Topological states and adiabatic pumping in quasicrystals

Yaacov E. Kraus*, Yoav Lahini, Zohar Ringel, Mor Verbin, Oded Zilberberg

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

815 Scopus citations


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.

Original languageAmerican English
Article number106402
JournalPhysical Review Letters
Issue number10
StatePublished - 4 Sep 2012
Externally publishedYes


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