Topological Hofstadter Insulators in a Two-Dimensional Quasicrystal

TL;DR

This paper demonstrates that two-dimensional quasicrystals under magnetic fields exhibit topologically nontrivial edge states, similar to Chern insulators, characterized by a real-space topological marker, expanding the scope of topological materials.

Contribution

It introduces a method to identify topological edge states in non-periodic quasicrystals using a local real-space Chern number, bridging a gap in topological insulator research.

Findings

Hofstadter butterfly structure observed in quasicrystals

Chiral edge states linked to non-zero Chern numbers

Topological characterization via real-space marker

Abstract

We investigate the properties of a two-dimensional quasicrystal in the presence of a uniform magnetic field. In this configuration, the density of states (DOS) displays a Hofstadter butterfly-like structure when it is represented as a function of the magnetic flux per tile. We show that the low-DOS regions of the energy spectrum are associated with chiral edge states, in direct analogy with the Chern insulators realized with periodic lattices. We establish the topological nature of the edge states by computing the topological Chern number associated with the bulk of the quasicrystal. This topological characterization of the non-periodic lattice is achieved through a local (real-space) topological marker. This work opens a route for the exploration of topological insulating materials in a wide range of non-periodic lattice systems, including photonic crystals and cold atoms in optical lattices.