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

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

See Focus story: Nobel Prize—Topological Phases of Matter

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 $\frac{U}{ℏ ω_{c}}$ .

Received 30 April 1982

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

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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