Non-Hermitian Photonic Spin Hall Insulators

TL;DR

This paper explores non-Hermitian effects on photonic topological insulators, demonstrating resilience of spin Chern phases and discovering a topological phase transition influenced by material dissipation.

Contribution

It introduces a classification of non-Hermitian, $ ext{P} ext{D}$-symmetric, reciprocal photonic insulators and analyzes a specific waveguide system revealing a topological phase transition due to loss.

Findings

Identification of two topologically distinct classes of non-Hermitian photonic insulators.

Discovery of a critical loss level inducing a topological phase transition.

Existence of an infinite number of edge states within the band gap.

Abstract

Photonic platforms invariant under parity ($\mathcal{P}$), time-reversal ($\mathcal{T}$), and duality ($\mathcal{D}$) can support topological phases analogous to those found in time-reversal invariant ${\mathbb{Z}_2}$ 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, $\mathcal{P}\mathcal{D}$-symmetric, and reciprocal photonic insulators fall into two topologically distinct classes. Our analysis focuses on the topology of a $\mathcal{P}\mathcal{D}$-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 $\mathcal{P}\mathcal{T}\mathcal{D}$-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.