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

TL;DR

This paper derives a modified effective theory for fractional quantum Hall edges, incorporating boundary effects, which explains experimentally observed deviations in tunneling exponents from traditional models.

Contribution

It introduces a boundary-induced self-interacting term in the chiral boson theory, providing a more accurate description of edge phenomena in fractional quantum Hall systems.

Findings

Shows non-universal reduction in tunneling exponent

Aligns with experimental observations of smaller exponents

Extends chiral Luttinger theory to include boundary effects

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.