Three-dimensional photonic Dirac points stabilized by point group symmetry

TL;DR

This paper reports the discovery of stable three-dimensional Dirac points in all-dielectric photonic crystals with specific symmetry, exhibiting nontrivial topology and robustness, which could enable advanced photonic applications.

Contribution

It identifies the conditions under which 3D photonic Dirac points are stabilized by point group symmetry, especially $C_6$, and characterizes their topological and physical properties.

Findings

Dirac points exhibit nontrivial $Z_2$ topology.

Dirac points are stabilized by $C_6$ symmetry.

Breaking inversion symmetry creates Weyl points.

Abstract

We discover a pair of stable 3D Dirac points, 3D photonic analog of graphene, in all-dielectric photonic crystals using structures commensurate with nano-fabrication for visible-frequency photonic applications. The Dirac points carry nontrivial $Z_2$ topology and emerge for a large range of material parameters in hollow cylinder hexagonal photonic crystals. From Kramers theorem and group theory, we find that only the $C_6$ symmetry lead to point group symmetry stabilized Dirac points in 3D all-dielectric photonic crystals. {The Dirac points are characterized using ${\vec k}\cdot{\vec P}$ theory for photonic bands in combination with symmetry analysis. Breaking inversion symmetry splites the Dirac points into Weyl points. The physical properties and experimental consequences of Dirac points are also studied. The Dirac points are found to be robust against parameter tuning and weak disorders.