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arXiv · 1904.09932

Higher-Order Topological Insulators in Quasicrystals

Rui Chen·Chui-Zhen Chen·Jin-Hua Gao·Bin Zhou·Dong-Hui Xu
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Abstract

Current understanding of higher-order topological insulators (HOTIs) is based primarily on crystalline materials. Here, we propose that HOTIs can be realized in quasicrystals. Specifically, we show that two distinct types of second-order topological insulators (SOTIs) can be constructed on the quasicrystalline lattices (QLs) with different tiling patterns. One is derived by using a Wilson mass term to gap out the edge states of the quantum spin Hall insulator on QLs. The other is the quasicrystalline quadrupole insulator (QI) with a quantized quadrupole moment. We reveal some unusual features of the corner states (CSs) in the quasicrystalline SOTIs. We also show that the quasicrystalline QI can be simulated by a designed electrical circuit, where the CSs can be identified by measuring the impedance resonance peak. Our findings not only extend the concept of HOTIs into quasicrystals but also provide a feasible way to detect the topological property of quasicrystals in experiments.

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Rui Chen, Chui-Zhen Chen, Jin-Hua Gao, Bin Zhou, Dong-Hui Xu. 2019-12-23. Higher-Order Topological Insulators in Quasicrystals. https://doi.org/10.1103/physrevlett.124.036803

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