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A fractional corner anomaly reveals higher-order topology

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Science  05 Jun 2020:
Vol. 368, Issue 6495, pp. 1114-1118
DOI: 10.1126/science.aba7604

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Topological insulators in the spotlight

In addition to having an insulating interior while at the same time supporting conducting surface states, topological insulators have many other interesting properties. Higher-order topological insulating states, where regions of interest are along edges and at corners, have been difficult to identify unambiguously. Peterson et al. developed a theoretical framework to help identify and characterize these exotic states, including a new topological marker—the fractional charge density—that can be used to detect topological states of matter when the spectroscopic probe of gapless surface states is not accessible. The agreement between experimental work and theory is encouraging for applicability to other topological platforms.

Science, this issue p. 1114

Abstract

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.

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