Topological States and adiabatic pumping in quasicrystals.
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TLDR
It is shown, 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.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.read more
Citations
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Topological Photonics
Tomoki Ozawa,Hannah M. Price,Alberto Amo,Nathan Goldman,Mohammad Hafezi,Ling Lu,Mikael C. Rechtsman,David Schuster,Jonathan Simon,Oded Zilberberg,Iacopo Carusotto +10 more
TL;DR: Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light as mentioned in this paper, which holds great promise for applications.
Journal ArticleDOI
Photonic Floquet topological insulators
Mikael C. Rechtsman,Julia M. Zeuner,Yonatan Plotnik,Yaakov Lumer,Daniel K. Podolsky,Felix Dreisow,Stefan Nolte,Mordechai Segev,Alexander Szameit +8 more
TL;DR: This work proposes and experimentally demonstrate a photonic topological insulator free of external fields and with scatter-free edge transport—a photonic lattice exhibiting topologically protected transport of visible light on the lattice edges.
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Imaging topological edge states in silicon photonics
TL;DR: In this paper, topological edge states of light are observed in a two-dimensional array of coupled optical ring resonators, which induce a virtual magnetic field for photons using silicon-on-insulator technology.
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Light-induced gauge fields for ultracold atoms
TL;DR: Different realized and proposed techniques for creating gauge potentials-both Abelian and non-Abelian-in atomic systems and their implication in the context of quantum simulation are reviewed.
Journal ArticleDOI
Direct measurement of the Zak phase in topological Bloch bands
Marcos Atala,Monika Aidelsburger,Julio T. Barreiro,Dmitry A. Abanin,Takuya Kitagawa,Takuya Kitagawa,Eugene Demler,Immanuel Bloch +7 more
TL;DR: In this article, the topological properties of Bloch bands in one-dimensional optical lattices were investigated using Bloch oscillations and Ramsey interferometry, and the Zak phase obtained by cold atoms moving across the Brillouin zone was extracted.
References
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Colloquium: Topological insulators
M. Z. Hasan,Charles L. Kane +1 more
TL;DR: In this paper, the theoretical foundation for topological insulators and superconductors is reviewed and recent experiments are described in which the signatures of topologically insulators have been observed.
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Quantized Hall conductance in a two-dimensional periodic potential
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Non-Abelian Anyons and Topological Quantum Computation
TL;DR: In this article, the authors describe the mathematical underpinnings of topological quantum computation and the physics of the subject using the nu=5/2 fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.
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Observation of a large-gap topological-insulator class with a single Dirac cone on the surface
Yuqi Xia,Dong Qian,Dong Qian,David Hsieh,Lewis Wray,Arijeet Pal,Hsin Lin,Arun Bansil,D. Grauer,Yew San Hor,Robert J. Cava,M. Z. Hasan +11 more
TL;DR: In this paper, an angle-resolved photo-emission spectroscopy study was conducted to reveal the first observation of a topological state of matter featuring a single surface Dirac cone realized in the naturally occurring Bi-2Se-3 class of materials.
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Topological field theory of time-reversal invariant insulators
TL;DR: In this paper, it was shown that the fundamental time-reversal invariant (TRI) insulator exists in $4+1$ dimensions, where the effective field theory is described by the $(4 + 1)$-dimensional Chern-Simons theory and the topological properties of the electronic structure are classified by the second Chern number.