Evolution of topological edge modes from honeycomb photonic crystals to triangular-lattice photonic crystals

The presence of topological edge modes at the interface two perturbed honeycomb photonic crystals with $C_6$ symmetry is often attributed to different signs Berry curvature K and K$'$ valleys. In contrast electronic counterpart, Chern number defined in valley Hall effect not a quantized quantity but can be tuned finite values including zero simply by changing geometrical perturbations. Here, we argue that exist even when vanishes. We numerically demonstrate zero-Berry-curvature triangular lattice crystal slab structures which $C_3$ maintained inversion broken. investigate evolution from honeycomb-lattice triangular-lattice show still support very wide bandgap. Additionally, find propagate extremely low bending loss.