We investigate, firstly, the competition between the Rashba spin-orbit coupling (SOC) and the intrinsic SOC in Kane-Mele model. For the small intrinsic SOC, we investigate the effects of the Rashba SOC on the touching point of the valence and conduction bands when the ratio of the Rashba SOC to the intrinsic SOC is greater than classical value [Formula: see text]. For the large intrinsic SOC, we find that the critical ratio of the two SOCs at which the band touching occurs decreases with the increasing intrinsic SOC and the locations of these touching points deviate from points K and K' of the Brillouin zone. Furthermore, effects of the Rashba SOC on these touching points are discussed in detail when the ratio is greater than the critical value. The Rashba SOC-driven topologically trivial and non-trivial transitions are also obtained in the first part of the work. Secondly, using the slave-rotor mean field method we investigate the influences of the correlation on the Rashba SOC-driven topologically trivial and non-trivial transitions in both the charge condensate and Mott regions. The topological Mott insulator with gapped or gapless spin excitations which arises from the interplay of the Rashba SOC and correlations is obtained in the work.

中文翻译：

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Kane-Mele 模型中内在和 Rashba 自旋轨道耦合之间的竞争以及相关性对 Rashba SOC 驱动跃迁的影响

我们首先研究了 Rashba 自旋轨道耦合 (SOC) 与 Kane-Mele 模型中的固有 SOC 之间的竞争。对于小的固有 SOC，我们研究了当 Rashba SOC 与固有 SOC 的比率大于经典值时，Rashba SOC 对价带和导带接触点的影响[公式：见正文]。对于大的固有 SOC，我们发现发生带接触的两个 SOC 的临界比率随着固有 SOC 的增加而降低，并且这些接触点的位置偏离布里渊区的点 K 和 K'。此外，当比率大于临界值时，详细讨论了 Rashba SOC 对这些接触点的影响。在工作的第一部分也获得了 Rashba SOC 驱动的拓扑平凡和非平凡转换。其次，使用从转子平均场方法，我们研究了相关性对 Rashba SOC 驱动的电荷凝聚和 Mott 区域中拓扑平凡和非平凡跃迁的影响。在工作中获得了具有间隙或无间隙自旋激发的拓扑莫特绝缘体，这种激发是由 Rashba SOC 和相关性的相互作用引起的。