Three-dimensional higher-order topological insulator protected by cubic symmetry

TL;DR

This paper proposes a three-dimensional cubic-symmetric photonic topological insulator with corner states arising from long-range interactions, expanding the understanding of higher-order topological phases beyond two dimensions.

Contribution

It introduces a novel 3D structure with cubic symmetry exhibiting topologically protected corner states mediated by long-range couplings, with topological invariants calculated to confirm their origin.

Findings

Corner states are demonstrated in a 3D cubic structure.

Long-range interactions are crucial for the formation of these states.

Topological invariants confirm the topological nature of the corner modes.

Abstract

Recently discovered photonic higher-order topological insulators enable unprecedented flexibility in the robust localization of light in structures of different dimensionality. While the potential of the two-dimensional systems is currently under active investigation, only a few studies explore the physics of the three-dimensional higher-order topological insulators. Here we propose a three-dimensional structure with cubic symmetry exhibiting vanishing bulk polarization but nonzero corner charge and hosting a zero-dimensional corner state mediated by the long-range interactions. We trace the evolution of the corner state with the next-nearest-neighbor coupling strength and prove the topological origin of the corner mode calculating the associated topological invariants. Our results thus reveal the potential of long-range couplings for the formation of three-dimensional higher-order topological phases.