Wilson Loop and Topological Properties in 3D Woodpile Photonic Crystal

TL;DR

This paper investigates topological electromagnetic states in 3D woodpile photonic crystals, introduces a Wilson loop-based method for calculating topological invariants, and discusses conditions for topological hinge states, aiding experimental realization.

Contribution

It presents a novel numerical method for calculating topological invariants in 3D photonic crystals and analyzes the emergence of topological states and hinge states.

Findings

Topological states arise from differences in winding or Chern numbers.

A Wilson loop-based calculation method for topological invariants is proposed.

Selection rules for topological hinge states are identified.

Abstract

We numerically study the first and the second order topological states of electromagnetic (EM) wave in the three-dimensional (3D) woodpile photonic crystal (PhC). The recent studies on 3D PhCs have mainly focused on the observation of the topological states. Here, we not only focus on finding the topological states but also propose a numerical calculation method for topological invariants, which is based on the Wilson loop. For the 3D woodpile PhC, the topological states emerge due to the finite difference in the winding number or partial Chern number. The selection rule for the emergence of topological hinge states is also pointed out based on the topological invariants. Our numerical calculation results are essential and put a step toward the experimental realization of topological waveguide in 3D PhCs.