Fig. 2: Design and construction of a Floquet higher-order topological insulator in an acoustic lattice.

a Tight-binding model and driving protocol. The drive consists of four steps with equal duration T/4, where T is the driving period. The order of the four steps is indicated by the green arrows. In each step, one lattice site couples to one of its four neighbouring sites. The coupling strength is γ in steps 1, 2 and 4, and θ in step 3. The dotted square in step 1 indicates the unit cell. b Numerically obtained quasienergy spectrum with θ = γ = 0.841π. c Photo of the fabricated acoustic structure that realises the tight-binding model in a. Here the z axis plays the role of time. The lattice constant \(a=20\sqrt{2}\ {{{{{{{\rm{mm}}}}}}}}\). The coupling strength θ = γ = 0.841π is accomplished by thin connecting channels that are not visible in the photo. d Measured acoustic intensity distributions at different evolution distances at 8000 Hz. The green arrow indicates the excitation position at z/L = 0.