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      Topologically robust sound propagation in an angular-momentum-biased graphene-like resonator lattice

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          Abstract

          Topological insulators do not allow conduction in the bulk, yet they support edge modes that travel along the boundary only in one direction, determined by the carried electron spin, with inherent robustness to defects and disorder. Topological insulators have inspired analogues in photonics and optics, in which one-way edge propagation in topologically protected two-dimensional materials is achieved breaking time-reversal symmetry with a magnetic bias. Here, we introduce the concept of topological order in classical acoustics, realizing robust topological protection and one-way edge propagation of sound in a suitably designed resonator lattice biased with angular momentum, forming the acoustic analogue of a magnetically biased graphene layer. Extending the concept of an acoustic nonreciprocal circulator based on angular-momentum bias, time-reversal symmetry is broken here using moderate rotational motion of air within each element of the lattice, which takes the role of the electron spin in determining the direction of modal edge propagation.

          Abstract

          Topological order for sound remains largely unexplored. Here, Khanikaev et al. introduce the concept of topological order in classical acoustics, realizing robust topological protection and one-way edge propagation of sound in a suitably designed resonator lattice, thus expanding the ability to tailor acoustic waves.

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          Most cited references15

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          Quantum Spin Hall Effect in Graphene

          We study the effects of spin orbit interactions on the low energy electronic structure of a single plane of graphene. We find that in an experimentally accessible low temperature regime the symmetry allowed spin orbit potential converts graphene from an ideal two dimensional semimetallic state to a quantum spin Hall insulator. This novel electronic state of matter is gapped in the bulk and supports the quantized transport of spin and charge in gapless edge states that propagate at the sample boundaries. The edge states are non chiral, but they are insensitive to disorder because their directionality is correlated with spin. The spin and charge conductances in these edge states are calculated and the effects of temperature, chemical potential, Rashba coupling, disorder and symmetry breaking fields are discussed.
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            Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells

            We show that the Quantum Spin Hall Effect, a state of matter with topological properties distinct from conventional insulators, can be realized in HgTe/CdTe semiconductor quantum wells. By varying the thickness of the quantum well, the electronic state changes from a normal to an "inverted" type at a critical thickness \(d_c\). We show that this transition is a topological quantum phase transition between a conventional insulating phase and a phase exhibiting the QSH effect with a single pair of helical edge states. We also discuss the methods for experimental detection of the QSH effect.
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              Topological Insulators in Three Dimensions

              (2007)
              We study three dimensional generalizations of the quantum spin Hall (QSH) effect. Unlike two dimensions, where the QSH effect is distinguished by a single \(Z_2\) topological invariant, in three dimensions there are 4 invariants distinguishing 16 "topological insulator" phases. There are two general classes: weak (WTI) and strong (STI) topological insulators. The WTI states are equivalent to layered 2D QSH states, but are fragile because disorder continuously connects them to band insulators. The STI states are robust and have surface states that realize the 2+1 dimensional parity anomaly without fermion doubling, giving rise to a novel "topological metal" surface phase. We introduce a tight binding model which realizes both the WTI and STI phases, and we discuss the relevance of this model to real three dimensional materials, including bismuth.
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                Author and article information

                Journal
                Nat Commun
                Nat Commun
                Nature Communications
                Nature Pub. Group
                2041-1723
                06 October 2015
                2015
                : 6
                : 8260
                Affiliations
                [1 ]Department of Physics, Queens College of The City University of New York , Queens, New York 11367, USA
                [2 ]Department of Physics, The Graduate Center of The City University of New York , New York, New York 10016, USA
                [3 ]The Department of Electrical and Computer Engineering, The University of Texas at Austin , 1616 Guadalupe Street, UTA 7.215, Austin, Texas 78701, USA
                Author notes
                [*]

                These authors equally contributed to the present work.

                Author information
                http://orcid.org/0000-0002-4297-5274
                Article
                ncomms9260
                10.1038/ncomms9260
                4600716
                26440700
                eb0923f1-9e6b-47ba-aa3d-eb4d7c273bd6
                Copyright © 2015, Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.

                This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

                History
                : 29 May 2015
                : 04 August 2015
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