Non-Hermitian photonic spin Hall insulators

Photonic platforms invariant under parity (P), time-reversal (T), and duality (D) can support topological phases analogous to those found in time-reversal invariant Z₂ electronic systems with conserved spin. Here, we demonstrate the resilience of the underlying spin Chern phases against non-Hermitian effects, notably material dissipation. We identify that non-Hermitian, PD-symmetric, and reciprocal photonic insulators fall into two topologically distinct classes. Our analysis focuses on the topology of a PD-symmetric and reciprocal parallel-plate waveguide (PPW). We discover a critical loss level in the plates that marks a topological phase transition. The Hamiltonian of the PTD-symmetric system is found to consist of an infinite direct sum of Kane-Mele-type Hamiltonians with a common band gap. This structure leads to the topological charge of the waveguide being an ill-defined sum of integers due to the particle-hole symmetry. Each component of this series corresponds to a spin-polarized edge state. Our findings present a unique instance of a topological photonic system that can host an infinite number of edge states in its band gap.