Fig. 1
From: Three-dimensional topological acoustic crystals with pseudospin-valley coupled saddle surface states

Band structure evolution. a Schematic of the crystal structure formed by stacked double-layer honeycomb lattices. Red and green colours represent two types of atoms. b The acoustic atom is constructed using a triangular prism cavity with tubes. Different atoms have different side lengths. c The schematic for one-half of the first Brillouin zone. d The band structures with identical acoustic atoms lg = lr = 0.7a (one-layer primary unit cell). e The case of a double-sized unit cell. f The band structures with two different acoustic atoms (lg = 0.6a and lr = 0.8a) possessing glide symmetry. Insets show schematics for the primary unit cells. The lower panels show the bulk bands projected onto kxy and kyz planes near the degenerate point (black dots)