Quasicrystalline Chern insulators

A Chern insulator or a quantum anomalous Hall state is a topological state with integer Hall conductivity but in absence of the Landau level. It had been well established on various two-dimensional lattices with periodic structure. Here, we report similar Chern insulators that can also be realized on a quasicrystal with fivefold 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, nonzero real-space Chern number, and quantized conductance. We further find the failure of integer conductivity but with the quantized Chern number at some special energies. Our study, therefore, provides a new opportunity to searching topological materials in aperiodic systems.