Abstract α-Sn is on the boundary of a couple of distinct topological phases. It will transform into a topological insulator under a suitable strain. However, a clear picture of its topological surface states (TSSs) is still lacking. Here we perform first-principles calculations on the electronic structure of α-Sn(111) surface to identify its TSSs and reveal their properties. The results show that the presence of valence band reorganizes the TSSs in the inverted sp gap into two Dirac cones. The lower one is in the valence band continuum; the upper one resides in the gap between the valence and conduction bands. We also demonstrate the transformation of the surface states by switching on or off of strain and/or spin-orbit coupling. Without spin-orbit coupling, only the TSSs associated with the lower Dirac cone survive, and they are spin unpolarized. The results are useful for understanding and engineering the topological properties of α-Sn.

中文翻译：

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α-Sn(111)拓扑表面态的第一性原理研究

摘要 α-Sn 位于几个不同拓扑相的边界上。它将在合适的应变下转变为拓扑绝缘体。然而，仍然缺乏其拓扑表面状态（TSS）的清晰图像。在这里，我们对 α-Sn(111) 表面的电子结构进行第一性原理计算，以识别其 TSS 并揭示其性质。结果表明，价带的存在将反向 sp 间隙中的 TSS 重组为两个狄拉克锥。较低的在价带连续谱中；上面的位于价带和导带之间的间隙中。我们还通过打开或关闭应变和/或自旋轨道耦合来演示表面状态的转换。在没有自旋轨道耦合的情况下，只有与下狄拉克锥体相关的 TSS 存活下来，并且它们是自旋非极化的。