Classifying topology in photonic heterostructures with gapless environments

TL;DR

This paper introduces a local spectral marker for topological properties in photonic heterostructures with gapless environments, enabling accurate topological classification and protection assessment beyond traditional band gap reliance.

Contribution

It develops a spectral localizer approach that works in any dimension and symmetry class, resolving bulk-boundary correspondence in gapless and radiative photonic systems.

Findings

Spectral localizer provides a local topological marker independent of bulk gap.

Approximating radiative losses as absorption overestimates protection.

Method applicable to various physical dimensions and symmetry classes.

Abstract

Photonic topological insulators exhibit bulk-boundary correspondence, which requires that boundary-localized states appear at the interface formed between topologically distinct insulating materials. However, many topological photonic devices share a boundary with free space, which raises a subtle but critical problem as free space is gapless for photons above the light-line. Here, we use a local theory of topological materials to resolve bulk-boundary correspondence in heterostructures containing gapless materials and in radiative environments. In particular, we construct the heterostructure's spectral localizer, a composite operator based on the system's real-space description that provides a local marker for the system's topology and a corresponding local measure of its topological protection; both quantities are independent of the material's bulk band gap (or lack thereof). Moreover, we show that approximating radiative outcoupling as material absorption overestimates a heterostructure's topological protection. As the spectral localizer is applicable to systems in any physical dimension and in any discrete symmetry class, our results show how to calculate topological invariants, quantify topological protection, and locate topological boundary-localized resonances in topological materials that interface with gapless media in general.