Widths of the Hall Conductance Plateaus

Details Widths of the Hall Conductance Plateaus Widths of the Hall Conductance Plateaus

2005-09-30

arxiv.org/abs/math-ph/0509070v5

J. Stat. Phys. 130 (2008) 843-934

Physics

Mathematical Physics

94 pages, v2: a revision of Sec. 5; v3: an error in Sec. 7 is corrected, major revisions of Sec. 7 and Appendix E, Sec. 7 is e

Scientific paper

10.1007/s10955-007-9432-8

We study the charge transport of the noninteracting electron gas in a two-dimensional quantum Hall system with Anderson-type impurities at zero temperature. We prove that there exist localized states of the bulk order in the disordered-broadened Landau bands whose energies are smaller than a certain value determined by the strength of the uniform magnetic field. We also prove that, when the Fermi level lies in the localization regime, the Hall conductance is quantized to the desired integer and shows the plateau of the bulk order for varying the filling factor of the electrons rather than the Fermi level.

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