Berry bands and pseudo-spin of topological photonic phases

TL;DR

This paper introduces a method to identify new symmetry-protected topological phases in photonic systems by reformulating energy eigenproblems as Berry curvature eigenproblems, revealing pseudo-spin structures in topological photonic crystals.

Contribution

It presents a novel approach to detect symmetry-protected topological phases via Berry bands, uniting theory and numerical methods in photonics and electronics.

Findings

Demonstrates the method on Wu & Hu's photonic crystal

Shows both crystals are in the same $ ext{C}_2 ext{T}$-protected $ ext{Z}_2$ topological phase

Provides a framework for identifying new topological phases

Abstract

Realising photonic analogues of the robust, unidirectional edge states of electronic topological insulators would improve our control of light on the nanoscale and revolutionise the performance of photonic devices. Here we show that new symmetry protected topological phases can be detected by reformulating energy eigenproblems as Berry curvature eigenproblems. The "Berry bands" span the same eigenspace as the original valence energy bands, but separate into pseudo-spinful and pseudo-spinless subspaces in $\mathrm{C}_2\mathcal{T}$-symmetric crystals. We demonstrate the method on the well-known case of Wu & Hu [Phys. Rev. Lett. 114, 223901 (2015)] and a recently discovered fragilely topological crystal, and show that both crystals belong to the same $\mathrm{C}_2\mathcal{T}$-protected $\mathbb{Z}_2$ topological phase. This work helps unite theory and numerics, and is useful in defining and identifying new symmetry-protected phases in photonics and electronics.