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

Abstract

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.

arXiv comment12 pages, minor changes, replaced by published version

References in corpus (8)

• Topological orders and Edge excitations in FQH states
• Sharp and Smooth Boundaries of Quantum Hall Liquids
• Quantum Hall states as matrix Chern-Simons theory
• Field Theoretical Description of Quantum Hall Edge Reconstruction
• The Structure of Fractional Edge States: A Composite Fermion Approach
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Cited by in corpus (3)

• Edge excitations of the Chern Simons matrix theory for the FQHE
• Matrix Effective Theories of the Fractional Quantum Hall effect
• Semiclassical Droplet States in Matrix Quantum Hall Effect