Topological nodal line semimetals with and without spin-orbital coupling
Open accessAbstract
We theoretically study three-dimensional topological semimetals (TSMs) with nodal lines protected by crystalline symmetries. Compared to TSMs with point nodes, e.g., Weyl semimetals and Dirac semimetals, where the conduction and the valence bands touch at discrete points, in these TSMs the two bands cross at closed lines in the Brillouin zone. We propose two different classes of symmetry protected nodal lines in the absence and in the presence of spin-orbital coupling (SOC), respectively. In the former, we discuss nodal lines that are protected by a combination of inversion symmetry and time-reversal symmetry, yet, unlike previously studied nodal lines in the same symmetry class, each nodal line has a ${Z}_{2}$ monopole charge and can only be created (annihilated) in pairs. In the second class, with SOC, we show that a nonsymmorphic symmetry (screw axis) protects a four-band crossing nodal line in systems having both inversion and time-reversal symmetries.
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Nodal lines in 3D can be captured by considering d' = 1 submanifolds, which can be classified according to -1 + 8 = 7 dimensional topological insulators in class AI, giving a Z2 classification.
“Therefore, nodal lines in 3D can be captured by considering a d ′ = 1 submanifolds, which can be classified according to -1 + 8 = 7 dimensional topological insulators in class AI. This has a Z 2 classification consistent with the more direct calculation of (Fang et al. , 2015; Morimoto and Furusaki, 2014).”
From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Fang et al., 2015
There is a second Z2 invariant associated with surfaces in momentum space, much like that used to characterize Weyl nodes.
“Surprisingly, there is a second Z 2 invariant associated with surfaces in momentum space, much like that used to characterize Weyl nodes (Fang et al. , 2015).”
From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Fang et al., 2015
There is an additional invariant for nodal lines in 3D that does not allow a nodal line to be shrunk to zero; as with Weyl nodes, nodal monopoles must come in pairs to give net zero charge in the Brillouin zone.
“Indeed, there is an additional invariant for nodal lines in 3D that does not allow us to simply shrink a nodal line to zero (Fang et al. , 2015). As with Weyl nodes, these nodal 'monopoles' must come in pairs to give net zero charge in the BZ.”
From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Fang et al., 2015
SrIrO3 is an example of a nodal line semimetal.
“An example of such a nodal line semimetal is furnished by SrIrO 3 (Chen et al. , 2016; Fang et al. , 2015).”
From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Fang et al., 2015
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Weyl and Dirac semimetals in three-dimensional solids
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“Indeed, there is an additional invariant for nodal lines in 3D that does not allow us to simply shrink a nodal line to zero (Fang et al., 2015).”
BackgroundInfluential
- Authors
- Fang, C., Chen, Y., Kee, H.-Y., & Fu, L.
- Affiliations
- Massachusetts Institute of Technology (US)
- Canadian Institute for Advanced Research (CA)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2015-08-10
- Volume
- 92
- Issue
- 8
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W1924841494
- Cited by
- 921
- References
- 10
- Citations by year
- 2026: 53 · 2025: 79 · 2024: 89 · 2023: 64 · 2022: 100 · 2021: 99 · 2020: 100 · 2019: 103 · 2018: 98 · 2017: 75 · 2016: 57 · 2015: 2 · 2014: 1
- FWCI
- 39.31
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Physical Review B (publishedVersion, cc-by)
- arXiv (Cornell University) (acceptedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion, cc-by)
- DSpace@MIT (Massachusetts Institute of Technology) (submittedVersion, cc-by-nc)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- arXiv (Cornell University)
- Physical Review Letters
- Funders
- U.S. Department of Energy (DE-SC0001299/DE-FG02-09ER46577)
- Natural Sciences and Engineering Research Council of Canada
- University of Toronto
- 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 › Materials Science › Materials Chemistry › 2D Materials and Applications
- Keywords
- topological nodal-line semimetal, spin-orbit coupling, nonsymmorphic symmetry, screw axis, inversion symmetry, time-reversal symmetry
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