Topology in quasicrystals

TL;DR

This paper reviews the classification of topological phases in quasicrystals, highlighting recent experimental advances and the robustness of topological properties in quasiperiodic systems.

Contribution

It provides a comprehensive overview of topological classification methods applied to quasicrystals and summarizes recent experimental findings in the field.

Findings

Topological phases can be classified in quasiperiodic systems.

Experimental evidence supports the existence of topological states in quasicrystals.

Topological properties in quasicrystals are robust to perturbations.

Abstract

Topological phases of matter have sparked an immense amount of activity in recent decades. Topological materials are classified by topological invariants that act as a non-local order parameter for any symmetry and condition. As a result, they exhibit quantized bulk and boundary observable phenomena, motivating various applications that are robust to perturbations. In this review, we explore such a topological classification for quasiperiodic systems, and detail recent experimental activity in the field.