Figure 4.

Gap functions ${\Delta }_0$ (red solid lines) and ${\Delta }_{\pi }$ (blue dashed lines) versus the imaginary part of vertical and diagonal hopping amplitudes $J_y^i$ and $J_d^i$ in panels (a,b), respectively. The system parameters are $(J_x,J_y^r,J_d,V)=(0.5\pi ,1.5\pi ,4\pi ,0.1\pi )$ for panel (a) and $(J_x,J_y,J_d^r,V)=(0.5\pi ,0.6\pi +6\mathrm{i},4\pi ,0.1\pi )$ for panel (b). The number of quartets of zero and $\pi$ edge modes $(n_0,n_{\pi })$ are denoted explicitly near ${\Delta }_0={\Delta }_{\pi }=0$ in both panels, which are related to the winding numbers $(w_0,w_{\pi })$ through the relations in Equation (21). The ticks along the horizontal axis denote the bulk gap closing points, whose numerical values are $(y_1^{\pi },y_1^0,y_2^0,y_2^{\pi },y_3^{\pi },y_3^0)\approx (1.09,2.14,3.02,3.97,5.05,6.47)$ in panel (a) and $(d_1,d_2)\approx (1.86,2.41)$ in panel (b).