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The space group classification of topological band-insulators

Nature Physics volume 9, pages 98–102 (2013)Cite this article

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Abstract

Topological band-insulators (TBIs) are bulk insulating materials, which in the presence of time-reversal symmetry feature topologically protected metallic states on their surface or edge. They have recently been discovered in two- and three-dimensional materials with a strong spin–orbit coupling. These unusual states of quantum matter may host Majorana fermions and provide the condensed-matter realization of the exotic theta-vacuum. The existing classification of TBIs departs from time-reversal symmetry, but the role of the crystal-lattice symmetries in the physics of these topological states has remained elusive. Here we provide the classification of TBIs protected not only by time-reversal, but also by crystalline symmetries. We find three broad classes of topological states: Γ states robust against general time-reversal invariant perturbations; translationally active states protected from elastic scattering, but susceptible to topological crystalline disorder; valley topological insulators sensitive to the effects of non-topological and crystalline disorder. These three classes give rise to 18 different two-dimensional, and, at least 70 three-dimensional TBIs, opening up a route for the systematic search for new types of TBIs.

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Figure 1: Phase diagram of the extended M–B tight-binding model.
Figure 2: Illustration of the role of lattice symmetries in the classification of topological states.

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Acknowledgements

This work is supported by the Dutch Foundation for Fundamental Research on Matter (FOM). V.J. acknowledges the support of the Netherlands Organization for Scientific Research (NWO).

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Authors and Affiliations

  1. Instituut-Lorentz for Theoretical Physics, Universiteit Leiden, PO Box 9506, 2300 RA Leiden, The Netherlands

    Robert-Jan Slager, Vladimir Juričić & Jan Zaanen

  2. Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, USA

    Andrej Mesaros

Authors
  1. Robert-Jan Slager
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  2. Andrej Mesaros
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  3. Vladimir Juričić
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  4. Jan Zaanen
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All authors contributed extensively to the work presented in this paper.

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Correspondence to Vladimir Juričić.

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The authors declare no competing financial interests.

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Slager, RJ., Mesaros, A., Juričić, V. et al. The space group classification of topological band-insulators. Nature Phys 9, 98–102 (2013). https://doi.org/10.1038/nphys2513

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