Incidence of the boundary shape in the effective theory of fractional quantum Hall edges

Details Incidence of the boundary shape in the effective theory of fractional quantum Hall edges Incidence of the boundary shape in the effective theory of fractional quantum Hall edges

2007-06-06

arxiv.org/abs/0706.0825v2

Phys.Rev. B77 (2008) 115107

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

12 pages, minor changes, replaced by published version

Scientific paper

10.1103/PhysRevB.77.115107

Starting from a microscopic description of a system of strongly interacting electrons in a strong magnetic field in a finite geometry, we construct the boundary low energy effective theory for a fractional quantum Hall droplet taking into account the effects of a smooth edge. The effective theory obtained is the standard chiral boson theory (chiral Luttinger theory) with an additional self-interacting term which is induced by the boundary. As an example of the consequences of this model, we show that such modification leads to a non-universal reduction in the tunnelling exponent which is independent of the filling fraction. This is in qualitative agreement with experiments, that systematically found exponents smaller than those predicted by the ordinary chiral Luttinger liquid theory.

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