We demonstrate by breaking the $C_6$ symmetry for higher-order at-$\mathrm{\Gamma }$ bound states in the continuum (BICs) with topological charge $-2$ in photonic crystals (i) deterministic generation of off-$\mathrm{\Gamma }$ BICs from the at-$\mathrm{\Gamma }$ BIC and (ii) a variety of pair-creation and annihilation processes of circularly polarized states with opposite topological charges and the same handedness. To explain these phenomena, we introduce the handedness-wise topological charge quantized to a half-integer. The handedness-wise charge gives a unified picture of various phenomena involving BICs and circularly polarized states.

• Received 23 January 2020
• Accepted 22 June 2020
• Corrected 20 January 2021

DOI:https://doi.org/10.1103/PhysRevLett.125.053902