In commonly employed models for two-dimensional (2D) topological insulators, bulk gapless states are well known to form at the band inversion points where the degeneracy of the states is protected by symmetries. It is thus sometimes quite tempting to consider this feature, the occurrence of gapless states, a result of the band inversion process under protection of the symmetries. Similarly, the band inversion process might even be perceived as necessary to induce 2D topological phase transitions. To clarify these misleading perspectives, we propose a simple model with a flexible Chern number to demonstrate that the bulk gapless states emerge at the phase boundary of topological phase transitions, despite the absence of a band inversion process. Furthermore, the bulk gapless states do not need to occur at the special $k$ points protected by symmetries. Given the significance of these fundamental conceptual issues and their widespread influence, our clarification should generate strong general interests and significant impacts. Furthermore, the simplicity and flexibility of our general model with an arbitrary Chern number should prove useful in a wide range of future studies of topological states of matter.

中文翻译：

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二维拓扑绝缘子中对于体无间隙状态和拓扑相变的能带反转过程没有必要

在二维（2D）拓扑绝缘体的常用模型中，众所周知，在带隙反转点会形成块状无间隙状态，在该状态下，状态的简并性受到对称性的保护。因此，有时会很想考虑此特征，即无间隙状态的出现，这是在对称性保护下的能带反转过程的结果。类似地，甚至可以将频带反转过程视为诱发2D拓扑相变的必要条件。为了阐明这些误导性观点，我们提出了一个具有灵活Chern数的简单模型，以证明尽管没有带反转过程，但大部分无间隙状态出现在拓扑相变的相界处。此外，不需要在特殊情况下出现大量无间隙状态$ķ$受对称性保护的点。考虑到这些基本概念问题的重要性及其广泛的影响，我们的澄清应引起强烈的普遍兴趣和重大影响。此外，具有任意Chern数的通用模型的简单性和灵活性在以后对物质拓扑状态的广泛研究中将被证明是有用的。