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Lett."],"published-print":{"date-parts":[[2026,2,1]]},"abstract":"<jats:p>The interplay between flat bands and topology has the potential to enhance the localization and robustness of topological edge modes, yet their realization in planar waveguide platforms remains challenging. Here, we introduce a synthetic gauge flux by leveraging degenerate modes in planar subwavelength grating waveguides, enabling Aharonov\u2013Bohm caging effect and the formation of a flat-band lattice. The resulting edge modes are ultracompact, which can be confined to the last two waveguides at the boundary. These robust modes remain highly localized against coupling coefficient and geometric variations. 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All rights, including for text and data mining (TDM), Artificial Intelligence (AI) training, and similar technologies, are reserved.","name":"copyright","label":"Copyright"}]}}