Flat-band engineering of interactions in spin-orbit coupled optical lattices

The recent experimental realization of spin-orbit coupled ultra cold atomic gases established a new platform to investigate many-body states of matter. In this talk we show that for such a system in optical lattices we can tune the spin-orbit coupling to achieve a flat energy band. We then model this system with a tight-binding Hamiltonian and further project the Hamiltonian to the Hilbert subspace of the lowest flat band. We will also discuss the important effect of interactions in such a projected flat-band system.