Twisted-bilayer FeSe and the Fe-based superlattices

We derive BM-like continuum models for the bands of superlattice heterostructures formed out of Fe-chalcogenide monolayers: ($\text{I}$) a single monolayer experiencing an external periodic potential, and ($\text{I}\mathbf{I}$) twisted bilayers with long-range moire tunneling. A symmetry derivation for the inter-layer moire tunnelling is provided for both the $\mathrm{\Gamma }$ and $M$ high-symmetry points. In this paper, we focus on moire bands formed from hole-band maxima centered on $\mathrm{\Gamma }$, and show the possibility of moire bands with $C=0$ or $\pm 1$ topological quantum numbers without breaking time-reversal symmetry. In the $C=0$ region for $\theta \to 0$ (and similarly in the limit of large superlattice period for $\text{I}$), the system becomes a square lattice of 2D harmonic oscillators. We fit our model to FeSe and argue that it is a viable platform for the simulation of the square Hubbard model with tunable interaction strength.