Spin-orbit coupled ultracold gases in optical lattices: High-band physics and insufficiency of tight-binding models

We study the interplay effect of spin-orbit coupling (SOC) and an optical lattice on the single-particle physics and superfluid-insulator transition in ultracold Fermi gases. We consider the type of SOC that has been realized in cold atom experiments via two-photon Raman processes. Our analyses are based on the knowledge of a full single-particle spectrum in lattices without relying on any tight-binding approximation. We evaluate existing tight-binding models and point out their limitations in predicting the correct single-particle physics due to the missed high-band contributions. Moreover, we show that the Raman field (creating SOC) can induce band-gap closing in a two-dimensional optical lattice, leading to the intriguing phenomenon of superfluidity reentrance for interacting fermions at integer filling. We present the superfluid-insulator phase diagram in a wide parameter regime of chemical potentials and Raman fields. All these results are far beyond any that a tight-binding model can predict and can be directly probed in current cold atoms experiments.