A higher-order topological insulator (HOTI) in two dimensions is an insulator without metallic edge states but with robust zero-dimensional topological boundary modes localized at its corners. Yet, these corner modes do not carry a clear signature of their topology as they lack the anomalous nature of helical or chiral boundary states. Here, we demonstrate using immunity tests that the corner modes found in the breathing kagome lattice represent a prime example of a mistaken identity. Contrary to previous theoretical and experimental claims, we show that these corner modes are inherently fragile: the kagome lattice does not realize a higher-order topological insulator. We support this finding by introducing a criterion based on a corner charge-mode correspondence for the presence of topological midgap corner modes in n-fold rotational symmetric chiral insulators that explicitly precludes the existence of a HOTI protected by a threefold rotational symmetry.

二维的高阶拓扑绝缘子（HOTI）是没有金属边缘状态但在其角处具有可靠的零维拓扑边界模式的绝缘子。然而，由于这些转角模式缺乏螺旋或手性边界态的异常性质，因此它们并未带有清晰的拓扑特征。在这里，我们使用免疫测试证明，在呼吸的舞果格子中发现的拐角模式代表了错误身份的一个典型例子。与先前的理论和实验主张相反，我们证明了这些转角模式本质上是脆弱的：kagome晶格无法实现高阶拓扑绝缘体。我们通过引入基于拐角电荷模式对应性的标准来支持该发现，该标准针对n中存在拓扑中带隙拐角模式折叠的旋转对称手性绝缘子明确排除了受到三重旋转对称性保护的HOTI的存在。