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Topological States and Adiabatic Pumping in Quasicrystals
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TLDR
In this paper, it was shown that one-dimensional quasicrystals are assigned two-dimensional Chern numbers and exhibit topologically protected boundary states equivalent to the edge states of a 2D 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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References
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Journal ArticleDOI
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.
Journal ArticleDOI
Quantized Hall conductance in a two-dimensional periodic potential
TL;DR: In this article, the Hall conductance of a two-dimensional electron gas has been studied in a uniform magnetic field and a periodic substrate potential, where the Kubo formula is written in a form that makes apparent the quantization when the Fermi energy lies in a gap.
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.
Journal ArticleDOI
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
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.