Quantized Hall Conductance in a Two-Dimensional Periodic Potential

D. J. Thouless; M. Kohmoto; M. P. Nightingale; M. den Nijs

doi:10.1103/PhysRevLett.49.405

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Quantized Hall Conductance in a Two-Dimensional Periodic Potential

D. J. Thouless, M. Kohmoto^*, M. P. Nightingale, and M. den Nijs

Department of Physics, University of Washington, Seattle, Washington 98195

^*Present address: Department of Physics, University of Illinois, Urbana, Ill. 61801.

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Phys. Rev. Lett. 49, 405 – Published 9 August, 1982

DOI: https://doi.org/10.1103/PhysRevLett.49.405

Abstract

The Hall conductance of a two-dimensional electron gas has been studied in a uniform magnetic field and a periodic substrate potential $U$ . The Kubo formula is written in a form that makes apparent the quantization when the Fermi energy lies in a gap. Explicit expressions have been obtained for the Hall conductance for both large and small $\frac{U}{ℏ ω_{c}}$ .

Focus

Nobel Prize—Topological Phases of Matter

Published 7 October, 2016

The 2016 Nobel Prize in Physics was awarded to theoretical physicists whose work established the role of topology in understanding exotic forms of matter.

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References (12)

K. von Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (1980)
R. B. Laughlin, Phys. Rev. B 23, 5632 (1981)
H. Aoki and T. Ando, Solid State Commun. 38, 1079 (1981)
R. E. Prange, Phys. Rev. B 23, 4802 (1981)
D. J. Thouless, J. Phys. C 14, 3475 (1981)
B. I. Halperin, to be published
A. Rauh, G. H. Wannier, and G. Obermair, Phys. Status Solidi (b) 63, 215 (1974)
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P. G. Harper, Proc. Phys. Soc., London, Sect. A 68, 874 (1955)
D. Hofstadter, Phys. Rev. B 14, 2239 (1976)
G. H. Wannier, Phys. Status Solidi (b) 88, 757 (1978)
P. Streda, to be published

[c1] K. von Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (1980)

[c2] R. B. Laughlin, Phys. Rev. B 23, 5632 (1981)

[c3] H. Aoki and T. Ando, Solid State Commun. 38, 1079 (1981)

[c4] R. E. Prange, Phys. Rev. B 23, 4802 (1981)

[c5] D. J. Thouless, J. Phys. C 14, 3475 (1981)

[c6] B. I. Halperin, to be published

[c7] A. Rauh, G. H. Wannier, and G. Obermair, Phys. Status Solidi (b) 63, 215 (1974)

[c8] J. Zak, Phys. Rev. 134, A1607 (1964)

[c9] P. G. Harper, Proc. Phys. Soc., London, Sect. A 68, 874 (1955)

[c10] D. Hofstadter, Phys. Rev. B 14, 2239 (1976)

[c11] G. H. Wannier, Phys. Status Solidi (b) 88, 757 (1978)

[c12] P. Streda, to be published

Physical Review Letters

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Quantized Hall Conductance in a Two-Dimensional Periodic Potential

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Nobel Prize—Topological Phases of Matter

References (12)

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