# Higher-Order Topological Insulators in Quasicrystals

## TL;DR

This paper demonstrates that higher-order topological insulators can exist in quasicrystals, revealing new types of corner states and proposing experimental detection methods using electrical circuits.

## Contribution

It introduces the realization of second-order topological insulators in quasicrystals, expanding HOTI concepts beyond crystalline materials with practical detection approaches.

## Key findings

- Two types of quasicrystalline SOTIs constructed with different tiling patterns.
- Identification of unique corner states in quasicrystalline SOTIs.
- Electrical circuit simulation of quasicrystalline quadrupole insulator with measurable corner states.

## 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.