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Cited by 973Topological Materials and PhenomenaAdvanced Condensed Matter PhysicsQuantum and electron transport phenomena

Topological phases and the quantum spin Hall effect in three dimensions

Open access
Roy, Rahul·2009·Physical Review B
DOI 10.1103/physrevb.79.195322
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Abstract

We show the existence of topological phases of Bloch insulators with time-reversal symmetry in three dimensions. These phases are characterized by topological ${Z}_{2}$ invariants whose stability is studied using band-touching arguments. Unlike insulators which break time-reveral symmetry, some of these topological phases are intrinsically three dimensional. The number of invariants (four) needed to specify the phase of these insulators also differs from the time-reversal-breaking case. The relation between these phases and the quantum spin Hall effect in three dimensions is investigated.

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  • The three-dimensional topological state in Bi_{1-x}Sb_x cannot be reduced to a quantum spin Hall state.

    “The 3D topological state in Bi 1 -x Sb x is a new state in the sense that it cannot be reduced to a quantum spin Hall state (4, 6, 14).”

    From Three-Dimensional Topological Insulators (2011) · cites this paper as [14]

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Flagged first, then by citations

Research works printed but not linked: 18

  1. [1]R. Roy, Arxiv preprint cond-mat/0604211 (2006). · arXiv
  2. [2]C. Kane and E. Mele, Physical Review Letters 95 , 146802 (2005).
  3. [3]C. Kane and E. Mele, Physical Review Letters 95 , 226801 (2005).
  4. [4]B. A. Bernevig and S.-C. Zhang, Arxiv preprint condmat/0504147 (2005).
  5. [5]R. Roy, Arxiv preprint cond-mat/0603271 (2006). · arXiv
  6. [6]C. Xu and J. E. Moore, Physical Review B 73 , 064417 (2006).
  7. [7]C. Wu, B. Bernevig, and S. Zhang, Physical Review Letters 96 , 106401 (2006).
  8. [8]L. Sheng, D. N. Sheng, C. S. Ting, and F. D. M. Haldane, Physical Review Letters 95 , 136602 (2005).
  9. [9]B. Bernevig and S. Zhang, Physical Review Letters 96 , 106802 (2006).
  10. [10]D. N. Sheng, Z. Y. Weng, L. Sheng, and F. D. M. Haldane, Arxiv preprint cond-mat/0603054 (2006). · arXiv
  11. [13]J. Bellissard, Arxiv preprint cond-mat/9504030 (1995). · arXiv
  12. [14]F. D. M. Haldane, Physical Review Letters 93 , 206602 (2004).
  13. [16]X.-L. Qi, Y.-S. Wu, and S.-C. Zhang, Arxiv preprint cond-mat/0505308 (2005). · arXiv
  14. [18]M. Kohmoto, B. Halperin, and Y. Wu, Physical Review B 45 , 13488 (1992).
  15. [19]A. de Blas and F. Axel, Journal of Physics: Condensed Matter 16 , 7673 (2004).
  16. [20]K. Sengupta, R. Roy, and M. Maiti, Arxiv preprint condmat/0604217 (2006).
  17. [21]L. Fu and C. L. Kane, Arxiv preprint cond-mat/0606336 (2006). · arXiv
  18. [23]J. E. Moore and L. Balents, Arxiv preprint condmat/0607314 (2006).

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Authors
Roy, R.
Affiliations
McMaster University (CA)
Corresponding author
Roy, Rahul
ORCID
Roy, Rahul
Venue
Physical Review B
Publisher
American Physical Society (APS)
Published
2009-05-21
Volume
79
Issue
19
ISSN
  • 1098-0121 (ISSN-L)
  • 1550-235X
DOI
10.1103/physrevb.79.195322
OpenAlex
W1524641833
Cited by
973
References
4
Citations by year
2026: 22 · 2025: 30 · 2024: 35 · 2023: 39 · 2022: 43 · 2021: 50 · 2020: 52 · 2019: 51 · 2018: 67 · 2017: 51 · 2016: 74 · 2015: 78 · 2014: 70 · 2013: 96 · 2012: 84
FWCI
39.71
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review B (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
  • Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
Keywords
topological phases, quantum spin Hall effect, time-reversal symmetry, Z2 topological invariant, topological invariants

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