Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA.
Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, IL, USA.
Science. 2020 Jun 5;368(6495):1114-1118. doi: 10.1126/science.aba7604.
Spectral measurements of boundary-localized topological modes are commonly used to identify topological insulators. For high-order insulators, these modes appear at boundaries of higher codimension, such as the corners of a two-dimensional material. Unfortunately, this spectroscopic approach is only viable if the energies of the topological modes lie within the bulk bandgap, which is not required for many topological crystalline insulators. The key topological feature in these insulators is instead fractional charge density arising from filled bulk bands, but measurements of such charge distributions have not been accessible to date. We experimentally measure boundary-localized fractional charge density in rotationally symmetric two-dimensional metamaterials and find one-fourth and one-third fractionalization. We then introduce a topological indicator that allows for the unambiguous identification of higher-order topology, even without in-gap states, and we demonstrate the associated higher-order bulk-boundary correspondence.
光谱测量边界局域拓扑模式通常用于识别拓扑绝缘体。对于高阶绝缘体，这些模式出现在更高维数的边界上，例如二维材料的角点。不幸的是，这种光谱方法只有在拓扑模式的能量位于体带隙内时才可行，而对于许多拓扑晶体绝缘体来说，这并不是必需的。这些绝缘体中的关键拓扑特征是来自填满的体带的分数电荷密度，但到目前为止，还无法测量这种电荷分布。我们在旋转对称的二维超材料中实验测量了边界局域分数电荷密度，并发现了四分之一和三分之一的分数化。然后，我们引入了一个拓扑指标，即使没有带隙态，也可以明确识别高阶拓扑，并演示了相关的高阶体边界对应关系。
