We numerically demonstrate that the topological corner states residing in the corners of higher-order topological insulator possess non-Abelian braiding properties. Such topological corner states are Dirac fermionic modes other than Majorana zero modes. We claim that Dirac fermionic modes protected by nontrivial topology also support non-Abelian braiding. An analytical description on such non-Abelian braiding is conducted based on the vortex-induced Dirac-type fermionic modes. Finally, the braiding operators for Dirac fermionic modes, especially their explicit matrix forms, are analytically derived and compared with the case of Majorana zero modes.

中文翻译：

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在高阶拓扑绝缘子中使用拓扑角状态的狄拉克费米模的非阿贝尔编织。

我们用数值方法证明驻留在高阶拓扑绝缘子角上的拓扑角状态具有非阿贝尔编织性质。这种拓扑拐角状态是除马约拉纳零模以外的狄拉克铁电体模。我们声称受非平凡拓扑保护的狄拉克费米离子模式也支持非阿贝尔编织。基于涡旋诱发的狄拉克型费米离子模式对这种非阿贝尔编织进行了分析描述。最后，分析得出了狄拉克费米子模的编织算子，尤其是它们的显式矩阵形式，并与马约拉纳零模的情况进行了比较。