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We design an interaction-driven topological insulator for fermionic coldatoms in an optical lattice, that is, we pose the question of whether we canrealize in a continuous space a spontaneous symmetry breaking induced by theinter-atom interaction into a topological Chern insulator. Such a state,sometimes called a "topological Mott insulator", has yet to be realized insolid-state systems, since this requires, in the tight-binding model, largeoffsite interactions on top of a small onsite interaction. Here we overcome thedifficulty by introducing a spin-dependent potential, where a spin-selectiveoccupation of fermions in $A$ and $B$ sublattices makes the onsite interactionPauli-forbidden, while a sizeable inter-site interaction is achieved by ashallow optical potential with a large overlap between neighboring Wannierorbitals. This puts the system away from the tight-binding model, so that weadopt the density functional theory for cold-atoms, here extended toaccommodate non-collinear spin structures emerging in the topological regime,to quantitatively demonstrate the phase transition to the topological Mottinsulator.

Interaction-Driven Topological Insulator in Fermionic Cold Atoms on an Optical Lattice: A Design with a Density Functional Formalism