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      Photonic Floquet Topological Insulators

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          Abstract

          The topological insulator is a fundamentally new phase of matter, with the striking property that the conduction of electrons occurs only on its surface, not within the bulk, and that conduction is topologically protected. Topological protection, the total lack of scattering of electron waves by disorder, is perhaps the most fascinating and technologically important aspect of this material: it provides robustness that is otherwise known only for superconductors. However, unlike superconductivity and the quantum Hall effect, which necessitate low temperatures or magnetic fields, the immunity to disorder of topological insulators occurs at room temperature and without any external magnetic field. For this reason, topological protection is predicted to have wide-ranging applications in fault-tolerant quantum computing and spintronics. Recently, a large theoretical effort has been directed towards bringing the concept into the domain of photonics: achieving topological protection of light at optical frequencies. Besides the interesting new physics involved, photonic topological insulators hold the promise for applications in optical isolation and robust photon transport. Here, we theoretically propose and experimentally demonstrate the first photonic topological insulator: a photonic lattice exhibiting topologically protected transport on the lattice edges, without the need for any external field. The system is composed of an array of helical waveguides, evanescently coupled to one another, and arranged in a graphene-like honeycomb lattice. The chirality of the waveguides results in scatter-free, one-way edge states that are topologically protected from scattering.

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          Most cited references14

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          Two-Dimensional Gas of Massless Dirac Fermions in Graphene

          Electronic properties of materials are commonly described by quasiparticles that behave as non-relativistic electrons with a finite mass and obey the Schroedinger equation. Here we report a condensed matter system where electron transport is essentially governed by the Dirac equation and charge carriers mimic relativistic particles with zero mass and an effective "speed of light" c* ~10^6m/s. Our studies of graphene - a single atomic layer of carbon - have revealed a variety of unusual phenomena characteristic of two-dimensional (2D) Dirac fermions. In particular, we have observed that a) the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; b) graphene's conductivity never falls below a minimum value corresponding to the conductance quantum e^2/h, even when carrier concentrations tend to zero; c) the cyclotron mass m of massless carriers with energy E in graphene is described by equation E =mc*^2; and d) Shubnikov-de Haas oscillations in graphene exhibit a phase shift of pi due to Berry's phase.
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            Topological Insulators

            , (2011)
            Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator, but have protected conducting states on their edge or surface. The 2D topological insulator is a quantum spin Hall insulator, which is a close cousin of the integer quantum Hall state. A 3D topological insulator supports novel spin polarized 2D Dirac fermions on its surface. In this Colloquium article we will review the theoretical foundation for these electronic states and describe recent experiments in which their signatures have been observed. We will describe transport experiments on HgCdTe quantum wells that demonstrate the existence of the edge states predicted for the quantum spin Hall insulator. We will then discuss experiments on Bi_{1-x}Sb_x, Bi_2 Se_3, Bi_2 Te_3 and Sb_2 Te_3 that establish these materials as 3D topological insulators and directly probe the topology of their surface states. We will then describe exotic states that can occur at the surface of a 3D topological insulator due to an induced energy gap. A magnetic gap leads to a novel quantum Hall state that gives rise to a topological magnetoelectric effect. A superconducting energy gap leads to a state that supports Majorana fermions, and may provide a new venue for realizing proposals for topological quantum computation. We will close by discussing prospects for observing these exotic states, a well as other potential device applications of topological insulators.
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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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                Author and article information

                Journal
                13 December 2012
                Article
                10.1038/nature12066
                23579677
                1212.3146
                2a0ee1e4-654d-40b3-8ddf-07b10720a79d

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                21 pages, 5 figures
                physics.optics cond-mat.mes-hall cond-mat.mtrl-sci cond-mat.other

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