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

TL;DR

This paper demonstrates that topological edge modes in photonic crystals can exist even with zero Berry curvature, showing their evolution from honeycomb to triangular lattices and highlighting low-loss propagation.

Contribution

It reveals the existence of zero-Berry-curvature edge modes in triangular lattice photonic crystals and explores their evolution from honeycomb structures, expanding understanding of topological photonics.

Findings

Zero-Berry-curvature edge modes exist in triangular lattice photonic crystals.

Edge modes can propagate with extremely low bending loss.

Topological edge modes persist across different lattice symmetries.

Abstract

The presence of topological edge modes at the interface of two perturbed honeycomb photonic crystals with $C_6$ 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 finite values 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 $C_3$ symmetry is maintained but inversion symmetry is broken. We investigate the evolution of the Berry curvature from the honeycomb-lattice photonic crystal slab to the triangular-lattice photonic crystal slab and show that the triangular-lattice photonic crystals still support edge modes in a very wide photonic bandgap. Additionally, we find that the edge modes with zero Berry curvature can propagate with extremely low bending loss.