Section Chern number for a 3D photonic crystal and the bulk-edge correspondence

TL;DR

This paper introduces the section Chern number for 3D photonic crystals, linking Weyl points to topological invariants and discussing the bulk-edge correspondence in systems with broken inversion symmetry.

Contribution

It defines and calculates the section Chern number in 3D photonic crystals, demonstrating its relation to Weyl points and the bulk-edge correspondence.

Findings

Weyl points cause discontinuous jumps in the section Chern number.

A divergence-free Gaussian basis set effectively computes the section Chern number.

The bulk-edge correspondence holds in 3D photonic crystals with broken inversion symmetry.

Abstract

We have characterized the robust propagation modes of electromagnetic waves in helical structures by the section Chern number that is defined for a two-dimensional (2D) section of the three- dimensional (3D) Brillouin zone. The Weyl point in the photonic bands is associated with a dis- continuous jump of the section Chern number. A spatially localized Gaussian basis set is used to calculate the section Chern numbers where we have implemented the divergence-free condition on each basis function in 3D. The validity of the bulk-edge correspondence in a 3D photonic crystal is discussed in relation to the broken inversion symmetry.