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Possible States for a Three-Dimensional Electron Gas in a Strong Magnetic Field
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If a three-dimensional semimetal or doped semiconductor is placed in a sufficiently strong magnetic field, then a change in its transport properties will occur. If the electron-impurity interaction is dominant, then the magnetic field will produce localization of the electron wavefunctions, sometimes described as magnetic freezeout. If the electron-electron interaction is more important, then some type of collective transition may occur. Spin-density waves, charge-density waves, valley-density waves, excitonic insulators, and Wigner crystallization have been proposed to occur under various circumstances. As a generalization to three-dimensions of the integral quantized Hall effect, we show that for electrons in periodic or quasiperiodic potential, when the Fermi level lies in an energy gap, the zero temperature conductivity tensor is given by σ i j =(e 2/2π h)∑ k ε i j k G k , where \vec G is a reciprocal-lattice-vector of the potential. We discuss the effect of impurities and dislocations on this result.
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“As γ → 1, the entire Brillouin zone is filled with unit Chern number along the k z direction, and a three dimensional version of the integer quantum Hall state is realized (Halperin, 1987).”
From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Halperin, 1987
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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 Halperin, 1987
In the citing paper
“A more physical way to view this is that a three-dimensional integer quantum Hall system consists of a single Chern number and a reciprocal lattice vector that describes the 'stacking' of integer quantum Hall layers (73).”
From Three-Dimensional Topological Insulators (2011) · cites this paper as [73]
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Research works printed but not linked: 11
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Metadata
- Authors
- Halperin, B. I.
- Affiliations
- Harvard University (US)
- Corresponding author
- Halperin, Bertrand I.
- Venue
- Japanese Journal of Applied Physics
- Publisher
- IOP Publishing
- Published
- 1987-01-01
- Volume
- 26
- Issue
- S3-3
- Pages
- 1913
- ISSN
- 0021-4922 (ISSN-L)
- 1347-4065
- OpenAlex
- W1994659789
- Cited by
- 321
- References
- 0
- Citations by year
- 2026: 8 · 2025: 16 · 2024: 18 · 2023: 19 · 2022: 14 · 2021: 27 · 2020: 16 · 2019: 15 · 2018: 17 · 2017: 14 · 2016: 13 · 2015: 5 · 2014: 6 · 2013: 2 · 2012: 4
- Type
- conference abstract
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Japanese Journal of Applied Physics (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Quantum and electron transport phenomena
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Physics of Superconductivity and Magnetism
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Topological Materials and Phenomena
- Keywords
- three-dimensional electron gas, high magnetic fields, electron localization, electron-impurity interaction, electron-electron interaction, collective transitions, spin density wave, charge density wave, excitonic insulator, Wigner crystallization, conductivity tensor, quasiperiodic potentials, dislocations, impurities
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