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Novel topological insulators from crystalline symmetries

  • Alexander Lau
  • Carmine Ortix
Open Access
Regular Article
  • 51 Downloads
Part of the following topical collections:
  1. Topological States of Matter: Theory and Applications

Abstract

We discuss recent advances in the study of topological insulators protected by spatial symmetries by reviewing three representative, theoretical examples. In three dimensions (3D), these states of matter are generally characterized by the presence of gapless boundary states at surfaces that respect the protecting spatial symmetry. We discuss the appearance of these topological states in both crystals with negligible spin–orbit coupling and a fourfold rotational symmetry, as well as in mirror-symmetric crystals with sizable spin–orbit interaction characterized by the so-called mirror Chern number. Finally, we also discuss similar topological crystalline states in one-dimensional (1D) insulators, such as nanowires or atomic chains, with mirror symmetry. There, the prime physical consequence of the non-trivial topology is the presence of quantized end charges.

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Copyright information

© The Author(s) 2018 2018

Open AccessThis is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://doi.org/creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  1. 1.Kavli Institute of Nanoscience, Delft University of TechnologyDelftThe Netherlands
  2. 2.Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht UniversityUtrechtThe Netherlands
  3. 3.Dipartimento di Fisica “E.R. Caianiello”, Università di SalernoFiscianoItaly

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