Electronic level degeneracy in nonsymmorphic periodic or aperiodic crystals
Abstract
The theory of space-group representations is extended to aperiodic crystals by reformulating it as the theory of symmetry-required degeneracies of electronic levels that emerges from the Fourier-space approach to crystal symmetry. As an illustration it is shown that the nonvanishing of a simple linear combination of phase functions belonging to commuting elements from the little group of q requires the degeneracy of all levels with generalized Bloch wave vector q. This condition is applied to all cubic and icosahedral centrosymmetric nonsymmorphic space groups, and to the two nonsymmorphic space groups of periodic crystals that have no systematic extinctions.
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Screw symmetries lead to double degeneracy for all Bloch states on certain planes in the Brillouin zone.
“It is known that screw symmetries lead to double degeneracy for all Bloch states on certain planes in the Brillouin zone (BZ).36,37”
From Type-II Dirac photons (2017) · cites this paper as [36]
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Topological order and absence of band insulators at integer filling in non-symmorphic crystals
Parameswaran, S. A., Turner, A. M., Arovas, D. P., & Vishwanath, A. (2013) · Nature Physics · doi:10.1038/nphys2600 · Cited by 184 · see citing works
Wang, H.-X., Chen, Y., Hang, Z. H., Kee, H.-Y., & Jiang, J.-H. (2017) · npj Quantum Materials · doi:10.1038/s41535-017-0058-z · Cited by 70 · 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
- Authors
- König, A., & Mermin, N. D.
- Affiliations
- Cornell University (US)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 1997-12-01
- Volume
- 56
- Issue
- 21
- Pages
- 13607-13610
- ISSN
- 0163-1829 (ISSN-L)
- 1095-3795
- OpenAlex
- W1980961217
- Cited by
- 41
- References
- 0
- Citations by year
- 2026: 1 · 2024: 1 · 2023: 1 · 2022: 1 · 2021: 3 · 2020: 1 · 2019: 4 · 2018: 3 · 2017: 3 · 2016: 6 · 2013: 1
- FWCI
- 1.63
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical review. B, Condensed matter (publishedVersion)
- Topics
- Physical Sciences › Materials Science › Materials Chemistry › Quasicrystal Structures and Properties
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Finite Group Theory Research
- Keywords
- aperiodic crystals, little group, icosahedral symmetry, phase function
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