The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
Quantized Hall effect in three dimensions
Abstract
When the Fermi level lies in a gap, the Hall conductivity of three-dimensional (3D) electrons in a periodic potential can be expressed in a topologically invariant form with a set of three integers. These integers are explicitly found as a solution of a Diophantine equation, the structure of which relies on the flux of the magnetic field through three areas of the periodic lattice. In a simple geometry, we detail a tight-binding model which is found to be reduced to a generalized 1D Harper equation. The existence of a complex gap structure is explicitly shown. The spectrum depends on the field orientation.
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“This triad of two-dimensional topological invariants leads to a linear three-dimensional quantum Hall effect, calculated by extending Eq. ( 10) to three spatial dimensions (Halperin, 1987;Montambaux and Kohmoto, 1990;Kohmoto, Halperin, and Wu, 1992).”
From Topological photonics (2019) · cites this paper as Montambaux and Kohmoto, 1990
Citations
Cites
Quantized Hall Conductance in a Two-Dimensional Periodic Potential
Thouless, D. J., Kohmoto, M., Nightingale, M. P., & den Nijs, M. (1982) · Physical Review Letters · doi:10.1103/physrevlett.49.405 · Cited by 6,973
Self-citationPossible States for a Three-Dimensional Electron Gas in a Strong Magnetic Field
Halperin, B. I. (1987) · Japanese Journal of Applied Physics · doi:10.7567/jjaps.26s3.1913 · Cited by 321
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Research works printed but not linked: 17
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Sorted by citations
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
Lu, L., Joannopoulos, J. D., & Soljačić, M. (2014) · Nature Photonics · doi:10.1038/nphoton.2014.248 · Cited by 3,655
Metadata
- Authors
- Montambaux, G., & Kohmoto, M.
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 1990-06-01
- Volume
- 41
- Issue
- 16
- Pages
- 11417-11421
- ISSN
- 0163-1829
- 1095-3795
- Cited by
- 74
- References
- 2
- Language
- en
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