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Systems with engineered flatband spectra are a postulate of high-capacitytransmission links and a candidate for high-temperature superconductivity.However, their operation relies on the edge or surface modes susceptible tofluctuations and fabrication errors. While the mode robustness can be enhancedby a combination of Aharonov-Bohm caging and topological insulation, the designof the corresponding flatbands requires approaches beyond the standard$k$-vector-based methods. Here, we propose a synthetic-flux probe as a solutionto this problem and a route to the realization of ultra-stable modes. We provethe concept in a laser-fabricated graphene-like ribbon photonic lattice withthe band-flattening flux induced by "P" waveguide coupling. The topologicalnon-triviality is witnessed by an integer Zak phase derived from the meanchiral displacement. Mode stability is evidenced by excellent mode localizationand the robustness to fabrication tolerances and variations of the input phase.Our results can serve as a basis for the development of multi-flat-bandmaterials for low-energy electronics.

Observation of topologically protected compact edge states in flux-dressed graphene photonic lattices