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  • Letter
  • Open Access

Topology of three-dimensional Dirac semimetals and quantum spin Hall systems without gapless edge modes

Alexander C. Tyner1,*, Shouvik Sur2,*, Danilo Puggioni3, James M. Rondinelli1,3,4, and Pallab Goswami1,2

  • 1Graduate Program in Applied Physics, Northwestern University, Evanston, Illinois 60208,USA
  • 2Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA
  • 3Department of Materials Science and Engineering, Northwestern University, Illinois 60208, USA
  • 4Northwestern Argonne Institute for Science and Engineering, Evanston, Illinois 60208, USA

  • *These authors contributed equally to this work.
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Phys. Rev. Research 5, L012019 – Published 13 February, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L012019

Abstract

The quantum spin Hall states are usually expected to possess gapless, helical edge modes. We show that the generic, n-fold-symmetric, momentum planes of three-dimensional, stable Dirac semimetals, which are orthogonal to the direction of nodal separation are examples of generalized quantum spin Hall systems, that possess quantized, spin or relative Chern numbers as bulk topological invariants, and gapped edge modes. We demonstrate these planes and the celebrated Bernevig-Zhang-Hughes model support identical quantized, non-Abelian Berry flux of magnitude 2π. Hence, they display identical quantized, topological response such as spin-charge separation and pumping of one Kramers-pair or SU(2) doublet, when probed with a magnetic flux tube. The Dirac points are identified as unit-strength, monopoles of SO(5) Berry connection, describing topological phase transitions between generalized quantum spin Hall and trivial insulators. Our work identifies precise bulk invariant and quantized response of Dirac semimetals, which are not diagnosed by nested Wilson loops and filling anomaly of corner-localized-states, and shows that many two-dimensional higher-order topological insulators can be understood as generalized quantum spin Hall systems.

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Outline

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Phys. Rev. Research 5, L012019– Published 13 February, 2023
  • Received 14 January 2022
  • Revised 20 November 2022
  • Accepted 28 November 2022
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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