One of the hallmarks of topological insulators is the correspondence between the value of its bulk topological invariant and the number of topologically protected edge modes observed in a finite-sized sample. This bulk-boundary correspondence has been well-tested for strong topological invariants, and forms the basis for all proposed technological applications of topology. Here, we report that a group of weak topological invariants, which depend only on the symmetries of the atomic lattice, also induces a particular type of bulk-boundary correspondence. It predicts the presence or absence of states localised at the interface between two inversion-symmetric band insulators with trivial values for their strong invariants, based on the space group representation of the bands on either side of the junction. We show that this corresponds with symmetry-based classifications of topological materials. The interface modes are protected by the combination of band topology and symmetry of the interface, and may be used for topological transport and signal manipulation in heterojunction-based devices.

中文翻译：

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反转对称原子绝缘体之间的拓扑状态

拓扑绝缘体的标志之一是其体积拓扑不变量的值与在有限大小的样本中观察到的拓扑保护边缘模式的数量之间的对应关系。这种批量边界对应已经过强拓扑不变量的充分测试，并构成了所有提出的拓扑技术应用的基础。在这里，我们报告了一组仅依赖于原子晶格对称性的弱拓扑不变量，也诱导了一种特定类型的体边界对应关系。它基于结任一侧带的空间群表示，预测位于两个反演对称带绝缘体之间的界面处的状态的存在或不存在，其强不变量的值很小。我们表明这与基于对称性的拓扑材料分类相对应。接口模式受能带拓扑和接口对称性的组合保护，并可用于基于异质结的器件中的拓扑传输和信号处理。