An Operator-based Approach to Topological Physics
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Cerjan, Alexander Witte↗
Engineering topics
Dixon, Kahlil Yusef
Publications and source records attributed to Dixon, Kahlil Yusef.
Classifying Topology in Photonic Heterostructures with Gapless Environments
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. Importantly, as the spectral localizer is applicable to systems in any physical dimension and in any discrete symmetry class (i.e., any Altland-Zirnbauer 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.
77 NANOSCIENCE AND NANOTECHNOLOGY↗