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

Abstract

The presence of edge modes at the interface of two perturbed honeycomb photonic crystals with C6 symmetry is often attributed to the different signs of Berry curvature at the K and K′ valleys. In contrast to the electronic counterpart, the Chern number defined in photonic valley Hall effect is not a quantized quantity but can be tuned to a finite value including zero simply by changing geometrical perturbations. Here, we argue that the edge modes in photonic valley Hall effect can exist even when Berry curvature vanishes. We numerically demonstrate the presence of the zero-Berry-curvature edge modes in triangular-lattice photonic crystal slab structures in which C3 symmetry is maintained but the inversion symmetry is broken. We investigate the evolution of the Berry curvature from the honeycomb-lattice slab structure to the triangular-lattice photonic crystal slab and show that the triangular-lattice photonic crystals still support edge modes in a very wide photonic band gap. We find that the edge modes with zero Berry curvature can propagate with extremely low bending loss along the interface formed by the triangular-lattice photonic crystals.