Classification of stable three-dimensional Dirac semimetals with nontrivial topology
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A three-dimensional (3D) Dirac semimetal (SM) is the 3D analogue of graphene having linear energy dispersion around Fermi points. Owing to the nontrivial topology of electronic wave functions, the 3D Dirac SM shows nontrivial physical properties and hosts various exotic quantum states such as Weyl SMs and topological insulators under proper external conditions. There are several kinds of Dirac SMs proposed theoretically and partly confirmed experimentally, but its unified picture is still missing. Here we propose a general framework to classify stable 3D Dirac SMs in systems having the time-reversal, inversion and uniaxial rotational symmetries. We show that there are two distinct classes of 3D Dirac SMs. In one class, the Dirac SM possesses a single Dirac point (DP) at a time-reversal invariant momentum on the rotation axis. Whereas the other class of Dirac SMs have a pair of DPs created by band inversion, and carry a quantized topological invariant. Three-dimensional Dirac semimetals are a recently discovered state of condensed matter considered as the 3D analogue of graphene. Here, Yang et al. propose a general framework to classify stable 3D Dirac semimetals in systems with time-reversal, inversion and uniaxial rotational symmetries.
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A unified treatment of 'band-inverted' and 'symmetry enforced' DSMs can be developed by studying the combined action of time reversal symmetry T, uniaxial rotational symmetry C_n, and inversion symmetry P on a minimal four state Hamiltonian that couples two spin and two orbital degrees of freedom (Gao et al., 2016b; Yang and Nagaosa, 2014).
“A unified treatment of 'band-inverted' and 'symmetry enforced' DSMs can be developed by studying the combined action of time reversal symmetry T , uniaxial rotational symmetry C n , and inversion symmetry P on a minimal four state Hamiltonian that couples two spin and two orbital degrees of freedom (Gao et al. , 2016b; Yang and Nagaosa, 2014).”
From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Yang and Nagaosa, 2014
In Class II 3D Dirac semimetals, the location of the 3D Dirac point is fixed either at the center or the edge of the rotation axis, i.e., at a TRIM on the rotation axis.
“In this Dirac semimetal phase, the location of the 3D Dirac point is fixed either at the center or the edge of the rotation axis, i.e., at a TRIM on the rotation axis.”
From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Yang and Nagaosa, 2014
Table I is a classification table for Class I 3D Dirac semimetals obtained by an accidental band crossing in systems having C_n rotational symmetry with respect to the z axis (adapted from Yang and Nagaosa, 2014).
“TABLE I Classification table for Class I 3D Dirac semimetals. Classification table for 3D topological Dirac semimetals obtained by an accidental band crossing in systems having C n rotational symmetry with respect to the z axis (adapted from Yang and Nagaosa, 2014).”
From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Yang and Nagaosa, 2014
The bulk Hamiltonian for a Class I DSM on the k_z=0 plane can support a gapped 2D state with nontrivial topology which requires boundary edge modes to occur on this symmetry plane.
“Nonetheless, as detailed in Table I, the bulk Hamiltonian for a Class I DSM on the k z = 0 plane can support a gapped 2D state with a nontrivial topology which requires boundary edge modes to occur on this symmetry plane (Yang and Nagaosa, 2014).”
From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Yang and Nagaosa, 2014
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- Authors
- Yang, B.-J., & Nagaosa, N.
- Affiliations
- RIKEN Center for Emergent Matter Science (JP)
- Corresponding author
- Yang, Bohm-Jung
- Venue
- Nature Communications
- Published
- 2014-09-15
- Volume
- 5
- Issue
- 1
- Pages
- 4898-4898
- ISSN
- 2041-1723 (ISSN-L)
- OpenAlex
- W2053877588
- Semantic Scholar
- c480572074a5cc67031474a3ba8259c7753a62dd
- Cited by
- 864
- References
- 44
- Citations by year
- 2026: 29 · 2025: 50 · 2024: 57 · 2023: 62 · 2022: 79 · 2021: 115 · 2020: 103 · 2019: 77 · 2018: 89 · 2017: 96 · 2016: 59 · 2015: 41 · 2014: 6 · 2013: 1
- FWCI
- 33.48
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Nature Communications (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- arXiv (Cornell University)
- Funders
- Ministry of Education, Culture, Sports, Science and Technology (24224009)
- Japan Society for the Promotion of Science (24224009)
- Japan Science and Technology Agency
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Physical Sciences › Materials Science › Materials Chemistry › 2D Materials and Applications
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
- Keywords
- three-dimensional Dirac semimetal, Dirac point, band inversion, topological invariants, time-reversal symmetry, inversion symmetry, Weyl semimetals, topological insulators
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