On the robustness of topological corner modes in photonic crystals

TL;DR

This paper investigates the robustness of topological corner modes in photonic crystals, demonstrating their protection by lattice symmetries despite long-range interactions breaking chiral symmetry.

Contribution

It provides a detailed analysis of topological corner modes in a $C_6$-symmetric photonic crystal, including effects of long-range interactions and symmetry protection mechanisms.

Findings

Corner modes are protected by lattice symmetries.

Long-range interactions break chiral symmetry but do not destroy corner modes.

Topological properties originate from an obstructed atomic limit phase.

Abstract

We analyze the robustness of corner modes in topological photonic crystals, taking a $C_6$-symmetric breathing honeycomb photonic crystal as an example. First, we employ topological quantum chemistry and Wilson loop calculations to demonstrate that the topological properties of the bulk crystal stem from an obstructed atomic limit phase. We then characterize the topological corner modes emerging within the gapped edge modes employing a semi-analytical model, determining the appropriate real space topological invariants. For the first time, we provide a detailed account of the effect of long-range interactions on the topological modes in photonic crystals, and we quantify their robustness to perturbations. We conclude that, while photonic long-range interactions inevitably break chiral symmetry, the corner modes are protected by lattice symmetries.