Fig. 3. Characterization of the NH topology.

a Loop traversed for extracting the winding number. The loop (gray solid line) is square-shaped with four vertices (0, 0), (λ_m, 0), (0, λ_m), and (λ_m, λ_m), where λ_m = 2π × 1 MHz. This loop surrounds an EP3 (red star), which connects two Fermi arcs consisting of EP2s (blue solid line). The arrow denotes the direction of the integral along the loop. b, e Normalized resultant vectors measured against λ₁ with λ₂ = 0 (b) and λ_m (d), and against λ₂ with λ₁ = λ_m (c) and 0 (e). The squares represent the components ${\mathcal{R}}_1/\mid \mathcal{R}\mid$ (blue) and ${\mathcal{R}}_2/\mid \mathcal{R}\mid$ (orange), respectively. The dotted lines denote the fitted ${\mathcal{R}}_1/\mid \mathcal{R}\mid$ and ${\mathcal{R}}_2/\mid \mathcal{R}\mid$ as functions of λ₁ or λ₂. The winding number, calculated with these fitted functions, is 1. f Trajectory of the rescaled unit resultant vector ${\mathcal{R}}^u=\left({\mathcal{R}}_1+i{\mathcal{R}}_2\right)/\mid \mathcal{R}\mid$. The symbols “1'', “2'', “3'', and “4'', label the sections associated with the four edges of the parameter-space loop, shown in (b–e), respectively.