  Recently spin-orbit (SO) coupled superfluids in free space or harmonic traps
have been extensively studied, motivated by the recent experimental realization
of SO coupling for Bose-Einstein condensates (BEC). However, the rich physics
of SO coupled BEC in optical lattices has been largely unexplored. In this
paper, we show that in suitable parameter region the lowest Bloch state forms
an isolated flat band in a one dimensional (1D) SO coupled optical lattice,
which thus provides an experimentally feasible platform for exploring the
recently celebrated topological flat band physics in lattice systems. We show
that the flat band is preserved even with the mean field interaction in BEC. We
investigate the superfluidity of the BEC in SO coupled lattices through
dynamical and Landau stability analysis, and show that the BEC is stable on the
whole flat band.
