Emergence of cascading flat bands in breathing superlattices

Flat bands have become a pillar of modern condensed matter physics and photonics owing to the vanishing group velocity and diverging density of states. Here, we present a paradigmatic scheme to construct arbitrary flat bands on demand by introducing a new type breathing superlattice, where both the number and spectral positions of isolated flat bands can be continuously tailored by simply controlling the breathing strength. Microscopically, the momentum-independent interband scatterings near the band edge protect them robust against weak intra-cell disorder. By dimensional reduction, we establish a duality between the one-dimensional (1D) breathing superlattice and the 2D Harper-Hofstadter model, where cascade flat bands naturally emerge as the different orders of Landau levels in the weak magnetic flux limit. As a proof of concept, photonic flat bands at optical frequencies are experimentally demonstrated with all-dielectric photonic crystal slabs. Finally, we generalize our scheme to 2D systems to realize partial and omnidirectional flat bands, and discuss the achievement of high-quality factors. Our findings shed new light on the manipulation of flat bands with high band flatness and large usable bandwidth, paving the way for the development of advanced optical devices.