Time-Reversal-Violating Photonic Topological Insulators with Helical Edge States

We theoretically demonstrate the realization of photonic topological insulators in photonic crystals made of circular cylinders with the Tellegen-type magnetoelectric coupling as a photospin–orbit interaction. Although the magnetoelectric coupling breaks the conventional (bosonic) time-reversal symmetry for photons, the electromagnetic duality between permittivity and permeability gives rise to a fermionic time-reversal symmetry. This symmetry along with the space-inversion symmetry enables us to imitate the Kane–Mele model of two-dimensional topological insulators in a photonics platform. Even if the space-inversion symmetry is broken, a photonic topological insulator can emerge owing to the photospin–orbit interaction. We present bulk and edge properties of the photonic topological insulators and discuss their possible realization.