Topological zero modes and Dirac points protected by spatial symmetry and chiral symmetry
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In this clear and thorough contribution, the authors present general arguments to show that topologically stable zero energy modes can be protected by the coexistence of both chiral symmetry and spatial symmetry.
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Creation and annihilation rules for Dirac points stabilized by rotational symmetries in both Class I and Class II DSMs have been identified.
“Creation and annihilation rules for Dirac points stabilized by rotational symmetries in both Class I and Class II DSMs have been identified (Koshino et al. , 2014).”
From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Koshino et al., 2014
Section VI (pp. 7–8) gives examples of three-dimensional Dirac nodes, and Section VII (pp. 8–11) classifies their protection by chiral and spatial symmetries, including rotations. The passages do not identify creation-and-annihilation rules or discuss Class I and Class II DSMs; searches for those terms and for annihilation did not find them. (LLM, conf=0.84)
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Cites
Wan, X., Turner, A. M., Vishwanath, A., & Savrasov, S. Y. (2011) · Physical Review B · doi:10.1103/physrevb.83.205101 · Cited by 4,718 · see citing works
Topological crystalline insulators in the SnTe material class
Hsieh, T. H., Lin, H., Liu, J., Duan, W., Bansil, A., & Fu, L. (2012) · Nature Communications · doi:10.1038/ncomms1969 · Cited by 1,449 · see citing works
Observation of a three-dimensional topological Dirac semimetal phase in high-mobility Cd3As2
Neupane, M., Xu, S.-Y., Sankar, R., Alidoust, N., Bian, G., Liu, C., Belopolski, I., Chang, T.-R., Jeng, H.-T., Lin, H., et al. (2014) · Nature Communications · doi:10.1038/ncomms4786 · Cited by 1,399 · see citing works
Murakami, S. (2007) · New Journal of Physics · doi:10.1088/1367-2630/9/9/356 · Cited by 1,176 · see citing works
Classification of stable three-dimensional Dirac semimetals with nontrivial topology
Yang, B.-J., & Nagaosa, N. (2014) · Nature Communications · doi:10.1038/ncomms5898 · Cited by 864 · see citing works
Topological crystalline insulator states in Pb1−xSnxSe
Dziawa, P., Kowalski, B. J., Dybko, K., Buczko, R., Szczerbakow, A., Szot, M., Łusakowska, E., Balasubramanian, T., Wojek, B. M., Berntsen, M. H., et al. (2012) · Nature Materials · doi:10.1038/nmat3449 · Cited by 820 · see citing works
Xu, S.-Y., Liu, C., Alidoust, N., Neupane, M., Qian, D., Belopolski, I., Denlinger, J. D., Wang, Y. J., Lin, H., Wray, L. A., et al. (2012) · Nature Communications · doi:10.1038/ncomms2191 · Cited by 691 · see citing works
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- 40 I. Affleck and J. B. Marston, Physical Review B 37 , 3774 (1988).
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Weyl and Dirac semimetals in three-dimensional solids
Armitage, N. P., Mele, E. J., & Vishwanath, A. (2018) · Reviews of Modern Physics · doi:10.1103/revmodphys.90.015001 · Cited by 4,528 · see citing works
“Creation and annihilation rules for Dirac points stabilized by rotational symmetries in both Class I and Class II DSMs have been identified (Koshino et al., 2014).”
BackgroundClassification of reflection-symmetry-protected topological semimetals and nodal superconductors
Chiu, C.-K., & Schnyder, A. P. (2014) · Physical Review B · doi:10.1103/physrevb.90.205136 · Cited by 339 · see citing works
Weyl and Dirac Semimetals in Three Dimensional Solids
Armitage, N. P., Mele, E. J., & Vishwanath, A. (2017) · arXiv
“Creation and annihilation rules for Dirac points stabilized by rotational symmetries in both Class I and Class II DSMs have been identified (Koshino et al., 2014).”
Background
- Authors
- Koshino, M., Morimoto, T., & Sato, M.
- Affiliations
- Tohoku University (JP)
- RIKEN (JP)
- Nagoya University (JP)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2014-09-22
- Volume
- 90
- Issue
- 11
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W2324722311
- Cited by
- 69
- References
- 7
- Citations by year
- 2026: 2 · 2025: 5 · 2024: 5 · 2023: 5 · 2022: 7 · 2021: 5 · 2020: 5 · 2019: 6 · 2018: 6 · 2017: 4 · 2016: 10 · 2015: 7 · 2014: 2
- FWCI
- 3.81
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review B (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Japan Society for the Promotion of Science (24740193, 25107005, 24840047, 22103005, 25287085)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Non-Hermitian Physics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
- Keywords
- topological zero modes, Dirac point, chiral symmetry, spatial symmetry, topological protection, zero modes, topological insulators
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