Higher-Order Topological Insulators in Quasicrystals

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

Published 2019-04-22Version 1

We propose the higher-order topological insulators with a quantized quadrupolar moment can be realized in quasicrystals. As a specific example, we consider a quasicrystalline Ammann-Beenker tiling with a square-shaped boundary. Most saliently, we find that topological corner states emerge when the site density exceeds a threshold value. Further, we theoretically design an electric circuit of the Ammann-Beenker tiling and show that the topological corner states in quasicrystals can be realized in classical electric circuits for the first time. We confirm that our findings of topological corner states are generic and can also be applied to the Penrose tiling and other aperiodic structures such as amorphous systems.