Accidental degeneracy and topological phase transitions in two-dimensional core-shell dielectric photonic crystals

TL;DR

This paper investigates how accidental degeneracies in a 2D core-shell photonic crystal lead to topological phase transitions, revealing critical states and photonic quantum spin Hall effects relevant for optical applications.

Contribution

It systematically analyzes accidental nodal points and their topological properties in a 2D photonic crystal, demonstrating topological phase transitions and edge state behaviors.

Findings

Identification of accidental nodal points with topological significance

Observation of topological phase transitions in photonic bands

Potential for realizing photonic quantum spin Hall insulators

Abstract

A simple core-shell two-dimensional photonic crystal is studied where the triangle lattice symmetry and $C_{6v}$ rotation symmetry leads to rich physics in the study of accidental degeneracy's in photonic bands. We systematically evaluate different types of accidental nodal points, depending on the dispersions around them and their topological properties, when the geometry and permittivity are continuously changed. These accidental nodal points can be the critical states lying between a topological phase and a normal phase and are thus important for the study of topological photonic states. In time-reversal systems, this leads to the photonic quantum spin Hall insulator where the spin is defined upon the orbital angular momentum for transverse-magnetic polarization. We study the topological phase transition as well as the properties of the edge and bulk states and their application potentials in optics.