# Circular edge states in photonic crystals with a Dirac node

## TL;DR

This paper investigates circular edge states in photonic crystals with a Dirac node, analyzing their polarization and Berry curvature properties, and how these are affected by boundary conditions and internal edges.

## Contribution

It introduces a detailed analysis of polarization vortex structures and Berry curvature in circular geometries with Dirac points, highlighting boundary condition effects.

## Key findings

- Polarization vortex structures form near the Dirac node.
- Berry curvature is sensitive to boundary conditions.
- Edge states are robust against internal step-like edges.

## Abstract

Edge states are studied for the two-dimensional Dirac equation in a circular geometry. The properties of the two-component electromagnetic field are discussed in terms of the three-component polarization field, which can form a vortex structure near the Dirac node with a vorticity changing with the sign of the Dirac mass. The Berry curvature of the polarization field is related to the Berry curvature of the Dirac spinor state. This quantity is sensitive to a change of boundary conditions. In particular, it vanishes for a geometry with a single boundary but not for a geometry with two boundaries. This effect is robust against the creation of a step-like edge inside the sample.