Filling constraints for spin-orbit coupled insulators in symmorphic and nonsymmorphic crystals
Open accessAbstract
Significance: Quantum spin liquids are exotic insulators in which the electron’s spin, charge, and fermionic statistics are carried by separate excitations. They have received attention for their potential as a quantum memory and as a parent state for high-temperature superconductivity. A key principle guiding the search for experimental candidate materials is the absence of conventional order in insulators at “fractional” electron filling. Previous results established what constitutes fractional filling, but assumed symmetries that are typically not respected in real materials or considered only simple lattices. Here, assuming only physical symmetries we establish filling conditions for all 230 space groups. This should aid in the search for quantum spin liquids and topological semimetals.
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Additional crystalline point group symmetries are needed to realize a stable DSM phase because a pair of degenerate Weyl nodes of opposite chiralities is generally unstable and may annihilate.
“Since a pair of degenerate Weyl nodes of opposite chiralities is in general unstable and may annihilate, additional crystalline point group symmetries are needed to realize a stable DSM phase (131).”
From Transport of Topological Semimetals (2019) · cites this paper as [131]
The Applications section says that the stability of Dirac cones in a diamond-lattice model arises from its nonsymmorphic space group. It does not discuss degenerate Weyl nodes of opposite chirality, their possible annihilation, or a general requirement for additional point-group symmetries. (LLM, conf=0.83)
Experimental — accuracy not yet measuredDSMs host Dirac fermions as low-energy quasiparticle excitations.
“DSMs host Dirac fermions as low-energy quasiparticle excitations (12-14, 38, 126-131).”
From Transport of Topological Semimetals (2019) · cites this paper as [131]
This presents an example of a 'filling enforced semimetal' where the zone boundary degeneracy requires that electron count for a filled band actually results in a gapless state where the conduction and valence bands contact each other.
“This presents an example of a 'filling enforced semimetal' (Parameswaran, 2015; Parameswaran et al. , 2013; Watanabe et al. , 2015) where the zone boundary degeneracy requires that electron count for a filled band actually results in a gapless state where the conduction and valence bands contact each other.”
From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Watanabe et al., 2015
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Cites
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Research works printed but not linked: 7
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Cited by
Sorted by citations
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
“This presents an example of a “filling enforced semimetal” (Parameswaran, 2015; Parameswaran et al., 2013; Watanabe et al., 2015) where the zone boundary degeneracy requires that electron count for a filled band actually results in a gapless state where the conduction and valence bands contact each…”
BackgroundSelf-citationBeyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals
Bradlyn, B., Cano, J., Wang, Z., Vergniory, M. G., Felser, C., Cava, R. J., & Bernevig, B. A. (2016) · Science · doi:10.1126/science.aaf5037 · Cited by 1,252 · see citing works
Unconventional Chiral Fermions and Large Topological Fermi Arcs in RhSi
Chang, G., Xu, S.-Y., Wieder, B. J., Sanchez, D. S., Huang, S.-M., Belopolski, I., Chang, T.-R., Zhang, S., Bansil, A., Lin, H., et al. (2017) · Physical Review Letters · doi:10.1103/physrevlett.119.206401 · Cited by 399 · see citing works
Symmetry-protected topological photonic crystal in three dimensions
Lu, L., Fang, C., Fu, L., Johnson, S. G., Joannopoulos, J. D., & Soljačić, M. (2016) · Nature Physics · doi:10.1038/nphys3611 · Cited by 329 · see citing works
Transport of Topological Semimetals
Hu, J., Xu, S.-Y., Ni, N., & Mao, Z. (2019) · Annual Review of Materials Research · doi:10.1146/annurev-matsci-070218-010023 · Cited by 265 · see citing works
Topological Semimetals from First Principles
Gao, H., Venderbos, J. W. F., Kim, Y., & Rappe, A. M. (2019) · Annual Review of Materials Research · doi:10.1146/annurev-matsci-070218-010049 · Cited by 263 · see citing works
Unconventional Photocurrents from Surface Fermi Arcs in Topological Chiral Semimetals
Chang, G., Yin, J.-X., Neupert, T., Sanchez, D. S., Belopolski, I., Zhang, S. S., Cochran, T. A., Chéng, Z., Hsu, M.-C., Huang, S.-M., et al. (2020) · Physical Review Letters · doi:10.1103/physrevlett.124.166404 · Cited by 72 · see citing works
Topological materials discovery using electron filling constraints
Chen, R., Po, H. C., Neaton, J. B., & Vishwanath, A. (2018) · Nature Physics · doi:10.1038/nphys4277 · Cited by 47 · see citing works
Self-citationWeyl and Dirac Semimetals in Three Dimensional Solids
Armitage, N. P., Mele, E. J., & Vishwanath, A. (2017) · arXiv
“This presents an example of a “filling enforced semimetal” (Parameswaran, 2015; Parameswaran et al., 2013; Watanabe et al., 2015) where the zone boundary degeneracy requires that electron count for a filled band actually results in a gapless state where the conduction and valence bands contact each…”
BackgroundSelf-citation
- Authors
- Watanabe, H., Po, H. C., Vishwanath, A., & Zaletel, M.
- Affiliations
- Massachusetts Institute of Technology (US)
- University of California, Berkeley (US)
- Lawrence Berkeley National Laboratory (US)
- University of California, Santa Barbara (US)
- Venue
- Proceedings of the National Academy of Sciences
- Publisher
- National Academy of Sciences
- Published
- 2015-11-10
- Volume
- 112
- Issue
- 47
- Pages
- 14551-14556
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- PMC
- PMC4664378
- OpenAlex
- W2096367297
- Cited by
- 195
- References
- 4
- Citations by year
- 2026: 7 · 2025: 11 · 2024: 19 · 2023: 17 · 2022: 15 · 2021: 24 · 2020: 16 · 2019: 16 · 2018: 20 · 2017: 26 · 2016: 24
- FWCI
- 11.86
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Proceedings of the National Academy of Sciences (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Rare & Special e-Zone (The Hong Kong University of Science and Technology) (submittedVersion)
- DSpace@MIT (Massachusetts Institute of Technology) (submittedVersion, cc-by-nc)
- eScholarship (California Digital Library) (submittedVersion)
- arXiv (Cornell University)
- Bulletin of the American Physical Society
- Funders
- National Science Foundation (1206728)
- John Templeton Foundation
- Division of Materials Research
- 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 many-body systems
- Keywords
- Lieb-Schultz-Mattis theorem, time-reversal symmetry, entanglement, space groups, fractionalized excitations, strongly interacting electrons, ground state degeneracy
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