Figure 2. Topological edge modes of acoustic Floquet topological insulators.

(a) Acoustic quasi-band structure for a supercell composed of a 1-by-6 array of unit cells, terminated by a hard-wall boundary at the top and bottom, and periodic boundary conditions along x. Blue dots refer to bulk modes. Green (red) dots refer to edge modes localized at the top (bottom) boundary of the supercell. (b–d) Acoustic pressure-field distribution for the three dominant harmonic components of an edge mode localized at the top boundary: component at ω−ω_m (b), ω (c) and ω+ω_m (d), where ω=21.9 kHz is the quasi-frequency. (e) Acoustic band structure for a supercell composed of a 1-by-6 array of unit cells supporting a domain wall at the centre: the modulation of the three unit cells at the bottom is right handed, and at the top it is left handed. The supercell is surrounded by periodic boundary conditions in all directions. Blue dots refer to bulk modes. Red and green dots refer to edge modes localized at boundaries with opposite handedness, as represented in the inset. (f–h) Same as b–d, but in the case of a domain wall boundary at the supercell centre.