The higher-order topological insulator (HOTI) states, such as two-dimension (2D) HOTI featured with topologically protected corner modes at the intersection of two gapped crystalline boundaries, have attracted much recent interest. However, physical mechanism underlying the formation of HOTI states is not fully understood, which has hindered our fundamental understanding and discovery of HOTI materials. Here we propose a mechanistic approach to induce higher-order topological phases via structural buckling of 2D topological crystalline insulators (TCIs). While in-plane mirror symmetry is broken by structural buckling, which destroys the TCI state, the combination of mirror and rotation symmetry preserves in the buckled system, which gives rise to the HOTI state. We demonstrate that this approach is generally applicable to various 2D lattices with different symmetries and buckling patterns, opening a horizon of possible materials to realize 2D HOTIs. The HOTIs so generated are also shown to be robust against buckling height fluctuation and in-plane displacement. A concrete example is given for the buckled $\beta $-Sb monolayer from first-principles calculations. Our finding not only enriches our fundamental understanding of higher-order topology, but also opens a new route to discovering HOTI materials.

中文翻译：

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结构屈曲引发的高阶拓扑

高阶拓扑绝缘体 (HOTI) 状态，例如二维 (2D) HOTI，在两个带隙晶界的交叉处具有拓扑保护的角模式，最近引起了很多兴趣。然而，HOTI 态形成的物理机制尚不完全清楚，这阻碍了我们对 HOTI 材料的基本理解和发现。在这里，我们提出了一种机械方法，通过二维拓扑晶体绝缘体（TCI）的结构屈曲来诱导高阶拓扑相。虽然面内镜像对称性被结构屈曲破坏，从而破坏了 TCI 状态，但镜像和旋转对称的组合保留在屈曲系统中，从而产生了 HOTI 状态。我们证明了这种方法通常适用于具有不同对称性和屈曲模式的各种 2D 晶格，为实现 2D HOTI 开辟了可能的材料视野。如此生成的 HOTI 也被证明对屈曲高度波动和平面内位移具有鲁棒性。根据第一性原理计算，给出了屈曲 $\beta $-Sb 单层的一个具体例子。我们的发现不仅丰富了我们对高阶拓扑的基本理解，而且为发现 HOTI 材料开辟了一条新途径。根据第一性原理计算，给出了屈曲 $\beta $-Sb 单层的一个具体例子。我们的发现不仅丰富了我们对高阶拓扑的基本理解，而且为发现 HOTI 材料开辟了一条新途径。根据第一性原理计算，给出了屈曲 $\beta $-Sb 单层的一个具体例子。我们的发现不仅丰富了我们对高阶拓扑的基本理解，而且为发现 HOTI 材料开辟了一条新途径。