Topological edge states in all-dielectric square-lattice arrays of bianisotropic microwave resonators

We demonstrate that a bianisotropic response associated with a broken mirror symmetry of a dielectric resonator allows opening a band gap in simple square lattice arrays of such resonators. Realizing the proposed system as an array of high-index ceramic resonators working at GHz frequencies, we numerically and experimentally demonstrate the presence of topological edge states at the interface between two domains with opposite orientations of the bianisotropic resonators, as well as at the boundary between a single domain and free space. For both cases, we experimentally characterize the dispersion of edge states, and we examine their propagation along sharp bends, their resilience to various types of geometrical defects, and a spin-momentum-locked unidirectional propagation in the case of circularly polarized excitation. Also, we develop a theoretical model based on a Green's function approach that describes the square lattice of resonators and features a quadratic degeneracies in the vicinity of $\mathrm{\ensuremath{\Gamma}}$ and $M$ high-symmetry points that are removed upon the introduction of bianisotropy, and apply this model to evaluate Berry curvature. The considered design extends possibilities in the construction of optical and microwave structures simultaneously featuring topological edge states at the interfaces between distinct resonator domains or a resonator domain and free space.