Emergent nontrivial lattices for topological insulators

Materials with nontrivial lattice geometries allow for the creation of exotic states of matter like topologically insulating states. Therefore searching for such materials is an important aspect of current research in solid-state physics. In the field of ultracold gases there are ongoing studies aiming to create nontrivial lattices using optical means. In this paper we study two species of fermions trapped in a square optical lattice and show how nontrivial lattices can emerge due to strong interaction between atoms. We theoretically investigate regimes of tunable parameters in which such self-assembly may take place and describe the necessary experimental conditions. Moreover, we discuss the possibility of such emergent lattices hosting topologically insulating states.