Magic configurations in Moir\'e Superlattice of Bilayer Photonic crystal: Almost-Perfect Flatbands and Unconventional Localization

We investigate the physics of photonic band structures of the moire patterns that emerged when overlapping two uni-dimensional (1D) photonic crystal slabs with mismatched periods. The band structure of our system is a result of the interplay between intra-layer and inter-layer coupling mechanisms, which can be fine-tuned via the distance separating the two layers. We derive an effective Hamiltonian that captures the essential physics of the system and reproduces all numerical simulations of electromagnetic solutions with high accuracy. Most interestingly, \textit{magic distances} corresponding to the emergence of photonic flatbands within the whole Brillouin zone of the moire superlattice are observed. We demonstrate that these flatband modes are tightly localized within a moire period. Moreover, we suggest a single-band tight-binding model that describes the moire minibands, of which the tunnelling rate can be continuously tuned via the inter-layer strength. Our results show that the band structure of bilayer photonic moire can be engineered in the same fashion as the electronic/excitonic counterparts. It would pave the way to study many-body physics at photonic moire flatbands and novel optoelectronic devices.