Topological states and adiabatic pumping in quasicrystals

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

Department of Condensed Matter Physics, Weizmann Institute of Science
Department of Complex Systems, Weizmann Institute of Science

We find a connection between quasicrystals and topological matter, namely that quasicrystals exhibit non-trivial topological phases attributed to dimensions higher than their own. Quasicrystals are materials which are neither ordered nor disordered, i.e. they exhibit only long-range order. This long-range order is usually expressed as a projection from a higher dimensional ordered system. Recently, the unrelated discovery of Topological Insulators defined a new type of materials classified by their topology. We show theoretically and experimentally using photonic lattices, that one-dimensional quasicrystals exhibit topologically-protected boundary states equivalent to the edge states of the two-dimensional Integer Quantum Hall Effect. We harness this property to adiabatically pump light across the quasicrystal, and generalize our results to higher dimensional systems. Hence, quasicrystals offer a new platform for the study of topological phases while their topology may better explain their surface properties.