Figure 8: Analytical acoustic band structure.

(a) Acoustic band structure of the tight-binding Hamiltonian equation (1) without temporal modulation (δω=0). The parameters used are ν₀=ω₀/2π=31.13 kHz, κ=0.3ν₀ and J=0.7 × 10⁻²ν₀. (b) Acoustic band structure obtained from the effective Hamiltonian describing the stroboscopic evolution of the system. Cases without the temporal modulation (δν=0, blue solid lines) and with the temporal modulation (δν=0.036ν₀, red dashed lines) are shown. The parameters used are the same as in a, with the modulation frequency ν_m=ω_m/2π=3 kHz.