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.

中文翻译：

---

蜂窝状光学晶格中原子费米气体的集体模式色散：半填充时有吸引力的 Kane-Mele-Hubbard 模型的声速

我们研究了 Kane-Mele 模型中由于现场短程吸引力相互作用 U 出现的超流体状态。集体模式色散由广义上的 Bethe-Salpeter (BS) 方程的解定义随机相位近似。在 BS 形式中计算的低能量 (Goldstone) 模式的斜率和半填充时的相应声速已与先前通过 T 矩阵近似获得的相应结果进行了比较。两种方法的区别在于 T 矩阵近似只考虑梯形图，而忽略了气泡图。因此，在 T 矩阵近似内计算的 M 点方向上的声速比使用 BS 方程获得的结果小约 4%。