 2D phononic systems, but it has received little attention for 3D phononic systems. Herein, it is recognized that the 3D 3,4 4 T19 type carbon allotrope (3,4 4 T19‐CA) possesses the possibility to attain the nontrivial phononic SW topology characterized by a nontrivial second SW number, specifically w 2 = 1. In addition, the 3D 3,4 4 T19‐CA has 2D surface vibrational modes and 1D hinge vibrational modes, providing an excellent platform for multi–dimensional topological phononic boundaries research.