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Cited by 321Quantum and electron transport phenomenaPhysics of Superconductivity and MagnetismTopological Materials and Phenomena

Possible States for a Three-Dimensional Electron Gas in a Strong Magnetic Field

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Halperin, Bertrand I.·1987·Japanese Journal of Applied Physics
DOI 10.7567/jjaps.26s3.1913
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Abstract

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 kz direction, and a three-dimensional version of the integer quantum Hall state is realized.

    “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

    Section 5 (p. 4) describes a three-dimensional generalization of the integer quantized Hall effect, and Appendix A (p. 7) shows that an integer topological invariant can remain constant across Brillouin-zone slices. The paper does not establish the cited claim’s γ → 1 limit, a unit Chern number, or the specified kz direction. (LLM, conf=0.88)

    Experimental — accuracy not yet measured

  • 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.

    “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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Cites

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Research works printed but not linked: 11

  1. [1]The Quantum Hall Effect, ed. R.E. Prange and S.M. Girvin (Springer-Verlag, New York, 1987).
  2. [9]Z. Tesanović and B.I. Halperin, Phys. Rev. B (in press).
  3. [11]B.I. Halperin.and T.M. Rice, in Solid State Physics, ed. F. Seitz, D. Turnbull and H. Ehrenreich (Academic Press, New York, 1968), Vol. 21, pp. 116–192.
  4. [10]The possibility of a field-induced superconducting state has been suggested by M. Rasolt, Phys. Rev. Lett. 58 (1987) 1482; Z. Tesanović and M. Rasolt, preprint.
  5. [13]Cf. M. Ya. Azbel and N.B. Brandt, Zh. Eksp. Teor. Fiz 48 (1965) 1902 [Sov. Phys.-JETP 21 (1965) 804]; N. Miura, G. Kido and S. Chikazumi, in Application of High Magnetic Fields in Semiconductor Physics ed. G. Landwehr (Springer, New York, 1983), p. 505; S. Nakajima and D. Yoskioka, J. Phys. Soc. Jpn. 40 (1976) 328.
  6. [16]See for example, K. Seeger, Semiconductor Physics, 2nd ed. (Springer-Verlag, Berlin, 1982).
  7. [22]G. Nimtz and J. Gebhardt, in Proceedings of the 18th International Conference on the Physics of Semiconductors (Stockholm, 1986), ed. O. Engström (World Scientific, Singapore, 1987), Vol. 2, p. 1197.
  8. [24]R.M. Westervelt, M.J. Burns, P.F. Hopkins, A.J. Rimberg and G.A. Thomas, preprint for Proceedings of the International Symposium on Anderson Localization, Tokyo, August 1987.
  9. [25]N.F. Mott and E.A. Davis, Electronic Processes in Non-crystalline Materials (Clarendon Press, Oxford, 1979); B.I. Shklovskii and A.L. Efros, Electronic Properties of Doped Semiconductors (SpringerVerlag, Berlin, 1984).
  10. [30]B.I. Halperin, in Condensed Matter Theories, ed. P. Vashishta, et al. (Plenum Press, in press), Vol. 2.
  11. [36]See D. Poilblanc, G. Montambaux, M. Héritier and P. Lederer, Phys. Rev. Lett 58 (1987) 270; M. Ya. Azbel, P. Bak and P.M. Chaikin (preprint) and references therein.

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Authors
Halperin, B. I.
Affiliations
Harvard University (US)
Corresponding author
Halperin, Bertrand I.
ORCID
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
DOI
10.7567/jjaps.26s3.1913
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
Licence
Locations
Japanese Journal of Applied Physics (publishedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
  • Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Physics of Superconductivity and Magnetism
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › 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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