Topological materials and more so insulators have become ideal candidates for spintronics and other novel applications. These materials portray band inversion that is considered to be a key signature of topology. It is not yet clear what drives band inversion in these materials and the basic inferences when band inversion is observed. We employed a state-of-the-art ab initio method to demonstrate band inversion in topological bulk Bi₂Se₃ and subsequently provided a reason explaining why the inversion occurred. From our work, a topological surface state for Bi₂Se₃ was described by a single gap-less Dirac cone at $\overrightarrow{k}$ = 0, which was essentially at the Γ point in the surface Brilloiun zone. We realized that band inversion in Bi₂Se₃ was not entirely dependent on spin–orbit coupling as proposed in many studies but also occurred as a result of both scalar relativistic effects and lattice distortions. Spin–orbit coupling was seen to drive gap opening, but it was not important in obtaining a band inversion. Our calculations reveal that Bi₂Se₃ has an energy gap of about 0.28 eV, which, in principle, agrees well with the experimental gap of ≈0.20 eV–0.30 eV. This work contributes to the understanding of the not so common field of spintronics, eventually aiding in the engineering of materials in different phases in a non-volatile manner.

中文翻译：

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Bi2Se3拓扑中能带反转的起源

拓扑材料以及更多的绝缘体已经成为自旋电子学和其他新颖应用的理想选择。这些材料描绘了被认为是拓扑结构关键特征的频带反转。尚不清楚是什么驱动了这些材料中的频带反转，以及观察到频带反转时的基本推论。我们采用了最先进的从头算方法，以证明拓扑本体Bi ₂ Se _3中的能带反转，随后提供了解释为何发生反转的原因。从我们的工作中，Bi ₂ Se ₃的拓扑表面状态由一个无间隙的Dirac锥描述为$\overrightarrow{ķ}$= 0，该值基本上位于布里渊区的Γ点。我们意识到，Bi ₂ Se ₃中的能带反转并不完全像许多研究中所提出的那样完全取决于自旋轨道耦合，而是由于标量相对论效应和晶格畸变而发生的。自旋-轨道耦合被认为驱动了间隙的打开，但是在获得带反转方面并不重要。我们的计算表明，Bi ₂ Se ₃的能隙约为0.28 eV，原则上与实验间隙≈0.20eV–0.30 eV吻合良好。这项工作有助于理解自旋电子学这个不太常见的领域，最终以非易失性方式协助不同阶段的材料工程。