Topological States and adiabatic pumping in quasicrystals.

By Yaacov E. Kraus, Y. Lahini, Z. Ringel, M. Verbin, Oded Zilberberg. Physical Review Letters, 2011

877 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/61bb5cc4025b0953a81ddf65856fa9fdc878ae25

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Citations in the corpus

Roadmap on topological photonics (2022, methodology): “An example of a 1D tight-binding charge pump [86, 87].”
Synthetic dimension in photonics (2018, methodology): “[111] made two important modification of the Aubry-”
Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport (2016, methodology): “adiabatic pumping [47] and by bulk phase transitions [48]”
Exciton-polaritons in lattices: A non-linear photonic simulator (2016, background): “Remarkable observations using these lattices include Bloch oscillations [22,23], dynamic localisation [24], modulation assisted tunnelling [25], Anderson localisation [5], transport in quasi-crystals [12,26], edge states in honeycomb lattices [27,28] or the implementation of artificial gauge fields ”
Perspective on topological states of non-Hermitian lattices (2019, background): “In this sense, the nonHermitian effective description is very much like a shadow (in the sense of a projection) of the higher-dimensional Hermitian ancestor, in a situation reminiscent of what happens in quasicrystals [100, 101].”
Topological photonics (2018, methodology): “From Kraus et al., 2012.”