Band-edge superfluid of Bose-Einstein condensates in the spin-orbit-coupled Zeeman lattice

Since the first experimental realization of Bose-Einstein condensates in a spin-orbit-coupled Zeeman lattice, a wide range of applications have been found in these systems. Here, we systematically study the ground-state phase diagram of the systems. We address that the band-edge phase in the ground-state phase diagram is exotic and exists in a very broad parameter regime. The superfluidity of the band-edge states is identified by elementary excitations and superfluid fraction.