Magnetic Translation Group
Abstract
In this paper a group-theoretical approach to the problem of a Bloch electron in a magnetic field is given. A magnetic translation group is defined and its properties, in particular its connection with the usual translation group, are established.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The minimum magnetic field normal to one face of a rectangular-prism unit cell that can be applied without destroying periodicity is one flux quantum per unit cell, or a field strength h/(eΩ), where Ω is the area of that face.
“The minimum magnetic field normal to one of the faces that can be applied to the cell without destroying the periodicity is one flux quantum per unit cell (83), or a field strength h/ ( e Ω), where Ω is the area of that face.”
From Three-Dimensional Topological Insulators (2011) · cites this paper as [83]
Cites
Bloch Electrons in a Uniform Magnetic Field
Brown, E. (1964) · Physical Review · doi:10.1103/physrev.133.a1038 · Cited by 420 · see citing works
Harper, P. G. (1955) · Proceedings of the Physical Society Section A · doi:10.1088/0370-1298/68/10/305 · Cited by 233 · see citing works
Über die Energieentartung der Gitterelektronen im Magnetfeld
Fischbeck, H. J. (1963) · physica status solidi (b) · doi:10.1002/pssb.19630030614 · Cited by 33 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Berry phase effects on electronic properties
Xiao, D., Chang, M.-C., & Niu, Q. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.1959 · Cited by 5,277 · see citing works
Ozawa, T., Price, H. M., Amo, A., Goldman, N., Hafezi, M., Lu, L., Rechtsman, M. C., Schuster, D., Simon, J., Zilberberg, O., et al. (2019) · Reviews of Modern Physics · doi:10.1103/revmodphys.91.015006 · Cited by 3,722 · see citing works
Lu, L., Joannopoulos, J. D., & Soljačić, M. (2014) · Nature Photonics · doi:10.1038/nphoton.2014.248 · Cited by 3,655 · see citing works
Nenciu, G. (1991) · Reviews of Modern Physics · doi:10.1103/revmodphys.63.91 · Cited by 374 · see citing works
Quantum systems with finite Hilbert space
Vourdas, A. (2004) · Reports on Progress in Physics · doi:10.1088/0034-4885/67/3/r03 · Cited by 321 · see citing works
Orbital magnetoelectric coupling in band insulators
Essin, A. M., Turner, A. M., Moore, J. E., & Vanderbilt, D. (2010) · Physical Review B · doi:10.1103/physrevb.81.205104 · Cited by 193 · see citing works
Algebraization of difference eigenvalue equations related to U(sl2)
Wiegmann, P. B., & Zabrodin, A. X. (1995) · Nuclear Physics B · doi:10.1016/0550-3213(95)00361-u · Cited by 55 · see citing works
Linear canonical transformations and quantum phase: a unified canonical and algebraic approach
Hakioglu, T. (1999) · Journal of Physics A: Mathematical and General · doi:10.1088/0305-4470/32/22/312 · Cited by 9 · see citing works
- Authors
- Zak, J.
- Venue
- Physical Review
- Publisher
- American Physical Society (APS)
- Published
- 1964-06-15
- Volume
- 134
- Issue
- 6A
- Pages
- A1602-A1606
- ISSN
- 0031-899X (ISSN-L)
- OpenAlex
- W2062489691
- Cited by
- 650
- References
- 3
- Citations by year
- 2026: 10 · 2025: 14 · 2024: 28 · 2023: 15 · 2022: 20 · 2021: 22 · 2020: 41 · 2019: 17 · 2018: 15 · 2017: 8 · 2016: 13 · 2015: 16 · 2014: 17 · 2013: 15 · 2012: 21
- FWCI
- 3.79
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
- Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Keywords
- magnetic translation group, Bloch electrons, magnetic field, translation group, group theory
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
