Combinatorics

Physics

Bound state

Topology (electrical circuits)

Charge (physics)

Annihilation

Symmetry breaking

Geometry

Symmetry (geometry)

Theoretical physics

Mathematics

Quantum mechanics

Topological quantum number

Physical Review Letters

We demonstrate by breaking the ${C}_{6}$ symmetry for higher-order at-$\mathrm{\ensuremath{\Gamma}}$ bound states in the continuum (BICs) with topological charge $\ensuremath{-}2$ in photonic crystals (i) deterministic generation of off-$\mathrm{\ensuremath{\Gamma}}$ BICs from the at-$\mathrm{\ensuremath{\Gamma}}$ 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.

Generation and Annihilation of Topologically Protected Bound States in the Continuum and Circularly Polarized States by Symmetry Breaking