Topological States and Adiabatic Pumping in Quasicrystals

Details Topological States and Adiabatic Pumping in Quasicrystals Topological States and Adiabatic Pumping in Quasicrystals

2011-09-27

arxiv.org/abs/1109.5983v3

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

9 pages, 2 figures, 3 appendices. Added details in the supplementary information for the benefit of the interested reader

Scientific paper

The discovery of topological insulators has sparked considerable interest in the study of topological phases of matter. The hallmark of these novel phases is the emergence of topologically protected boundary phenomena, e.g. quantum pumping, surface states related to exotic models from particle physics, and quasi-particles with non-Abelian statistics. Yet, realizations of these phases of matter are scarce. Additionally, one-dimensional systems without any additional symmetries are considered to lack such topological phenomena. In this Letter, we show, both theoretically and experimentally, that quasicrystals possess high-dimensional topological phases. We demonstrate that one-dimensional quasicrystals exhibit topological properties that were, thus far, thought to be limited to two-dimensional systems. Using photonic quasicrystals, we observe localized boundary states, which manifest these topological properties. The topological nature of these boundary states is used to realize an adiabatic optical pumping effect in which photons are uni-directionally pumped across the sample. Generalization to various types of quasicrystals and higher dimensions are also discussed, suggesting the existence of topological effects on surfaces of three-dimensional quasicrystals. This work opens a path to the realization of new types of topological phases, and provides new insights to the physics of quasicrystals.

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