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.
Dixon, Kahlil Yusef, Loring, Terry A., & Cerjan, Alexander Witte (2023). Classifying Topology in Photonic Heterostructures with Gapless Environments. Physical Review Letters, 131(21). https://doi.org/10.1103/physrevlett.131.213801
Dixon, Kahlil Yusef, Loring, Terry A., and Cerjan, Alexander Witte, "Classifying Topology in Photonic Heterostructures with Gapless Environments," Physical Review Letters 131, no. 21 (2023), https://doi.org/10.1103/physrevlett.131.213801
@article{osti_2311527,
author = {Dixon, Kahlil Yusef and Loring, Terry A. and Cerjan, Alexander Witte},
title = {Classifying Topology in Photonic Heterostructures with Gapless Environments},
annote = {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.},
doi = {10.1103/physrevlett.131.213801},
url = {https://www.osti.gov/biblio/2311527},
journal = {Physical Review Letters},
issn = {ISSN 0031-9007},
number = {21},
volume = {131},
place = {United States},
publisher = {American Physical Society (APS)},
year = {2023},
month = {11}}
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division (MSE); USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities (SUF); National Science Foundation (NSF)