Rashba Spin-Orbit-Coupled Atomic Fermi Gases in a Two-Dimensional Optical Lattice

The collective-mode excitation energy of a population-imbalanced spin-orbit-coupled atomic Fermi gas loaded in a two-dimensional optical lattice at zero temperature is calculated within the Gaussian approximation, and from the Bethe-Salpeter equation in the generalized random-phase approximation assuming the existence of a Sarma superfluid state. It is found that the Gaussian approximation overestimates the speed of sound of the Goldstone mode. More interestingly, the Gaussian approximation fails to reproduce the roton-like structure of the collective-mode dispersion which appears after the linear part of the dispersion in the Bethe-Salpeter approach. We investigate the speed of sound of a balanced spin-orbit-coupled atomic Fermi gas near the boundary of the topological phase transition driven by an out-of-plane Zeeman field. It is shown that the minimum of the speed of sound is located at the topological phase transition boundary, and this fact can be used to confirm the existence of a topological phase transition.