Continuum model for iron-based superlattices

We derive a BM-like continuum model for the bands of superlattice heterostructures formed out of Fe-chalcogenide monolayers: (1) a single monolayer experiencing an external periodic potential, and (2) twisted bilayers with long-range Moire tunneling. A symmetry derivation for the inter-layer Moire tunnelling is provided for both the $\Gamma$ and $M$ high-symmetry points. We show the possibility for Moire bands with non-zero topological quantum numbers without breaking time-reversal symmetry.