Fig. 5. Energy spectra for the bilayer topological system with the same periodically modulated on-site potentials.

a–c Energy spectra versus ϕ of a finite ladder with 30 sites for the same modulated amplitudes Δ_↑/2π = Δ_↓/2π = 12 MHz with J_⊥/2π = 1 MHz (a), J_⊥/2π = 7 MHz (b), and J_⊥/2π = 15 MHz (c). Other parameters used are J_∥/2π = 8 MHz, $J_{\parallel }^{\prime }=0.1J_{\parallel }$, and J_× = 0.2J_∥.