Quasicrystalline Chern Insulators

TL;DR

This paper demonstrates the realization of Chern insulators in quasicrystals with 5-fold symmetry, showing topological edge states and quantized conductance despite aperiodicity, expanding the scope of topological materials.

Contribution

It introduces quasicrystalline Chern insulators with specific topological features, a novel extension beyond periodic lattices, and explores their unique electronic properties.

Findings

Robust edge states in quasicrystalline Chern insulators

Non-zero real-space Chern number in quasicrystals

Quantized conductance at specific energies despite non-integer conductivity

Abstract

Chern insulator or quantum anomalous Hall state is a topological state with integer Hall conductivity but in absence of Landau level. It had been well established on various two-dimensional lattices with periodic structure. Here, we report similar Chern insulators can also be realized on the quasicrystal with $5$-fold rotational symmetry. Providing the staggered flux through plaquettes, we propose two types of quasicrystalline Chern insulators. Their topological characterizations are well identified by the robustness of edge states, non-zero real-space Chern number, and quantized conductance. We further find the failure of integer conductivity but with quantized Chern number at some special energies. Our study therefore provide a new opportunity to searching topological materials in aperiodic system.