Energy gaps Δ_n versus the amplitudes V₀ of the barrier potential at different time points ωt = 0 (blue), π/8 (red), π/4 (yellow), 3π/8 (purple), π/2 (green). Panels (a)–(f) correspond to n=1–6 gaps with V_SAW = 30E_R. The zeros of the curves indicate that the gaps vanish. As a comparison, panels (g) and (h) respectively illustrate Δ₅ and Δ₆ for a larger SAW amplitude V_SAW = 60E_R where the 6th gap is reopened because of nonzero Δ₆. It means that the amplitude of the SAW modifies the topology of the energy bands.