Topological invariant and the quantization of the Hall conductance

The topological aspects of wavefunctions for electrons in a two dimensional periodic potential with a magnetic field are discussed. Special attention is paid to the linear response formula for the Hall conductance σ xy. It is shown that the quantized value of σ xy is related to the number of zeros o...

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Bibliographic Details
Published in:Annals of physics 1985-04, Vol.160 (2), p.343-354
Main Author: Kohmoto, Mahito
Format: Article
Language:English
Subjects:
Applied sciences
Electronics
Exact sciences and technology
Interfaces
Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices
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Summary:The topological aspects of wavefunctions for electrons in a two dimensional periodic potential with a magnetic field are discussed. Special attention is paid to the linear response formula for the Hall conductance σ xy. It is shown that the quantized value of σ xy is related to the number of zeros of wavefunctions in the magnetic Brillouin zone. A phase of wavefunctions cannot be determined in a unique and smooth way over the entire magnetic Brillouin zone unless the magnetic subband carries no Hall current.
ISSN:0003-4916
1096-035X
DOI:10.1016/0003-4916(85)90148-4