Figure 1.

Topological nanoparticle photonics in context: Most topological condensed matter concepts can be separated into phases with topological order and symmetry protected topological (SPT) phases. Various platforms are used to study topological physics. Band structure of Bi₂Se₃, adapted with permission from ref (24). Copyright 2009 Nature Publishing Group. Schematic of platform for acoustic topological insulator, adapted with permission from ref (25), copyright 2019 Nature Publishing Group. Schematic of soft bosons in a cavity taken from ref (26). Topological photonics draws mainly from SPT phases. Common platforms are waveguide arrays (figure adapted with permission from ref (27), copyright 2013 Nature Publishing Group. Bianisotropic materials, figure adapted with permission from ref (28), copyright 2017 Nature Publishing Group. Microring resonators, figure adapted with permission from ref (29), copyright 2018 Nature Publishing Group. Microstructures, figure adapted with permission from ref (30), copyright 2017 Nature Publishing Group. Photonic topological crystalline insulators using dielectric materials, figure adapted with permission from ref (31), copyright 2020 American Physical Society. Systems with nanoscale dimensions operating from visible to THz frequencies: Dielectric nanoparticles (adapted with permission from ref (32), Copyright 2015 American Physical Society), plasmonic nanoparticles,³³ dielectric nanostructures, figure adapted with permission from ref (34), copyright 2019 Nature Publishing Group. 2D arrays of nanoparticles³⁵ and plasmonic metasurfaces.³⁶ Semiconductor nanocavity arrays,³⁷ 2D materials and hybrid systems including photonic structures,³⁸ and topological insulator nanoparticles.²³ Figures from refs (23,26,29,33,35−37) licensed under CC BY 4.0, https://creativecommons.org/licenses/by/4.0/. Figure from ref (38) licensed under CC BY 3.0, https://creativecommons.org/licenses/by/3.0/.