论文标题
琐碎的拓扑中受保护的无间隙边缘状态
Protected Gapless Edge States In Trivial Topology
论文作者
论文摘要
散装的对应关系是强大的拓扑绝缘子的重要特征，包括Chern绝缘子和$ Z_2 $拓扑绝缘子。在非平凡的带拓扑结构下，受保护的无间隙边缘状态对应于散装中的Wannier阻塞或Wilson-loop绕组。最近的研究表明，批量拓扑特征可能并不意味着受保护的无间隙边缘状态的存在。在这里，我们解决了一个相反的问题：受保护的无间隙边缘状态的存在是否一定意味着障碍物或威尔逊 - 环绕线？我们提供了一个例子，其中受保护的无间隙边缘状态在没有上述散装拓扑特征的情况下出现。这种微不足道的拓扑绝缘子属于具有非二型型渗透功能的新型系统。有趣的是，无间隙边缘状态不受晶体对称性的保护。相反，保护起源于镜子反对称性，手性和镜子对称性的组合。尽管受保护的无间隙边缘状态不能被散装拓扑特征捕获，但它们的特征是纠缠光谱中的光谱流。
Bulk-boundary correspondence serves as an important feature of the strong topological insulators, including Chern insulators and $Z_2$ topological insulators. Under nontrivial band topology, the protected gapless edge states correspond to the Wannier obstruction or Wilson-loop winding in the bulk. Recent studies show that the bulk topological features may not imply the existence of protected gapless edge states. Here we address the opposite question: Does the existence of protected gapless edge states necessarily imply the Wannier obstruction or Wilson-loop winding? We provide an example where the protected gapless edge states arise without the aforementioned bulk topological features. This trivialized topological insulator belongs to a new class of systems with non-delta-like Wannier functions. Interestingly, the gapless edge states are not protected by the crystalline symmetry; instead the protection originates from the mirror antisymmetry, a combination of chiral and mirror symmetries. Although the protected gapless edge states cannot be captured by the bulk topological features, they can be characterized by the spectral flow in the entanglement spectrum.
