Collective-mode dispersion of atomic Fermi gases in a honeycomb optical lattice: speed of sound of the attractive Kane–Mele–Hubbard model at half filling

We examine the superfluid states that emerge in the Kane–Mele model as a result of the on-site short-range attractive interaction U. The collective-mode dispersion is defined by the solutions of the Bethe–Salpeter (BS) equation in the generalized random phase approximation. The slope of the low-energy (Goldstone) mode and the corresponding sound velocity at half filling, calculated within the BS formalism, has been compared with the corresponding results obtained previously by the T-matrix approximation. The difference between the two approaches is that the T-matrix approximation takes into account only the ladder diagrams, and neglects the bubble ones. For this reason, the sound velocity in the direction toward point M, calculated within the T-matrix approximation, is about 4% less than the result obtained by employing the BS equation. (author)