Fractional-quantum-Hall edges at filling factor 1-1/m

TL;DR

This paper microscopically analyzes the edge modes of a fractional quantum Hall system at filling factor 1-1/m, predicting the neutral mode's velocity and edge width to guide experimental verification of fundamental quantum Hall physics.

Contribution

It provides a detailed microscopic calculation of the neutral mode's properties at fractional quantum Hall edges, which has not been thoroughly characterized before.

Findings

Calculated the neutral mode velocity considering Coulomb interactions.

Determined the edge width for fractional quantum Hall states.

Guided experimental efforts to detect the neutral mode.

Abstract

We consider the edge of a two-dimensional electron system that is in the quantum-Hall-effect regime at filling factor 1-1/m with m being an odd integer, where microscopic theory explaining the occurrence of the quantum Hall effect in the bulk predicts the existence of two counterpropagating edge-excitation modes. These two modes are the classical edge-magnetoplasmon mode and a slow-moving neutral mode. Assuming the electrons to be confined by a coplanar neutralizing background of positive charges, and taking careful account of long-range Coulomb interactions, we determine microscopically the velocity of the neutral mode and the edge width. Our results are intended to guide experimental efforts aimed at verifying the existence of the neutral mode, which would provide a powerful confirmation of the current microscopic understanding of quantum-Hall physics at the simplest hierarchical filling Factors 1-1/m.