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      Complete theory of symmetry-based indicators of band topology

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      1 , 2 , 1 , 2 , , 3
      Nature Communications
      Nature Publishing Group UK

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          Abstract

          The interplay between symmetry and topology leads to a rich variety of electronic topological phases, protecting states such as the topological insulators and Dirac semimetals. Previous results, like the Fu-Kane parity criterion for inversion-symmetric topological insulators, demonstrate that symmetry labels can sometimes unambiguously indicate underlying band topology. Here we develop a systematic approach to expose all such symmetry-based indicators of band topology in all the 230 space groups. This is achieved by first developing an efficient way to represent band structures in terms of elementary basis states, and then isolating the topological ones by removing the subset of atomic insulators, defined by the existence of localized symmetric Wannier functions. Aside from encompassing all earlier results on such indicators, including in particular the notion of filling-enforced quantum band insulators, our theory identifies symmetry settings with previously hidden forms of band topology, and can be applied to the search for topological materials.

          Abstract

          Understanding the role of topology in determining electronic structure can lead to the discovery, or appreciation, of materials with exotic properties such as protected surface states. Here, the authors present a framework for identifying topologically distinct band-structures for all 3D space groups.

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          Most cited references29

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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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            Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface

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              Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator

              In 5d transition metal oxides such as the iridates, novel properties arise from the interplay of electron correlations and spin-orbit interactions. We investigate the electronic structure of the pyrochlore iridates, (such as Y2Ir2O7) using density functional theory, LDA+U method, and effective low energy models. A remarkably rich phase diagram emerges on tuning the correlation strength U. The Ir magnetic moment are always found to be non-collinearly ordered. However, the ground state changes from a magnetic metal at weak U, to a Mott insulator at large U. Most interestingly, the intermediate U regime is found to be a Dirac semi-metal, with vanishing density of states at the Fermi energy. It also exhibits topological properties - manifested by special surface states in the form of Fermi arcs, that connect the bulk Dirac points. This Dirac phase, a three dimensional analog of graphene, is proposed as the ground state of Y2Ir2O7 and related compounds. A narrow window of magnetic `axion' insulator, with axion parameter θ=π, may also be present at intermediate U. An applied magnetic field induces ferromagnetic order and a metallic ground state.
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                Author and article information

                Contributors
                avishwanath@g.harvard.edu
                Journal
                Nat Commun
                Nat Commun
                Nature Communications
                Nature Publishing Group UK (London )
                2041-1723
                30 June 2017
                30 June 2017
                2017
                : 8
                : 50
                Affiliations
                [1 ]ISNI 0000 0001 2181 7878, GRID grid.47840.3f, Department of Physics, , University of California, ; Berkeley, CA 94720 USA
                [2 ]ISNI 000000041936754X, GRID grid.38142.3c, Department of Physics, , Harvard University, ; Cambridge, MA 02138 USA
                [3 ]ISNI 0000 0001 2151 536X, GRID grid.26999.3d, Department of Applied Physics, , University of Tokyo, ; Tokyo, 113-8656 Japan
                Article
                133
                10.1038/s41467-017-00133-2
                5493703
                28667305
                92cfffb0-327f-4602-8c5a-3ca9bcf4900a
                © The Author(s) 2017

                Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

                History
                : 11 March 2017
                : 2 June 2017
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