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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
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