Current and charge distributions of the fractional quantum Hall liquids with edges

Details Current and charge distributions of the fractional quantum Hall liquids with edges Current and charge distributions of the fractional quantum Hall liquids with edges

1996-07-18

arxiv.org/abs/cond-mat/9607130v3

Physics

Condensed Matter

21 pages, REV TeX file

Scientific paper

10.1103/PhysRevB.54.17667

An effective Chern-Simons theory for the quantum Hall states with edges is studied by treating the edge and bulk properties in a unified fashion. An exact steady-state solution is obtained for a half-plane geometry using the Wiener-Hopf method. For a Hall bar with finite width, it is proved that the charge and current distributions do not have a diverging singularity. It is shown that there exists only a single mode even for the hierarchical states, and the mode is not localized exponentially near the edges. Thus this result differs from the edge picture in which electrons are treated as strictly one dimensional chiral Luttinger liquids.

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