Breakdown of topological phases due to periodic perturbation in a gyromagnetic photonic crystals

In the known field of topological photonics, what remains less so is the breakdown effect of topological phases deteriorated by perturbation. In this paper, we investigate the variance on topological invariants for a periodic Kekul\'e medium perturbed in unit cells, which is a gyromagnetic photonic crystal holding topological phases induced by \emph{synchronized rotation} of unit cells. Two parameters for geometric and material perturbation are respectively benchmarked to pinpoint the topological degradation. Our calculation demonstrates that such a periodic perturbation easily destructs the original topological phase, and thus calls for further checkups on robustness under such unit-cell-perturbation in possible realization.