(a) The illustration of vortex-lattice: the distance between two nearest vortices is 6a. The parameters are chosen as u = −4t_s, λ = 0.5t_s, h = 0.8t_s, Δ = 0.5t_s. Each vortex traps a Majorana mode. (b) The DOS of TSC with square vortex-lattice: the mid-gap states are induced by the vortex-lattice. The inset shows the details of the mid-gap energy band. (c) The spectrum flow of TSC with square vortex-lattice on a cylinder for the case of u = −4t_s, h = 0.8t_s, λ = 0.5t_s, Δ = 0.5t_s. There exist gapless edge states. (d) The spectrum flow of non-topological SC with square vortex-lattice on a cylinder for the case of u = −4t_s, h = 0.8t_s, λ = 0.5t_s, Δ = 0.5t_s. There exist no edge states. From Ref. [15].