Topological photonics enables unusual and robust properties of electromagnetic waves, including reflections-free photon propagation along strongly curved interfaces and localization at the corners and other discontinuities of photonic structures. Of particular interest are the so-called photonic higher-order topological insulators (PHOTIs) enabling light localization at their corners. I will discuss several examples of the PHOTIs based on coupled microwave cavities (emulating quadrupolar insulators) and new PHOTIs based on topological crystalline insulators emulating spin-orbit coupling. Strategies for developing nanoscale PHOTIs will be discussed, including metagate-controlled 2D materials. Finally, a novel regime of quantum landscaping of single-layer graphene, where periodic patterns of chemical potential simultaneously modify electronic and photonic propagation bands, will be introduced.
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