Fig. 3. Topological forces with perturbation.

(A) Force distribution around lower-band BIC with untwisted PhCS when the nanosphere is displaced 100 nm along positive x axis. (B) Force distribution around lower-band BIC when the nanosphere is displaced both 100 nm along positive x axis and 100 nm along positive y axis. (C) Map of F_x in momentum space when the nanosphere is displaced 100 nm along positive x axis. The arrow indicates the shift of F_x = 0. (D) F_x as a function of k_x at k_y = 0 with the nanosphere displaced 50 and 100 nm along positive x axis. The optical forces in (C) and (D) are normalized to a value of F₀ = 10⁻¹⁶N. Force distribution above the PhCS around (E) lower-band BIC and (F) upper-band BIC when the PhCS has a rotation angle with α_top = 25° and α_bot = 0°. Insets in (E) show the structure of the perturbed PhCS.