Hybrid Morié flatbands in triple-layer superlattices via flatbands coupling

Flatband moiré superlattices exhibit a wealth of exotic phenomena, demonstrating significant potential for groundbreaking applications across diverse fields, from condensed matter physics to photonics. In this work, we explore the intricate physics of nontrivial flatband superlattices with photonic multi-layer architectures. We introduce a universal framework for generating hybrid moiré flatbands via the strategic coupling of fundamental moiré flatbands. Following the framework, we construct series of triple-layer superlattices by stacking different pairs of double-layer superlattices, where the double-layer superlattices host two sets of fundamental moiré flatbands. Through comprehensive full-wave simulations, we validate the proposed framework by demonstrating that the coupling of different fundamental flatband pairs consistently yields hybrid flatbands, fully in agreement with our theory. Notably, we find that the flatness of the hybrid bands could be better compared to the fundamental flatbands, suggesting new opportunities for enhancing moiré localization in multi-layer configurations. Importantly, the obtained hybrid flatbands inherit the spatial features of the fundamental flatbands, offering a new degree of freedom for manipulating the field patterns of moiré localized modes. Our work establishes a new paradigm for engineering complex multi-layer superlattices with precisely tailored flatbands, paving the way for advanced on-chip light manipulation using moiré superlattice architectures.