Aharonov-Bohm effect in the chiral Luttinger liquid

TL;DR

This paper develops a bosonization approach for chiral Luttinger liquids in quantum Hall edge states to analyze the Aharonov-Bohm effect, revealing universal scaling and the suppression of perfect resonances due to strong renormalization.

Contribution

It introduces a bosonization formalism for finite-size chiral Luttinger liquids and uncovers a universal scaling function for Aharonov-Bohm resonances.

Findings

A universal scaling function G(X,Y) describes Aharonov-Bohm resonances.

Strong renormalization prevents perfect resonances at zero temperature.

The formalism connects mesoscopic effects with highly correlated electron systems.

Abstract

Edge states of the quantum Hall fluid provide an almost unparalled opportunity to study mesoscopic effects in a highly correlated electron system. In this paper we develop a bosonization formalism for the finite-size edge state, as described by chiral Luttinger liquid theory, and use it to study the Aharonov-Bohm effect. The problem we address may be realized experimentally by measuring the tunneling current between two edge states through a third edge state formed around an antidot in the fractional quantum Hall effect regime. A renormalization group analysis reveals the existence of a two-parameter universal scaling function G(X,Y) that describes the Aharonov-Bohm resonances. We also show that the strong renormalization of the tunneling amplitudes that couple the antidot to the incident edge states, together with the nature of the Aharonov-Bohm interference process in a chiral system, prevent the occurrence of perfect resonances as the magnetic field is varied, even at zero temperature.