# Manipulation of Topological Edge States and Realization of Zero-Dimensional Higher-Order Topological Point States

## TL;DR

This paper introduces a honeycomb photonic crystal structure that enables precise control of topological edge states and robust corner states for advanced photonic devices.

## Contribution

A new mechanism for manipulating topological edge states via mirror-symmetric interfaces and inducing topological phase transitions.

## Key findings

- Adjusting coupling pillar spacing causes energy band closure and reopening with band inversion, indicating topological phase transitions.
- Zero-dimensional high-order topological corner states are observed with strong field confinement and robustness against defects.

## Abstract

Topological photonics has provided revolutionary ideas for the design of next-generation photonic devices due to its unique light transmission properties. This paper proposes a honeycomb photonic crystal structure based on a mirror-symmetric interface and numerically simulates the precise manipulation of topological edge states and the robust excitation of high-order topological corner states in this structure. Specifically, two honeycomb photonic crystals with non-trivial topological properties form an interface through mirror-symmetric stitching. Continuous adjustment of the spacing between their coupling pillars can induce the closure and reopening of topological edge state energy bands, accompanied by significant band inversion, revealing the dynamic process of topological phase transitions. Furthermore, zero-dimensional high-order topological corner states are observed at the junction of boundaries with different topological properties. Their localized field strengths are strictly confined and exhibit strong robustness against structural defects. This study not only provides a new mechanism for the local symmetry manipulation of topological edge states but also lays a foundation for the design of high-order topological photonic crystals and the practical application of topological photonic devices.