Non-Hermitian $\mathbb{Z}_2$ Photonic Topological Insulators

Photonic platforms invariant under the action of parity, time-reversal, and duality ($\mathcal{P} \cdot \mathcal{T} \cdot \mathcal{D}$) operators may host topological phases that are the counterpart of those supported by time-reversal invariant $\mathbb{Z}_2$ electronic systems. Here, we uncover the robustness of the $\mathbb{Z}_2$ photonic phases to non-Hermitian effects, e.g., to material dissipation. In particular, it is shown that non-Hermitian $\mathcal{P} \mathcal{D}$-reciprocal photonic insulators may be split into two classes of topologically inequivalent materials, whose interfaces may support spin-polarized states. To illustrate our theory, we study in detail how the non-Hermitian effects may sculpt the topology of a $\mathcal{P} \mathcal{D}$-symmetric parallel-plate waveguide (PPW). We find that there is a critical level for the plates loss that separates two different topological phases. We identify the phases by their spin Chern numbers and analyze the transition.