Three-Dimensional Topological States of Phonons with Tunable Pseudospin Physics
(a) Schematic evolution of I (blue) and O (red) vibrational bands near under the influence of intrinsic pseudo-SOC and Rashba-Dresselhause pseudo-SOC . The -induced pseudospin splittings of I and O vibrational bands have same (opposite) signs when (), which can result in phononic TIs or topological semimetals (TSMs) as summarized in the topological phase diagram (b). (c) Dispersion curves of a phononic topological nodal-ring semimetal. Blue (red) color is used to denote the contribution of I (O) vibrational modes. (d) Zak phases along the (001) direction of the lowest two bands for the 2D surface BZ. (e) LDOS of the (001) surface, where higher (lower) LDOS are colored red (blue).