Photonic $\mathbb{Z}_2$ topological Anderson insulators

That disorders can bring about nontrivial topology is a surprising discovery in topological physics. As a typical example, Chern topological Anderson insulators have been realized in photonic systems, where the topological phases exist without symmetry protection. In this work, by taking TM and TE polarizations as pseudo-spin degrees of freedom, we go further to realize disorder-induced symmetry-protected topological (SPT) phase transitions in two-dimensional photonic crystals (PCs) with a combined time-reversal, mirror and duality symmetry $\mathcal{T}_f=\mathcal{T}M_z\mathcal{D}$. In particular, we demonstrate that the disorder-induced SPT phase persists even without spin conservation (SC), thereby realizing a photonic $\mathbb{Z}_2$ topological Anderson insulator, in contrast to a $\mathbb{Z}$-classified quantum spin Hall (QSH) Anderson insulator with SC. By formulating a new scattering approach, we show that the topology of QSH and $\mathbb{Z}_2$ Anderson insulators can be manifested and differentiated by the accumulated spin rotations of the reflected waves from the PCs. Using a transmission structure, we also illustrate the trivialization of a disordered QSH phase with an even topological index caused by spin coupling.