Berry bands and pseudo-spin of topological photonic phases

Samuel J Palmer,Vincenzo Giannini

doi:10.1103/physrevresearch.3.l022013

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.

Highlights

When guiding light on the nanoscale, impurities, imperfections, and sharp corners can scatter light in unintended ways and limit the performance of photonic devices
Nontrivial topological phases were first observed in the electronic bands of atomic crystals [2,3,4,5,6,7], photonic analogs of topological phases such as the quantum Hall effect (QHE) [8,9] and symmetry-protected phases such as the quantum spin-Hall effect (QSHE) [2,3,4] have been built using photonic crystals: periodic nanostructures with tunable photonic bands [10,11]
For example, the well-known crystal of Wu and Hu shown in Fig. 1(c) where the spectra of Wilson loops applied directly to the energy bands imply the existence of corner states but not necessarily helical edge states [36,37], we show that taking Wilson loops of the Berry bands reveals the photonic analogy to the QSHE

Summary

Introduction

When guiding light on the nanoscale, impurities, imperfections, and sharp corners can scatter light in unintended ways and limit the performance of photonic devices This unintended scattering could be reduced if light can be guided using the robust, unidirectional states that arise at the surfaces of crystals with nontrivial band topologies. The photonic QHE has robust surface states, but requires time-reversal symmetry to be broken [12,13,14,15]. An elegant photonic analog of the QSHE was proposed by Wu and Hu [21] where the angular momentum of light mimics the spin space of the electrons, and crystalline symmetries produce a fermionic pseudo-time-reversal symmetry that protects the edge states at.

Published by the American Physical Society

Findings

Conclusion