The effect of inter-edge Coulomb interactions on the transport between quantum Hall edge states

TL;DR

This paper investigates how long-range Coulomb interactions influence transport between quantum Hall edge states, explaining experimental discrepancies with Luttinger liquid theory through renormalization group analysis.

Contribution

It introduces a renormalization group approach to model the crossover from Luttinger liquid behavior to Coulomb interaction dominance in quantum Hall edge transport.

Findings

Crossover behavior aligns theory with experimental data

Long-range Coulomb interactions are crucial at low temperatures

Provides a unified framework for edge state transport analysis

Abstract

In a recent experiment, Milliken {\em et al.} demonstrated possible evidence for a Luttinger liquid through measurements of the tunneling conductance between edge states in the $\nu=1/3$ quantum Hall plateau. However, at low temperatures, a discrepancy exists between the theoretical predictions based on Luttinger liquid theory and experiment. We consider the possibility that this is due to long-range Coulomb interactions which become dominant at low temperatures. Using renormalization group methods, we calculate the cross-over behaviour from Luttinger liquid to the Coulomb interaction dominated regime. The cross-over behaviour thus obtained seems to resolve one of the discrepancies, yielding good agreement with experiment.