title: Topological States and adiabatic pumping 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.
authors.affiliation: Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel.
authors.forename: Yaacov E
authors.initials: YE
authors.lastname: Kraus
authors.forename: Yoav
authors.initials: Y
authors.lastname: Lahini
authors.forename: Zohar
authors.initials: Z
authors.lastname: Ringel
authors.forename: Mor
authors.initials: M
authors.lastname: Verbin
authors.forename: Oded
authors.initials: O
authors.lastname: Zilberberg