Boundary-dominated photonic Chern insulators with hyperbolic lattice geometry

The photonic Chern insulator without time-reversal symmetry has received great attention in recent years because it possesses truly backscattering-immune one-way edge modes, which are robust against any local perturbations and play crucial roles in robustly controlled electromagnetic fields. However, the implementation of topological boundary channels necessitates a substantial number of trivial bulk domains, significantly limiting the utilization efficiency of topological photonic structures. In this work, we theoretically propose and numerically demonstrate the construction of photonic Chern insulators with yttrium-iron-garnet cylinders with hyperbolic lattices, which are regular tessellations in non-Euclidean space with constant negative curvature. In particular, two types of hyperbolic lattices, the dice and kagome hyperbolic lattices, are applied to design the photonic Chern insulators. Interestingly, we demonstrate that magnetic photonic crystals with hyperbolic lattice can support boundary-dominated one-way edge modes with nontrivial real-space Chern numbers even with significantly reduced bulk sites compared to that of traditional photonic Chern insulators. Our work extends photonic Chern insulators into the non-Euclidean space, and is anticipated to have potential applications in designing highly efficient photonic devices with strong robustness.