Classifying Topology in Photonic Heterostructures with Gapless Environments

Area of Science:

• Condensed Matter Physics
• Photonics
• Materials Science

Background:

• Photonic topological insulators rely on bulk-boundary correspondence, where boundary states form at interfaces between distinct materials.
• A critical challenge arises when topological photonic devices interface with gapless free space, complicating the understanding of boundary states above the light line.

Purpose of the Study:

• To resolve bulk-boundary correspondence in heterostructures with gapless materials and radiative environments.
• To introduce a local theory for topological materials that accurately quantifies topological protection.

Main Methods:

• Development of a spectral localizer, a real-space operator, to mark topology and measure protection.
• Analysis of heterostructures in radiative environments, considering the behavior of photons above the light line.

Main Results:

• The spectral localizer provides a local, gap-independent measure of topological protection.
• Approximating radiative outcoupling as absorption overestimates topological protection.
• The method is applicable across dimensions and symmetry classes (Altland-Zirnbauer classes).

Conclusions:

• The spectral localizer offers a robust tool for analyzing topological materials interfacing with gapless media.
• This work enables accurate calculation of topological invariants and localization of boundary states in complex photonic systems.