Topological States and Adiabatic Pumping in Quasicrystals

TL;DR

This paper reveals that one-dimensional quasicrystals possess nontrivial topological properties characterized by higher-dimensional invariants, enabling topologically protected states and adiabatic pumping, thus connecting quasicrystals with topological insulators.

Contribution

The study demonstrates, both theoretically and experimentally, that quasicrystals exhibit topological properties linked to higher dimensions, expanding the understanding of their surface states and potential applications.

Findings

Quasicrystals have nontrivial topological invariants.

Topologically protected boundary states are observed in 1D quasicrystals.

Adiabatic pumping of light is achieved in quasicrystals.

Abstract

The unrelated discoveries of quasicrystals and topological insulators have in turn challenged prevailing paradigms in condensed-matter physics. We find a surprising connection between quasicrystals and topological phases of matter: (i) quasicrystals exhibit nontrivial topological properties and (ii) these properties are attributed to dimensions higher than that of the quasicrystal. Specifically, we show, both theoretically and experimentally, that one-dimensional quasicrystals are assigned two-dimensional Chern numbers and, respectively, exhibit topologically protected boundary states equivalent to the edge states of a two-dimensional quantum Hall system.We harness the topological nature of these states to adiabatically pump light across the quasicrystal. We generalize our results to higher-dimensional systems and other topological indices. Hence, quasicrystals offer a new platform for the study of topological phases while their topology may better explain their surface properties.